strategic extremism: why republicans and democrats …€¦ · by seven percentage points from...

STRATEGIC EXTREMISM WHY REPUBLICANS ANDDEMOCRATS DIVIDE ON RELIGIOUS VALUES

EDWARD L GLAESER

GIACOMO A M PONZETTO

JESSE M SHAPIRO

Party platforms differ sharply from one another especially on issues withreligious content such as abortion or gay marriage Given the high return toattracting the median voter why do vote-maximizing politicians take extremepositions In this paper we find that strategic extremism depends on an intensivemargin where politicians want to induce their core constituents to vote (or makedonations) and the ability to target political messages toward those core constitu-ents Our model predicts that the political relevance of religious issues is highestwhen around one-half of the voting population attends church regularlyUsing data from across the world and within the United States we indeed finda nonmonotonic relationship between religious extremism and religiousattendance

I INTRODUCTION

In the United States religious attendance predicts Republi-canism at least as well as income does [Fiorina 2005] Figure Ishows the share who voted for Bush in November 2004 by raceand income bracket using data from the National Election PoolExit Poll Figure II shows the share of respondents who voted forBush by religious attendance using the same sample Figure IIIshows that the correlation between income and party affiliationhas been roughly constant since the 1960s but the correlationbetween religious attendance and party affiliation has risen overthis period1 This trend has accompaniedmdashand may even becaused bymdashincreasing divergence of party positions on religiousissues For example in 2004 the Republican party platform saysthat ldquothe unborn child has a fundamental right to life that cannot

We are grateful to Alberto Alesina Robert Barro Gary Becker MorrisFiorina Elhanan Helpman David Laibson Rachel McCleary Andrei ShleiferLawrence Summers and seminar participants at Harvard University BrownUniversity and Boston University for helpful comments Ponzetto acknowledgesfinancial assistance from the Marco Fanno Foundation Shapiro acknowledgesfinancial assistance from the Institute for Humane Studies the Center for BasicResearch in the Social Sciences and the National Science Foundation e-maileglaeserharvardedu ponzettofasharvardedu and jmshapiruchicagoedu

1 Figure III also illustrates the impact that individual candidates have onthe correlation between religious attendance and voting Republican For examplethat correlation was minimal in the 1976 election when the Democratic candidatewas a born-again Christian

copy 2005 by the President and Fellows of Harvard College and the Massachusetts Institute ofTechnologyThe Quarterly Journal of Economics November 2005

1283

be infringedrdquo while the Democrats in the same year ldquostandproudly for a womanrsquos right to chooserdquo We will refer to suchdivergent party platforms as extremism

Traditional median-voter results (eg Hotelling [1929])make extremism difficult to understand After all vote-maximiz-ing politicians are supposed to cater to the middle not the edgesof the distribution (see Downs [1957] and Becker [1958]) at leastin majoritarian systems [Cox 1990] Political theorists who try toexplain extremism emphasize the primary system or the ideologi-cal preferences of the candidate or party leaders (as in Alesina[1988])2 While the primary system is important and politiciansrsquopreferences certainly matter this paper explains why extremismoccurs for purely strategic ie vote-maximizing reasons in amajoritarian system with only one issue

2 But see Murphy and Shleifer [2004] and Kirchgassner [2003] for recentexceptions Murphy and Shleifer [2004] show that the effects of social networks onbeliefs can lead to an incentive to move away from the political center Fiorina[1999] reviews the political science literature on polarization

FIGURE IIncome and Republicanism in the 2004 Election

Data are from the National Election Pool Exit Poll 2004 Data include votersvoting for Democratic or Republican candidate in the November 2004 presidentialelection Shares are weighted as recommended by the data providers

1284 QUARTERLY JOURNAL OF ECONOMICS

There are two necessary conditions for extreme political plat-forms that deviate sharply from the median voterrsquos preferences tobe vote-maximizing First as Downs [1957] recognized theremust be two electoral margins an extensive margin where apolitician competes for voters from the other party and an inten-sive margin where the politician attempts to bring his own votersinto the voting booth or elicit financial contributions If there is nointensive margin and therefore no reason to cater to the partyfaithful politicians will lose votes if they move their policies awayfrom the preferences of the median voter Second a move awayfrom the center must increase turnout (or donations) among apoliticianrsquos own supporters more than among his opponentrsquossupporters3

In this paper we present a new model of strategic extrem-ism that explains why a politician deviating from the median

3 Riker and Ordeshook [1973] satisfy these formal requirements with amodel in which voters care more about the position of their preferred candidatethan about the position of the other candidate In Section IV we provide evidenceinconsistent with this preference-based explanation for extremism

FIGURE IIChurch Attendance and Republicanism in the 2004 Election

Data are from the National Election Pool Exit Poll 2004 Data include respon-dents who voted for a Democratic or Republican candidate in the November 2004presidential election Shares are weighted as recommended by the data providers

1285STRATEGIC EXTREMISM

will gain more from energizing his own supporters than heloses by further alienating his opponentrsquos supporters Our keyassumption is that awareness of a politicianrsquos message ishigher among the politicianrsquos supporters than among his op-ponentrsquos supporters This asymmetry means that when a poli-ticianrsquos policies deviate from those preferred by the medianvoter he energizes his own supporters (who are more likely tobe aware of this deviation) more than he energizes his oppo-nentrsquos supporters (who are less likely to be aware of thisdeviation) Recent efforts by the Bush and Kerry campaignsillustrate the edge that politicians have in communicating withtheir own supporters For example during the RepublicanNational Convention there was a ldquoclosed invitation-only Bushcampaign rally for Christian conservativesrdquo at which ldquoSenatorSam Brownback of Kansas called for a broad social conserva-tive agenda notably different from the televised presentationsat the Republican conventionrdquo [Kirkpatrick 2004b] The Kerry

FIGURE IIITrends in the Determinants of Voting Republican

Data are from the General Social Survey Data reflect marginal effects evalu-ated at sample means from probit models of the propensity to vote RepublicanSample includes respondents who voted for a Democratic or Republican candidatein the previous presidential election All regressions include controls for years ofschooling age age2 race gender and a dummy for missing income data


campaign also appeared to be targeting public appearances toreach loyal Democrats [Borsuk 2004]4

In Section II we begin by briefly addressing the issue of voterturnout Is it plausible that politicians can be tailoring theirmessages to increase turnout Both politicians and commentatorsargue that Democrats and Republicans target messages at par-ticular voters in an attempt to increase turnout Voter turnoutappears to respond to the dimensions along which politiciansdiffer For example turnout among the highly religious increasedby seven percentage points from 1976 when Republicans andDemocrats barely differed on religion-related issues to 1984when Reagan faced Mondale in a race with much starkerdivisions

In Section III we present our model of strategic extremismWith only one political issue extremism increases with the vari-ance of voter preferences the informational asymmetry betweena politicianrsquos supporters and his opponentrsquos and the ability ofpoliticians to target political messages to their supporters Whenvoters differ along two attributes such as the desire for incomeredistribution and abortion-related policies extremism is morelikely along the issue where there is greater heterogeneity ofpreferences [Mullainathan and Shleifer 2005 Irmen and Thisse1998] Extremism is also more likely along the issues that deter-mine informational groups If a candidatersquos audience is particu-larly defined by religion than the candidate will be more extremein his religious positions If the candidatersquos audience is defined byeconomics the economic policies will become more importantThese findings echo Murphy and Shleiferrsquos [2004] discussion ofthe role of social groups in politics5

After presenting the model Section IV discusses alternativeexplanations for extremism A key difference between a model ofstrategic extremism and a model in which extremism reflectspoliticiansrsquo preferences is that when extremism is strategic poli-ticiansrsquo policies will be more moderate than their messages Whenextremism reflects leadersrsquo preferences policies will be moreextreme than political messages We examine policies and plat-

4 See Farrell and Gibbons [1989] for a different approach to communicationwith multiple audiences

5 We use the term social group to distinguish these groups from pressuregroups and interest groups which have received considerable attention in theliterature (see Becker [1983] Dixit and Londregan [1995] and Grossman andHelpman [2002])


forms on tax policy and abortion over the last 25 years to testthese implications The economic messages in platforms are ex-tremely moderate but there are big differences in mean tax ratesbetween Democratic and Republican regimes Conversely politi-cal messages about abortion tend to extremes but abortion ratesare independent of the party in power These results suggest thatdifferences in economic policies between the parties reflect thepreferences of party leaders but that differences in abortion andother religion-related policies reflect political strategy

In Section V we examine a key prediction of the modelreligious determinants of political orientation will be maximizedwhen about 50 percent of the population attends church regu-larly There is a strong nonmonotonic relationship across coun-tries between church attendance at the national level and theextent to which religion determines right-wing orientation Incountries with very low levels of church attendance such asNorway or Russia religion is uncorrelated with political prefer-ences The same fact is true in countries like the Philippineswith very high levels of religious attendance The countries withstrong connections between religion and political orientation areall those like the United States where about one-half of thepopulation attends church once per month or more This factpersists when we examine changes in religiosity across countriesover time rather than cross-sectional differences in religiosityacross countries After looking across countries we turn toAmerican states Since there are few states where much less thanone-half of the population attends church regularly we focus onwhether increased church attendance decreases the extent towhich religiosity determines voting Republican In states likeMississippi with high attendance levels there is little connectionbetween religion and political orientation In low-attendancestates like California there is much more connection betweenreligiosity and being a Republican

II MOTIVATING EVIDENCE ON EXTREMISM AND VOTER TURNOUT

IIA Divergence of Party Platforms

Over the last three decades Republican and Democratic plat-forms have moved definitively away from the center on religiousvalues Consider for example trends in party platform state-ments about abortion Between 1976 the first year in which


either partyrsquos platform mentioned abortion and 2004 the Repub-lican party moved to the right on this issue

We protest the Supreme Courtrsquos intrusion into the family structurethrough its denial of the parentsrsquo obligation and right to guide their minorchildren The Republican Party favors a continuance of the public dialogue onabortion and supports the efforts of those who seek enactment of a constitu-tional amendment to restore protection of the right to life for unborn children[Republican Party Platform 1976]

As a country we must keep our pledge to the first guarantee of theDeclaration of Independence That is why we say the unborn child has afundamental individual right to life which cannot be infringed We support ahuman life amendment to the Constitution and we endorse legislation tomake it clear that the Fourteenth Amendmentrsquos protections apply to unbornchildren Our purpose is to have legislative and judicial protection of thatright against those who perform abortions We oppose using public revenuesfor abortion and will not fund organizations which advocate it We supportthe appointment of judges who respect traditional family values and thesanctity of innocent human life [Republican Party Platform 2004]

At the same time the Democratic platforms trended leftward

We fully recognize the religious and ethical nature of the concernswhich many Americans have on the subject of abortion We feel howeverthat it is undesirable to attempt to amend the U S Constitution to overturnthe Supreme Court decision in this area [Democratic National Platform1976]

We will defend the dignity of all Americans against those who wouldundermine it Because we believe in the privacy and equality of women westand proudly for a womanrsquos right to choose consistent with Roe v Wadeand regardless of her ability to pay We stand firmly against Republicanefforts to undermine that right At the same time we strongly support familyplanning and adoption incentives Abortion should be safe legal and rare[Democratic National Platform 2004]

As Figure III illustrates and as many political scientistshave noted this trend in party language has been accompaniedby a strengthening of the connection between religious atten-dance and party affiliation (see Layman [1997] and Fiorina[2005]) Recent decades have also witnessed a rise in evangelicalChristianity among Republicans and increasing secularizationamong Democrats (see Layman [1999 2001])

In contrast to positions on issues with religious contentmuch of the verbiage in both platforms on economic issues seemsquite moderate and similar across platforms Indeed both partiesappear to be sending the message that they will reduce the taxburden on American businesses


We believe that the private sector not government is the engine ofeconomic growth and job creation Under John Kerry and John Ed-wards 99 percent of American businesses will pay less in taxes than they dotoday [Democratic Party Platform 2004]

Small business deserve far better treatment from governmentthan they have received We will provide it through many of the initiativesexplained elsewhere in his platform lower tax rates ending the death taxcutting through red tape [Republican Party Platform 2004]

A strong theory of extremism should be able to explain not onlywhy there has been an increase in extremism on religion-relatedissues over the last three decades but why extremism seems to bemore prevalent on these issues than on matters of economic policysuch as taxation

IIB The Importance of Voter Turnout

Our model will depend on party leadersrsquo ability to increaseturnout by targeting specific populations There is abundant an-ecdotal information suggesting that politicians target specificpopulations and tailor their messages to increase enthusiasm inthose populations Platforms and citizensrsquo information aboutthese platforms can meaningfully affect voter turnout Currentmobilization efforts make it clear that politicians are trying toincrease turnout by using organizations such as churches tocommunicate platforms and stimulate voter participation At theWest County Assembly of God outside of St Louis

They hold open meetings for parishioners each month They informchurch members about socially conservative electoral issues They registerthem to vote at stands outside the sanctuary on designated ldquovoter registra-tionrdquo Sundays Last week the ldquomoral action teamrdquo even drove church mem-bers to the polls and they plan to do the same for this fallrsquos general electionas well

According to campaign memorandums [the Bush campaign] has askedldquopeople of faith team leadersrdquo to help identify thousands of ldquofriendly congre-gationsrdquo around the country It asked religious outreach volunteers to peti-tion their pastors to hold voter registration drives and to speak on behalf ofthe campaign to Bible studies and church groups [Kirkpatrick 2004a]

These coordination activities are part of a more general strategywhich puts ldquotop priority on maximizing voter turnout amongconservative constituencies already disposed to back the presi-dentrdquo [Calmes and Harwood 2004] Such anecdotes support theidea that political messages sent to these groups are more ex-treme than the messages broadcast to the general public While


the Republican and Democratic conventions both tried to presenta mainstream message there were abundant reports of muchmore extreme discussions behind closed doors

A related phenomenon known as ldquodog whistle politicsrdquo re-cently emerged in the United Kingdom The term dog whistlerefers to a message that can be heard only by some members ofthe electorate For example Tory language on immigration em-phasized that ldquosome immigration is essentialrdquomdasha message per-ceived by some as telegraphing to anti-immigration voters thatthe amount of immigration permitted by the current governmentis excessive [The Economist 2005] Widespread discussion of dogwhistle messages in the popular press suggests that such two-pronged language now plays an important role in British politicsperhaps because of a desire on the part of politicians to ignite theparty faithful without energizing their opponentsrsquo supporters

Are politicians right Is turnout an important margin thatcan shape presidential elections Certainly there have been ex-amples where turnout changed significantly at least in part dueto more extreme political platforms The Republican (and Demo-cratic) move toward extremes on abortion was discussed above Ifturnout responds to these more extreme views then we shouldexpect to see increased turnout among particularly pro-choice orpro-life voters during this period To examine this possibility welooked at changes in turnout between 1976 and 1984 by religiousattendance In 1976 both Carter and Ford were relatively centriston religious issues In 1984 there was a big gap between theplatforms of Reagan and Mondale

As Figure IV illustrates the move away from the center onreligious issues appears to have had a disproportionately positiveimpact on turnout among more religious Americans Among thosewho attend church more than once a week the probability of aneligible citizen voting increased by almost five percentage pointsReaganrsquos more extreme policies on abortion and other issuesappear to have had a significant impact on the level of voterturnout among religious Americans

A similar pattern can be detected in the changes in voterturnout among American states between the 2000 and 2004 presi-dential elections Among nonbattleground states in which lessthan half the population attended church monthly in 2000 therate of turnout among the voting-eligible population increased by47 percentage points By contrast in nonbattleground states


with a majority of residents attending church monthly in 2000the increase in turnout was 67 percentage points This differenceis economically significant in comparison to the standard devia-tion of changes in turnout (about 23 percentage points) and incomparison to Bushrsquos margin of victory in the two-party popularvote (about 28 percentage points) Additionally when we regressthe change in turnout on the share of the population attendingchurch monthly and a control for whether the state was a battle-ground in 2000 we find a statistically significant positive effect ofchurch attendance6 Evidence such as this suggests that voterturnout does create incentives for candidates to move their plat-forms away from the political center

6 Data on voter turnout as a share of voting-eligible population are fromMcDonald [2004] and are calculated using the methodology of McDonald andPopkin [2001] Data on share attending church monthly are from years 1990ndash1998 of the DDB Needham Lifestyle Survey described in Putnam [2000]

FIGURE IVReligion and Voter Turnout 1976ndash1984

Data are from the General Social Survey 1972ndash2002 cumulative file Datareflect shares of respondents in each group participating in the most recentpresidential election ldquoNeverrdquo refers to those never attending church ldquoA few timesa yearrdquo refers to those who report attending less than once a year about once ortwice a year or several times a year ldquoA few times a monthrdquo refers to those whoreport attending about once a month two to three times a month or nearly everyweek ldquoOnce a week or morerdquo refers to those who report attending every week orseveral times a week


III A MODEL OF STRATEGIC EXTREMISM

In this section we present a model where two parties choosepolicies to attract voters Our critical assumption is that politi-ciansrsquo policy statements are not directly observed by all citizensbut rather that some party affiliates have a higher probability oflearning the party platform This targeted information assump-tion generates extremism in cases where standard models predictconvergence to the median voterrsquos ideal point

To see why targeted information generates divergent plat-forms in equilibrium consider an extreme case in which eachpoliticianrsquos platform is known only to members of his own campConsider a proposed equilibrium in which both politiciansrsquo plat-forms agree with the politics of the median voter In this case aright-wing politician who treats the left-wing politicianrsquos policiesas fixed will obtain half of the total vote by sticking at the centerBut if he moves slightly to the right he will look more attractiveto his own supporters making them more likely to show up at thepolls Since this deviation would be hidden from left-wing citi-zens his move will not help to energize his opponentrsquos supportersThus the right-wing politician will be tempted to move to theright and thus platform convergence is not an equilibrium of thegame

By contrast consider a proposed equilibrium where bothpoliticians propose policies close to the average preferences oftheir supporters In this case a deviation to the right wouldalienate a right-wing politicianrsquos more moderate supporters anda move to the left would do the same for the extremists in hisparty When these forces offset each other he will want to main-tain his position This is true even when all citizensmdashincludingthose on the leftmdashcorrectly anticipate the platform that the right-wing politician will pursue in equilibrium Even if left-wing citi-zens know that the right-wing politician will take an extremeposition the right-wing politician has no incentive to move to thecenter As new policies are only observed by the right-wing poli-ticianrsquos own supporters moving to the center will alienate theseright-wing voters and generate no support among opposing vot-ers The important force that maintains divergent platforms isnot hidden information in equilibrium but rather hidden infor-mation out of equilibrium the fact that politicians can deviatefrom their equilibrium strategies in ways known only to membersof their own camp


Formally we assume that two parties labeled L and Rcompete for votes Each party chooses a policy proposal to maxi-mize the difference between its votes and the votes of its oppo-nent7 After a party chooses its policy proposal a set of citizenssee that proposal others do not see the proposal In equilibriumall citizens have correct beliefs about partiesrsquo platforms butimportantly some would not directly observe deviations fromequilibrium play

Citizens receive utility from voting for politicians whose pro-posed policies are close enough to their own and utility fromvoting against politicians whose policies are different enoughfrom their own There are also costs of voting which differ amongindividuals and people vote only when the utility gains fromvoting outweigh the costs of voting8 By assuming that people getutility directly from voting we are deliberately sidestepping thethorny issue of why people vote The most straightforward justi-fication for this assumption is that votersrsquo decisions are emo-tional not based on any estimation of how their votes will impactgovernment policy [Schuessler 2000] It is also possible to inter-pret the changes to voter utility from voting as reflecting votersrsquoutility under different policy regimes However this interpreta-tion requires policy proposals to have predictive content (or bebinding) and for individuals to overestimate the relevance of theirvote to political outcomes

There exists an n-dimensional policy space represented by[11]n We refer to policies with negative values as left-wingpositions and policies with positive values as right-wing posi-tions Voters have preferences represented by an ideal point inthis space and parties propose policies or platforms which arealso points in this space The distribution of citizensrsquo ideal policiesalong each dimension of the policy space is independent andsymmetric around the origin As the origin represents the pre-ferred policy of the median voter we will refer to the distancebetween the origin and partiesrsquo proposed policies as the extent ofextremism Each citizen is also characterized by a cost of voting

7 This specification would be consistent with politicians maximizing theprobability of victory if for example each partyrsquos vote totals were affected byexogenous shocks whose difference is uniformly distributed We therefore take itto be an approximation of politiciansrsquo objective functions in a deterministic contextsuch as the one we analyze

8 The phenomenon of voters basing turnout on the intensity of their prefer-ence for the preferred candidate has sometimes been called ldquoabstention fromalienationrdquo [Guttman Hilger and Shachmurove 1994]


c which is independent of policy preferences and characterizedby cumulative distribution function Z(c) The timing of the modelis the following

1 All citizens have conjectures x P [11]n about thepolitical proposal of each party P and potentially an in-formational affiliation with one or both parties

2 Parties simultaneously choose platforms in the space xP [11]n to maximize their margin of victory and theseplatforms are observed by a fraction of the partyrsquos affili-ates and by a fraction of nonaffiliates Citizens whodo not observe the platform maintain their initial conjec-tures x P about party platforms

3 The election is held and citizens decide whether to voteand if so for which party

We will define an equilibrium as a set of conjectures andplatforms where all conjectures are correct given the eventualplatforms and each partyrsquos platform maximizes its margin ofvictory holding constant the actions of the other party and thebeliefs of those who do not observe the platform directly (share(1 ) of nonaffiliates and share (1 ) of affiliates) Althoughthe assumption of correct conjectures in equilibrium is standardit is not necessary and our proofs allow for more general beliefs

We solve the model recursively starting at period 3 and thevoting decision Each citizen receives utility from voting for partyP equal to

SP B i1

n

iMxiP xi where

i1

n

i 1

where B measures the psychological gain from expressing sup-port for onersquos favorite policy vector x the weights i representsthe salience of each dimension of the policy space in citizensrsquominds and M is an increasing convex and bounded functionThe function M captures the fact that citizens will receive lessutility if they vote for a candidate whose perceived policy propos-als xP differ from their own ideal proposals People also receiveutility from voting against party P equal to SP The benefit fromvoting is then given by

VxxLxR max i1n i[M(xi

L xi ) M(xiR xi )]

i1n i[M(xi

R xi ) M(xiL xi )]

which is less than an upper bound V Conditional on voting


people will support the party that is closer to their ideal platformand as the act of voting imposes a cost c people will vote when

c Vx xL xR

We assume that c has full support on the interval [0V ] so thatfor every possible vector of voter preferences there are alwaysvoters who abstain Parties anticipate that voters will make theirdecisions in this manner and in period 2 of the game they selecttheir proposed policy to maximize their votes minus the oppo-nentrsquos votes taking the opponentrsquos proposed policy as given

We make two assumptions about functional forms thatgreatly simplify calculations

ASSUMPTION 1 The loss function is quadratic

MxiP xi xi

P xi 2

ASSUMPTION 2 The distribution of the cost of voting is uniform

Zc 0 if c 0cV if c [0V ]1 if c V

Assuming functional forms for preferences is costly becausewe have lost the ability to consider the empirical implications ofdifferent forms of loss functions As loss functions are not directlyobservable this problem may not be too severe The assumptionof a uniform distribution of voting costs is also restrictive and inProposition 2 below we consider the implications of a possiblegeneralization

IIIA Political Competition with One Issue

Extremism requires that immoderation has a stronger posi-tive impact on onersquos own supporters than it has a negative impacton the opponentrsquos voters In this model differential impact occursbecause the politicianrsquos affiliates are more aware of changes inthe politicianrsquos policies This differential awareness might occurbecause individuals pay more attention to their own candidatebut it can also result from politicians strategically targetingwhere they broadcast their messages Examples of this targetinginclude direct mailing television ads in particular marketsspeeches to the party faithful and the use of allies like religiousleaders or unions to broadcast information to a particular groupThe model requires politicians to have some ability to provide


their own supporters with more information about proposedpolicies

In this section we assume that there is only one policy di-mension As such a voter whose ideal policy is xi and whobelieves that the two parties are offering policies xi

R and xiL will

perceive net benefits of 2xi( xiR xi

L) ( xiR)2 ( xi

L)2 c ofvoting for the right-wing candidate R When xi

R 0 xiL then

the net benefits of voting for the right-wing candidate always risewith xi and the net benefits of voting for the L candidate alwaysfall with xi so these assumptions predict the pattern of voterturnout seen in Figure V

Given these assumptions about voting behavior if a partyhas some affiliates who are more likely to be aware of the partyplatform and if those affiliates do not have views that perfectlymirror those of society as a whole then the median voter resultvanishes

PROPOSITION 1 A party with a positive measure of affiliates willadopt a platform that coincides with the position of the me-

FIGURE VIdeology and Voter Turnout

Data are from the General Social Survey 1972ndash2002 cumulative file Datareflect shares of respondents in each group participating in the most recentpresidential election


dian voter if and only if there is no informational differencebetween affiliates and nonaffiliates ( ) or there is nodifference between the ideal policies of the average affiliateand the average voter

The proposition tells us that any informational differenceamong voters is enough to break down the rush to the center Wenow consider the platform decision of a party with right-wingaffiliates and the determinants of the extremism of this partyrsquosplatform A natural measure of extremism is the value of xR

which captures the distance between the partyrsquos platform and theideal platform of the median voter (Symmetric results apply toparty L)

PROPOSITION 2 If party affiliates are on average better informedabout the party platform ( ) and more conservative thannonaffiliates the party will adopt a right-wing platform soxR 0

The partyrsquos extremism (ie the value of xR) is increasingin its ability to convey information to its affiliates () anddecreasing in its tendency to convey information to nonaffili-ates () The value of xR increases as the number of partyaffiliates increases (holding their average ideal policy con-stant) and increases as the average ideal policy within partyaffiliates becomes more conservative (holding the number ofparty affiliates constant)

If right-wing party affiliates include all citizens i forwhom xi 0 and no others then extremism is increasing inthe heterogeneity of votersrsquo preferences (as measured by themean deviation of their distribution)

If the distribution of the cost of voting is generalized toinclude a point mass z0 [01] of voters with zero cost ofvoting as well as a uniform density of voters z(c) (1 z0)V for all c [0V ] extremism can only emerge if z0 1and its extent (ie the value of xR) is monotone decreasingin z0

This proposition has several elements First it shows thatany party whose affiliates are more conservative than the na-tional norm will tend to choose a conservative platform Thisresult will be true even if both parties have an informationadvantage in reaching conservative voters In that case bothparties will choose conservative platforms so the first result


highlights that policies will cater to groups that are more likely tobe aware of party platforms

This proposition also yields comparative statics on the extentof extremism Extremism is more likely when the informationasymmetry between affiliates and nonaffiliates is greater If thenews media rapidly ensure that any speech given to the partyfaithful is broadcast universally then this will reduce extremismrelative to a world in which these speeches are kept privateExtremism is also a function of the number of party affiliatesWhen there are few party affiliates then it makes little sense tocater to them by taking an extreme position As the number ofparty affiliates rises the gains from appealing to them also riseThe amount of extremism will also rise with the amount ofsorting into the affiliate group As the group that is particularlyaware of changes to party platforms becomes more extreme thenpolicies will also become more extreme If we further assume thateveryone whose views are to the right of some cutoff is a partyaffiliate then extremism rises with the heterogeneity of votersrsquopreferences

The last result in the proposition shows that further compara-tive-statics results can be obtained by generalizing the distribu-tion of the cost of voting Specifically we modify the uniformdistribution by adding a point mass in the origin representing agroup of people who always turn out to vote The larger thisgroup the less important is the turnout margin and the closer isthe outcome to the median-voter result

IIIB Political Competition with Two Issues

We now focus on the case with two issues A and T whereissue T carries weight (01) in votersrsquo utility function Theseletters might stand for abortion and taxes An individual whoperceives the two parties has having platforms (TLAL) (TRAR)and whose ideal policies are (ta) receives benefits from voting forthe R candidate equal to two times

ta TR TL t TL TR

2 1 AR ALa

AL AR

2

where is the belief set ((TLAL)(TRAR)) The benefits of votingfor the L candidate are 1 times that amount


We consider the optimal policy choice for party R the choicefor party L remains symmetric The probability of a voter beingan affiliate is described by the function 13R(ta) of his ideal poli-cies Extremism in the T dimension equals TR and extremism in theA dimension is AR ie the difference between the policy platformsand the preferences of the median voter The core results of theprevious section extend to two dimensions but now we can alsomake predictions about which issues are most prone to extremism

PROPOSITION 3 A party with a positive measure of affiliates willadopt a platform that coincides with the position of the me-dian voter if and only if there is no informational differencebetween affiliates and nonaffiliates ( ) or there is nodifference between the ideal policies of the average affiliateand the average voter along either policy dimension If partyaffiliates are on average better informed about the partyplatform ( ) and more conservative than nonaffiliatesalong both dimensions then the party will choose a platformthat is right-wing along both dimensions The partyrsquos extrem-ism along both dimensions will increase with its ability toconvey information to its affiliates () and to withhold it fromnonaffiliates () moreover it will increase as the number ofparty affiliates increases (keeping their average ideal policyconstant) or their average conservatism increases (keepingtheir number constant)

The party platform will be more extreme on the issuewhere the average preference of affiliates is more differentfrom the median-voter position (TR AR N E(tR) E(aR)) If all voters for whom t a 0 are party affiliatesthen a monotonic increase in the heterogeneity of votersrsquopreferences on one issue increases extremism on that issueand reduces it on the other

The first part of this proposition directly repeats the coreresults of the previous subsection Extremism occurs when-ever there is some ability to target information to a groupwhose preferences differ from the preferences of the nation asa whole Again extremism rises with the degree to whichinformation can be targeted and also with the size and bias ofthe group of party affiliates

The second part addresses the question of which dimensionswill tend to dominate party politics Will parties differ from themedian voter primarily along dimension T or dimension A


Partiesrsquo extremism is determined by the preferences of theiraffiliates If their affiliates are particularly chosen on the basis ofdimension A then the parties will divide more clearly over thatdimension As such if religious views exert a stronger pushtoward political involvement then we might expect religious is-sues to divide parties

The final result in the proposition emphasizes the impor-tance of belief heterogeneity in the population as a whole Differ-ences of opinion or circumstance will also increase extremismand extremism will be more likely on the issue with greaterheterogeneity Greater heterogeneity of opinion on religion-re-lated issues over the past 30 years might explain some part of therising political differentiation based on religion Presumably ris-ing income inequality would tend to create further differentiationon economic grounds although this does not seem to have hap-pened over the last 30 years There is however a case that risinginequality during the late nineteenth century led to a politicalshift where parties such as the Democrats with William Jen-nings Bryan began to become more extreme in economic plat-forms (as opposed to classic divisions based on the Civil WarProhibition and religion or ldquoRum Romanism and Rebellionrdquo)

Thus far we have demonstrated that the presence of affiliategroups whose members are privy to information about partyplatforms can generate extremism and that the degree of extrem-ism depends on the importance of the turnout margin the degreeof informational differences between affiliates and nonaffiliatesthe heterogeneity of voter preferences and the size and prefer-ences of the affiliate group In the next two subsections we turn tothe question of how affiliate groups are formed

IIIC Social Organizations and Party Affiliation

In our model party affiliation means differential access toinformation about the party platforms One way in which partiesmay gain the ability to broadcast messages is to have access to aselected subgroup of the population such as a church or a unionIn this subsection we take the existence of such subgroups asgiven and ask how their existence influences the choice of politi-cal platform We assume that there is no way to target votersother than to have access to these particular groups We assumethat there are two groups whose membership is deterministicand not exclusive nor exhaustive The first which we label ldquothechurchrdquo comprises all voters with a sufficiently conservative pref-


erence with respect to issue a the second which we label ldquotheunionrdquo comprises all voters with a sufficiently progressive pref-erence with respect to issue t If we further assume that party Rhas a relationship with the church and can broadcast its platformto church members and party L can broadcast its message par-ticularly to union members then Proposition 4 follows

PROPOSITION 4 If party R has access through the church to allvoters for whom a and party L has access through theunion to all voters for whom t then both parties willmove away from the median-voter position whenever The R party platform will differ from zero only along the adimension and the L party platform will differ from zero onlyalong the t dimension

R-party extremism is maximized at a value of in theinterval (0( )( )) and L party extremism is maxi-mized at a value of in the interval (( )( )0) Thevalue of that maximizes R-party extremism is increasing inthe partyrsquos ability to convey information to its affiliates ()and to withhold it from nonaffiliates () the value of thatmaximizes L-party extremism is decreasing in the sameparameters

Since the value of that maximizes extremism is in theinterior of the interval (0( )( )) the relationship betweenextremism and group size is necessarily nonmonotonic Moreoverextremism is maximized when less than one-half of the popula-tion is in the group As group size decreases from its extremism-maximizing level the gains from extremism fall because thegroup becomes increasingly small and politically marginalizedAs group size increases from its extremism-maximizing level thegains from extremism also fall because the group itself becomesincreasingly moderate and representative of the country as awhole When we make stronger assumptions about preferencesthe relationship between extremism and group size becomes morestraightforward

Consider for example the case of a uniform distribution ofpreferences on the interval (11) with ( )( ) 02 Theassumption that ( )( ) 02 means that the probabilitythat a church member learns of the R party platform is 32 of theprobability that a nonchurch member learns of that platformGiven this assumption extremism is maximized when the churchcontains 45 percent of the population When ( )( ) 02


ie there is less information asymmetry the extremism-maxi-mizing church size lies between 45 and 5 When ( )( ) 03 the extremism-maximizing church size is 42 and when ( ( ) 01 the extremism-maximizing church size is 47

Are affiliate groups beneficial to their respective parties Infact if citizensrsquo beliefs about partiesrsquo positions are correct inequilibrium each party would prefer to drop its affiliate groupSince all citizens correctly anticipate the strategy each party willplay any gains from secret moves to the right or left are elimi-nated in equilibrium By dropping its affiliate group a partyessentially commits not to make secret deviations and it there-fore achieves the benefits of being expected to stick to the middleOf course affiliate groups can be beneficial if some voters haveincorrect beliefs or if affiliate groups provide other advantages9

IIID Endogenous Affiliation

We have so far assumed that groups are formed exogenouslyand then used by politicians In some settings however it is morenatural to think of voters as choosing their own group affiliationswhich in turn affect the messages they receive For examplevoters with different views may choose to use news media withdifferent political orientations (see Mullainathan and Shleifer[2005] Gentzkow and Shapiro [2005] and Gentzkow Glaeserand Goldin [2004]) or may affiliate with a church or organizationbecause of their political opinions In this section we show thatour core results are robust to allowing citizens to choose their owngroup in an initial stage of the model

This stage will be based on initial beliefs about party plat-forms and must occur before the parties broadcast their plat-forms A natural basis for affiliation could be the original positionof the parties specifically we suggest that the electorate is ini-tially split among right-wingers and left-wingers based on theirrelative preference for the platforms x L and x R that they origi-nally believe the parties to be adopting The benefit from affiliat-ing with a party equal

JPx i1

n

ix iP xi 2 with

i1

n

i 1

9 For example if voters incorrectly believed that a party had unpopularpolicies for historical reasons the ability to access an affiliate group and changeits opinions could be quite valuable


We further assume that this is always positive which meansthat everyone will always affiliate with one of the two parties10

(This assumption will tend to reduce extremism since many mod-erates will avoid party affiliation if affiliation can be costly) Aparticularly natural assumption is that the values of i thatdetermine affiliation are the same as the parameters i thatdetermine voting but we present results here for the more gen-eral case Finally we will specialize for simplicity to the unidi-mensional case (n 1) noting that we provide a partial charac-terization of equilibria in the two-dimensional game in GlaeserPonzetto and Shapiro [2004]

We assume that peoplersquos initial beliefs about party platformsare rational in the sense that they correctly anticipate the partiesrsquoequilibrium platforms moreover we focus on equilibria in whichthe partiesrsquo positions in the policy space are symmetric aroundthe origin We can then prove the following11

PROPOSITION 5 The one-dimensional political game with endoge-nous affiliation has a unique pure-strategy rational-expecta-tions equilibrium in which the partiesrsquo positions are symmet-ric around the origin and in this equilibrium party R locatesat ( ) E(x)( ) Extremism (or ) increases with decreases with and increases with the heterogeneity ofvotersrsquo preferences (as measured by the mean deviation oftheir distribution)

Thus the key comparative statics of our model remain in the casewhere affiliation is determined endogenously

This model helps us consider the welfare consequences ofstrategic extremism Since partiesrsquo positions are symmetric bothparties have an even shot at victory just as they do in a standard

10 We assume that affiliation is randomized with equal probabilities ifJL JR

11 It is possible to have an equilibrium where both parties are expected tochoose the median position affiliation with the two parties is completely randomand parties do therefore continue to choose the median policy However thisequilibrium is highly unstable in the sense that it would break down if there is anydeviation in affiliation so that both parties do not have ideologically identicalaffiliates As soon as there is any deviation in the distribution of affiliates theparties have an incentive to choose extreme policies

We do not find this equilibrium interesting because of its instability and weassume that there is some differentiation in initial beliefs about the partiesrsquoplatform As long as there is some difference in initial beliefs even if thatdifference is arbitrarily close to zero citizens affiliate with party R if their idealpolicy is x 0 and with party L if x 0 Symmetry then means that both finalpolicies and initial beliefs about policies will be symmetric around the origin


Hotelling model with no private information Thus political par-tiesrsquo welfare is unaffected by the option to secretly go extremeThe median voter on the other hand is made worse off bytargeted messages since they lead to equilibrium deviations fromthe median voterrsquos ideal point and thus to welfare losses for theaverage citizen

IV ALTERNATIVE EXPLANATIONS OF EXTREMISM

IVA Political Extremism as a Result of Votersrsquo Preferences

In the previous section extremism had a stronger positiveimpact on onersquos own supporters than it had a negative impact onthe opponentrsquos voters because of different awareness of changesin the political platform However extremism can also comeabout because citizens care more about the platform of the can-didate they support than about the candidate they oppose Insuch a model (presented formally in Riker and Ordeshook [1973p 359] as well as in Glaeser Ponzetto and Shapiro [2004])parties will have an incentive to diverge from the median voterrsquospreferred party because of the turnout margin since the gainfrom increases in turnout among a candidatersquos own supportersexceeds the losses from increasing turnout among his opponentrsquossupporters

Technically such a model has the undesirable property thatit requires greater mass away from the median votermdashthat iscitizensrsquo preferences must be clustered at the extremes of thedistribution More substantively the assumption that voters caremore about the platforms of their own candidates seems arbi-trary as well as at odds with much anecdotal description of themotivations of John Kerryrsquos supporters in the 2004 United Statespresidential election Finally this model generates the testableprediction that voter turnout will be highest for voters whosepolicies exactly match those of the candidates not for voters inthe extreme tails of the ideological distribution Yet Figure Vshows that voter turnout is monotonically rising with self-de-scribed ideological extremism (data from the General Social Sur-vey 1972ndash2002)12 Unless we believe that party platforms are atthe extremes of the preference distribution these data seem to

12 Rosenstone and Hansen [1993] also find that individuals with strongerparty identification are more likely to participate in elections


reject the prediction that turnout is declining in distance from theplatform By contrast our model of strategic extremism predictsthat turnout will be higher in the extremes of the preferencedistribution as long as there is any difference between the plat-forms of the two candidates

Taken together these arguments suggest that votersrsquo pref-erences are not a satisfactory explanation for the divergence inparty platforms from the preferences of the median voter In thenext subsection we consider the alternative view that the prefer-ences of candidates or parties are instead responsible for thisbehavior

IVB Strategic Extremism versus Candidate PreferenceExtremism

In this subsection we allow politicians to have preferencesover policies and we address the policy decisions of politiciansafter they have been elected The key implication of the theory isthat platforms will be more extreme than policy outcomes whenextremism is strategic but less extreme when extremism reflectscandidate preferences (or the primary process) We assume thatpoliticians weigh their desire to fulfill their own policy prefer-ences against their desire not to contradict their stated partyplatforms We assume that politiciansrsquo choices in the election arenot impacted by these ex post considerations (This assumptioncan be justified if politiciansrsquo preferences are lexicographic andthey care about winning more than anything else)

The party that wins the election subsequently decides whichpolicy to enact by weighing two considerations the personal pref-erences of the politician in office and the political cost of beingseen to deviate from onersquos electoral platform Specifically weassume that

UPx G i1

n

iLxi xi 1 i1

n

iLxi xiP

where i1

n

i 1

where x denotes the preferences of the politician and xP hiselectoral platform [01] and L is an increasing and strictlyconvex function on such that L(0) 0 We assume that


R-party politicians have preferences that are equally conserva-tive on all issues x xi xR 0i 1 n whileanalogously L-party politicians have preferences that are equallyprogressive on all issues x xi xL 0i 1 n

For simplicity suppose that L is quadratic so that L( z) z2 for all z Then considering the standard case where party Rrsquosplatform is unambiguously right-wing and party Lrsquos unambigu-ously left-wing (xR 0 and xL 0) the first-order condition for amaximum immediately proves the following

PROPOSITION 6 The enacted policy is a linear combination of theelectoral platform and the elected politicianrsquos ideal policy

x xP 1 xP

where P denotes the party of the electoral winner Thereforethe enacted policy is more extreme on one issue than onanother if and only if the electoral platform is

This provides some intuition about the issues on which policyextremism ought to exceed platform extremism and vice versaIn particular consider a two-dimensional case in which party Rwins the election Let (TR AR) denote the partyrsquos platform andxR its ideal policy on both issues It then follows immediately thatthe enacted policy of party R is more conservative than its plat-form on issue T and less conservative than its platform on issueA if and only if TR xR AR Therefore if extremism is drivenby strategic concerns not preferences then we should expect tosee extreme platforms and less difference in actual policies Ifextremism is driven by preferences then platforms will be moremoderate than eventual policies

A clean test of these predictions is beyond the scope of thispaper As a starting point however we note that the number ofabortions per 1000 live births from 1970ndash2000 was about 313 inyears with a Democrat in the White House and 294 in years witha Republican in the White Housemdasha small and statistically in-significant difference ( p 04710 in a two-sided t-test) Bycontrast in the case of taxes the data show more divergence inpolicy than in rhetoric Under Democratic administrations meantax rate as a share of GDP was about 11 percent as comparedwith 10 percent under Republican and administrations duringfiscal years 1970ndash2000 This difference is statistically distin-guishable from zero ( p 00002) and large representing about


one-standard deviation in the tax share over this time periodMoreover the difference survives controls for the average annualunemployment rate Though these facts are consistent with theview that platforms diverge more than policies on abortionwhereas the reverse occurs on taxes the myriad institutionalfactors that come between the president and the outcomes wemeasure mean that these findings must be taken as preliminaryand suggestive rather than conclusive Hopefully future workwill undertake more careful measurement of the differences be-tween stated platforms and realized policies in order to teaseapart the alternatives we have outlined in this subsection

V EVIDENCE ON ORGANIZATION SIZE AND POLITICAL EXTREMISM

The previous section emphasized that strategic extremism isa function of social organizations and underlying belief heteroge-neity In our empirical work we will focus primarily on socialorganizations largely because organization size is more straight-forward to measure in a way that is comparable across space andtime Additionally heterogeneity in beliefs seems more likely toitself be caused by political strategies which seems a less signifi-cant concern in the case of organization strength

We focus on churches one of the developed worldrsquos mostimportant social organizations This organization is without peerfor its combination of size significance to its members and his-tory Within the United States 89 percent of respondents in theGeneral Social Survey since 1990 report being a member of areligious group Churches are also particularly natural topics ofinvestigation because we know that they regularly connect withpolitics In many European countries while the Church does notexplicitly endorse candidates church resources and preachinghave often backed Christian Democratic candidates Within theUnited States as well right-wing candidates today regularly seeksupport from church leaders and try to connect to the churchfaithful13 Churches are natural social organizations to study alsobecause they have obvious policy domains Churches do not nat-urally sort along economic or foreign policy lines and as such weshould particularly expect to see links between the size of reli-

13 Additionally while the historical relationship between the right and thechurch may explain anticlericalism in the European left it is hard to tell a similarstory for the United States Some role for the endogenous formation of partyplatforms seems essential


gious organizations and the degree to which politics is polarizedalong religious grounds

We will focus on the key and perhaps somewhat surprisingimplication of the model about the role of social groups that thelink between group size and political polarization along the issuerelated to that group is nonmonotonic This leads us to tworelated tests of the hypothesis First in situations where churchmembership size varies between zero and 100 percent we willtest for the existence of a nonmonotonic relationship betweenchurch size and the political relevance of religion Second insituations where church membership is mostly greater than one-half of the population we will look for a decreasing relationshipbetween group size and the political relevance of the grouprsquos coreissue

Our basic measure of polarization along religious grounds isthe extent to which religiosity predicts supporting the right-wingcandidate In almost no cases is there a reversal where religiouspeople are more likely to support the left If there is a tightconnection between religion and supporting the right-wing can-didate we will consider a place to be highly polarized alongreligious grounds

As such for our cross-country work on church size our coreregression will take the form

Support for the Right b Religious Belief

c Religious Belief National Church Size

d Religious Belief National Church Size2

Controls Country and Year Fixed Effects

The model predicts that c will be positive and d will be negativeand that the maximum impact of religious belief occurs in coun-tries where around one-half of respondents attend churchregularly

In our cross-state work on religion we will estimate

Support for the Right b Religious Beliefs

c Religious Beliefs Church Size Controls

State and Year Fixed Effects

The model predicts that c will be negative in this case since morethan one-half of the population are generally religious adherents


Before turning to the regressions we discuss our data sourcesand core stylized facts

VA Data Sources The World Values Survey and the GeneralSocial Survey

Our work uses two primary data sets the World ValuesSurvey [Inglehart et al 2000] and the General Social Survey[Davis Smith and Marsden 2003] The General Social Survey(GSS) is an annual survey taken of a random sample of UnitedStates residents It contains questions on a host of demographicsas well as religion Religious attendance is scored on a nine-category scale ranging from never attending a religious institu-tion to attending more than once per day The key political vari-able will be whether the respondent voted for a Republican in thelast election We will eliminate those observations where individ-uals either did not vote or voted for an independent

The World Values Survey (WVS) was loosely modeled on theGeneral Social Survey and its questions are quite similar Thesurvey was conducted in three major waves in 1981ndash1984 1990ndash1993 and 1995ndash1997 and we will use data from all three wavesLike the General Social Survey the World Values Survey hasquestions on many basic demographic variables and a categoricalvariable on church attendance Instead of using votes in the lastelection since electoral differences across countries make thisquite problematic we will use respondentsrsquo self-reported politicalorientation as our measure of support for the right The WorldValues Survey asks people to self-report their political orienta-tion (left versus right) on a ten-point scale which we have stan-dardized by subtracting the mean for each country-wave pair anddividing by the standard deviation Our measure of support forthe right will be a personrsquos value on this scale

We also require measures of church attendance (We use thephrase ldquochurch attendancerdquo throughout the paper to refer to theattendance of religious services more generally) We take attend-ing once per month or more as our measure of membership in areligious organization For some purposes it may make sense torely on different cutoff values and our results are robust toslightly different definitions but we believe that monthly atten-dance comes closest to the spirit of the model People who attendless than once per month are unlikely to receive much informa-tion either from the pulpit or from other church-related activities


People who attend once per month or more can be thought of asregularly receiving some information through the church

All of our regressions will include country or state fixedeffects to capture the extent that political support differs overspace We also allow religion to have different effects in differentelections In our fixed-effect regressions we also include an in-teraction between country (in the World Values Survey) or state(in the General Social Survey) and religiosity14

VB Cross-National Evidence on Church Attendance

Our first regressions look at the connection between churchsize and religious polarization in politics There is remarkableheterogeneity in the World Values Survey in the amount ofchurch attendance across countries In some places such as theScandinavian countries or the Russian Federation 10 percent orless of the population attends church once per month or more Inthe United States in wave 3 of the survey around 60 percent ofrespondents attend church once per month or more In the Phil-ippines 90 percent attend church once per month or more Assuch cross-national investigation of church attendance gives usour best chance of measuring the connection between organiza-tional size and polarization for a wide range of organizationalsize

There are many different measures of religious belief that wecan use In the regressions in Table I we use self-reported an-swers to the question how important is God in your life Thisquestion is scored on a ten-point scale ranging from ldquonot at allrdquo toldquoveryrdquo We have standardized this measure by subtracting themean for the country-wave and dividing by the standard devia-tion so that a unit increase can be interpreted as an increase ofone standard deviation from the mean Our results are generallyrobust to alternative measures of religious belief Our regressionsinclude controls for gender income age age squared and yearsof completed schooling

In the first column of Table I we show the basic connection

14 As the World Values Survey and the General Social Survey contain manyobservations with missing data especially for income and since these missingobservations do not appear to be randomly selected we include observations thatare missing one or more of the control variables We then give that observation avalue for missing variable equal to the mean in the control and include a set ofdummy variables each of which takes on a value of one when a particular controlvariable is missing We never impute values for any of the variables whosecoefficients are reported in the tables


between identification with the political right and peoplersquos opin-ions about the importance of God The coefficient on the impor-tance of God is 16 meaning that as the importance of God to therespondent rises by one standard deviation the respondentrsquostendency to support the right rises by 16 standard deviationsThis coefficient is extremely significant statistically and it alsoseems economically significant to us

This pooled regression masks the considerable heteroge-neity that exists across countries Figure VI shows the coeffi-cients from country-level versions of regression (1) where thetendency to identify with the right is regressed on self-reportedimportance of God15 In some countries such as India or Tur-key the correlation is more than double our pooled estimates

15 Norris and Inglehart [2004] also study the connection between religiosityand political orientation in the World Values Survey We note that our results arerobust to using party preference rather than stated left-right political orientationas a dependent variable

TABLE ICROSS-COUNTRY DETERMINANTS OF RIGHT-WING ORIENTATION

DEPENDENT VARIABLE RESPONDENTrsquoS IDENTIFICATION

WITH THE POLITICAL RIGHT (STANDARDIZED)

(1) (2) (3) (4) (5) (6)

Importance of God inlife (standardized)

01639 00301(00149) (00334)

Importance of God Share monthly

08215 07965 07748 08321 11488(02105) (01933) (03305) (01761) (03028)

Importance of God (Share monthly)2

09135 08876 08138 07673 15635(02385) (02140) (04103) (01923) (03255)

Importance of God SD(religious beliefs)

13176(04395)

Imp of God wave NO NO YES YES YES YESImp of God country NO NO NO NO NO YESShare monthly

attendance thatmaximizesextremism

04497 04487 04760 05423 03674(00262) (00228) (00579) (00537) (00549)

Sample All All All Democracies All AllN 111883 111883 111883 67813 109930 111883

Data are from World Values Survey cumulative file waves 1ndash3 All estimates are from OLS regressionsStandard errors in parentheses are adjusted for correlation within country of residence All specificationsinclude dummies for country of residence survey wave gender and controls for income age age2 years ofcompleted schooling and dummies for missing data on these controls Standard errors for share maximizingextremism are calculated using the delta method SD(religious beliefs) is the standard deviation acrossindividuals the country-wave pair of the share of the following beliefs held belief in God life after death thesoul the Devil hell heaven and sin


(34 and 32 respectively) The estimated coefficient in theUnited States is slightly higher than that for the world as awhole Then there are many countries such as Norway Bang-ladesh and the Philippines where the coefficient is essentiallyzero

The model predicts a nonmonotonic relationship and that isexactly what we see With few exceptions most countries withreligious attendance below 25 percent have weak connectionsbetween religious identification and right-wing status There isalso no country with religious attendance above 60 percent thathas an above-average connection between right-wing status andreligiosity All the countries with extremely tight connectionsbetween religion and political orientation have monthly churchattendance values between 3 and 6

Perhaps it is unsurprising that the countries with little reli-gion also have little connection between religion and politicalorientation It seems to us somewhat more counterintuitive thatthere is no connection between religion and politics in those

FIGURE VIThe Political Role of Religion Across Countries

Data are from Wave 3 of the World Values Survey Vertical axis shows theestimated effect of a one-standard deviation increase in the importance of God inthe respondentrsquos life on the respondentrsquos identification with the political rightHorizontal axis shows the share of respondents in the country who report attend-ing church (or analogous religious institution) once a month or more


countries with extremely high levels of religious attendance al-though this is exactly what is predicted by the model The coun-tries with moderate attendance levels that do not conform wellwith the theory are Chile Brazil the Dominican Republic andVenezuela One potential explanation for these observations isthe history of liberation theology and left-wing clerics opposingmilitary regimes

To test for the nonmonotonic impact of church membershipon the religion-right-wing connection in regression (2) of TableI we interact the self-report of the importance of God with theshare of the countryrsquos respondents attending church more thanonce per month and the square of that variable We also in-clude the raw values of the church attendance variable in theregression and allow importance of God to differ during thedifferent waves of World Value Survey Regression (2) showsboth a strong positive interaction between national churchattendance and the impact of the importance of God for lowlevels of national church attendance and a strong negativequadratic term Both the linear and quadratic terms are highlysignificant statistically The connection between right-wingstatus and self-reported importance of God appears to be maxi-mized when about 45 percent of the population attends churchSpecification (3) demonstrates that this finding is robust toallowing the effect of religiosity to vary with survey wave thusidentifying our key interaction terms only using cross-sectionalvariation in church attendance

In the fourth regression of the table we repeat regression (3)only for those countries with Polity III democracy scores averag-ing at least 5 from 1970ndash1995 Of course political competitionalso occurs in countries that are not democracies and people havepolitical preferences even when they do not have a chance to voteNonetheless our model is specifically based on political competi-tion in a democratic setting so it makes sense to ensure thatthese results are robust to excluding nondemocracies for thesample In this case the linear term remains significantly posi-tive and the quadratic term remains significantly negative Theeffect of religion on being right-wing is now maximized when 48percent of the population attends church at least once per month

Column (5) incorporates a test of another of the modelrsquospredictions that increasing heterogeneity is associated withgreater extremism In particular we include an interaction be-tween the stated importance of God in the respondentrsquos life and


the standard deviation of religious beliefs in his country (andsurvey wave)16 These interaction terms are positive and statis-tically significant as predicted by the model Equally importantis the fact that including these measures of heterogeneity doesnot eliminate the nonmonotonic relationship between country-level church attendance and religious extremism Since theprediction that group size enters nonmonotonically is far morespecific to our model than the prediction that heterogeneityexacerbates divergence it is reassuring that our key findingsare not eliminated by including heterogeneity measures in theestimation

In regression (6) we return to our entire sample of countriesand allow each country to have a different inherent connectionbetween religiosity and right-wing status This specification isakin to a country fixed effects specification where the countryfixed effect is not in the level of right-wing status (we always havethat fixed effect) but rather in the connection between religiousintensity and being right-wing In this case all of our identifica-tion comes from changes in church attendance over time Putdifferently we ask in regression (6) whether changes in churchattendance across countries are related to changes in the connec-tion between religiosity and political affiliation in the mannerpredicted by our model In this specification we again find asignificant positive linear impact of national church attendanceon the importance of God coefficient and a significant negativequadratic impact of national church attendance on the samecoefficient In this case the impact of importance of God is max-imized when 37 percent of the population attends church once permonth or more Thus evidence from changes as well as levelsconfirms the basic result that medium-sized groups are mostconducive to polarization

While we have focused on the role of churches in definingreligious cleavages we can also ask whether trade unions have ananalogous impact on economic cleavages Figure VII shows therelationship between the correlation between income and right-wing orientation and trade union density (from Blanchflower[1996]) for wave 2 of the World Values Survey In some countriessuch as France and Austria the coefficient is less than 05 (the

16 We measure an individualrsquos religious beliefs by computing the share ofthe following items the individual reports believing in God life after death thesoul the Devil hell heaven and sin


United States coefficient is also quite low) In other places such asthe Netherlands or the United Kingdom the coefficient is muchlarger and there is a strong connection between income andright-wing status The figure shows a strong tendency of thecoefficient on income to rise with trade union density for tradeunion density levels below 40 percent and then little pattern afterthat Small samples make it difficult to discern whether there isindeed a nonmonotonic relationship but it does seem that at lowlevels of unionization increases in the density of unions areassociated with greater partisanship along economic lines

VC United States Evidence on Church Attendance

In Table II we regress voting for a Republican in the lastelection on church attendance and controls for income educa-tion age age squared and gender We include state and yearfixed effects Reported coefficients are marginal effects from pro-bits evaluated at sample means The first specification looks atthe impact of going to church at least once per month on voting

FIGURE VIIUnions and the Political Importance of Income across Countries

Data are from Wave 2 of the World Values Survey Vertical axis shows theestimated effect of a one-standard deviation increase in income on the respon-dentrsquos identification with the political right Horizontal axis shows Blanchflowerrsquos[1996] measure of trade union density in 1994


Republican There is a strong positive effect People who attendchurch once per month are ten percentage points more likely tovote Republican than people who attend church less frequentlythan that This basic result can be found using a large number ofdifferent measures of religiosity such as the continuous measureof church attendance or qualitative variables about the impor-tance of God

This basic coefficient on religious attendance obscures theconsiderable variation that exists among states17 Figure VIIIshows the coefficients from regressions like regression (1) thatwere run separately for each state In some places like Washing-ton or Oregon the coefficient is more than 2 In other places suchas the Carolinas the coefficient is less than 05 Figure VIIIshows the relationship between these estimated coefficients andthe share of respondents in the state who attend church at leastonce per month Since these shares are generally more than 50

17 We identify a respondentrsquos state by matching primary sampling units tometropolitan areas and connecting metropolitan areas with states

TABLE IICHURCH ATTENDANCE AND THE ROLE OF RELIGION IN VOTING (GSS)

DEPENDENT VARIABLE DID RESPONDENT VOTE FOR REPUBLICAN CANDIDATE

IN LAST PRESIDENTIAL ELECTION

(1) (2) (3) (4) (5)

Attend church at least once 00999 03261a month (00127) (00503)

Attend at least once amonth Shareattending monthly instate

04888 04214 02698 02279(01139) (01169) (01393) (02087)

Attend at least once amonth SD(religiousbeliefs)

05804(02552)

Attend monthly election NO NO YES YES YESAttend monthly state NO NO N0 NO YESN 16641 16641 16641 16066 16641

Data are from General Social Survey cumulative file 1972ndash2002 Only respondents voting for eitherDemocrat or Republican in previous election have been included All estimates are marginal effects fromprobit models evaluated at sample means Standard errors in parentheses are adjusted for correlation withinstate of residence SD(religious beliefs) is the standard deviation across individuals the state in the 1991sample of the share of the following beliefs held belief in God life after death miracles the Devil hell andheaven All specifications include dummies for state of residence year of most recent election race genderand controls for the log of real income age age2 years of completed schooling and dummy for missing incomedata Samples exclude Utah residents


percent across states (and almost always more than 40 percent)the model predicts a negative relationship and that is indeedwhat we observe in the graph The highly religious states haveless connection between religion and voting Republican than themoderately religious states

In regression (2) of Table II we estimate the interactionbetween the share in the state attending church at least once permonth and the individualrsquos own religious attendance The impactof religion on voting Republican decreases sharply with the shareof the state that is itself religious In regression (4) we augmentthis specification by allowing the effect of monthly attendance tovary with election year so that we identify the interaction effectsolely from cross-sectional differences among the states The re-sults are quite similar

Regression (4) incorporates a test of the modelrsquos prediction

FIGURE VIIIThe Political Role of Religion across American States

Data are from General Social Survey cumulative file 1972ndash2002 Only respon-dents voting for either Democrat or Republican in previous election have beenincluded Vertical axis shows the marginal effect of monthly church attendancefrom probit models evaluated at sample means The dependent variable is adummy for Republican vote in the previous presidential election and all specifi-cations are run separately for each state including dummies for year of mostrecent election race gender and controls for the log of real income age age2years of completed schooling and a dummy for missing income data Sampleexcludes Utah residents


that greater heterogeneity in preferences increases the degreeof extremism In particular we interact monthly attendancewith a measure of the heterogeneity in religious beliefs in theindividualrsquos state of residence taking advantage of a 1991 GSSmodule18 As the model predicts we find that religious atten-dance is a stronger predictor of Republicanism in states withgreater heterogeneity in religious beliefs Including this termreduces the point estimate of the interaction between individ-ual attendance and state religiosity but it remains marginallystatistically significant and comparable in magnitude to theestimate in column (3)

In regression (5) we include interactions between statedummies and individual religious attendance This procedureduplicates our methodology in the previous table where weallowed each country to have its own connection between reli-gion and right-wing orientation This estimation relies onchanges in religious attendance within the state not on varia-tion across states The estimate of the cross effect betweenaverage religious attendance in the state is still negative andnot statistically distinguishable from the estimate in regres-sion (3) However the standard error on this estimate is solarge that it is also not statistically distinguishable from zeroOur variation in state church attendance over time is ex-tremely noisy and as such it is unsurprising that our resultsare not precise

Table III reproduces the specifications of Table II using theAmerican National Election Studies [Sapiro and Rosenstone2002] The National Election Studies (NES) have been conductedsince 1948 and are designed to track the determinants of voterbehavior over time As in Table II our main interest will be inasking whether church attendance matters less for voting behav-ior in highly religious states

In specification (1) of Table III we reproduce the basic find-ing that monthly churchgoers are significantly more likely to voteRepublican during the period 1972ndash2002 In specification (2) weinteract the monthly attendance dummy with a measure of theshare of people who attend church monthly or more in the re-spondentrsquos state and election year As in Table II we find a

18 We measure an individualrsquos religious beliefs by computing the share ofthe following items the individual reports believing in God life after deathmiracles the Devil hell and heaven


statistically significant negative interaction church attendancehas less of an effect on the probability of voting Republican inhighly religious states The coefficient is similar in magnitude tothe analogous coefficient in Table II In regression (3) we includedummies for most recent presidential election year interactedwith monthly attendance to control for time effects and findsimilar results Column (4) includes an interaction betweenmonthly attendance and the standard deviation in religious be-liefs in the respondentrsquos state measured using data from the 1991GSS Religiosity is a stronger predictor of Republicanism in stateswith greater heterogeneity although the effect is only marginallystatistically significant Including this term does not eliminatethe economic or statistical significance of the interaction betweenindividual attendance and state-level religiosity Column (5) ofTable III repeats the specification of column (3) allowing theeffect of monthly attendance to differ freely by state Again wefind a significant negative interaction although the standard

TABLE IIICHURCH ATTENDANCE AND THE ROLE OF RELIGION IN VOTING (NES)



(1) (2) (3) (4) (5)

Attend church at least oncea month

01237 02676(00115) (00685)


02954 03419 02841 03820(01402) (01464) (01336) (01756)


07509(04381)

Attend monthly election NO NO YES YES YESAttend monthly state NO NO NO NO YESN 8882 8882 8882 7046 8882

Data are from National Election Study cumulative file 1948ndash2000 Only years 1972ndash2000 are used dueto a change in the survey question about religious attendance beginning in 1970 Only respondents voting foreither Democrat or Republican in previous presidential election have been included All estimates aremarginal effects from probit models evaluated at sample means Standard errors in parentheses are adjustedfor correlation within state of residence SD(religious beliefs) is the standard deviation across individuals thestate in the 1991 GSS sample of the share of the following beliefs held belief in God life after death miraclesthe Devil hell and heaven All specifications include dummies for state of residence year of most recentelection race gender income category (as shown in Figure I) and controls for the age age2 and years ofcompleted schooling


errors are larger due to the inclusion of state fixed effects inter-acted with monthly attendance19

Given these results it is natural to wonder whether the riseof religion as a determinant of political affiliation can be attrib-uted to a broad secular decline in religious adherence The evi-dence is mixed however on whether such a decline actuallyoccurred during the time period we study In the General SocialSurvey the share of people attending church monthly went from509 percent to 472 percent between the 1972 and 2000 electionsBy contrast the World Values Survey shows no decline in religi-osity over a similar period [Norris and Inglehart 2004] Given theambiguity in these data it seems reasonable to conclude that if adecline did occur it was probably too small by itself to have hada substantial impact on political platforms

Relatedly given the political importance of unions one mightexpect the decline in unions during this period to have led to adecline in the political importance of income since union densityhas now fallen far below the point where the model predicts thatthe impact of the group would be the largest As Figure III showshowever there does not seem to be any significant decline in thepolitical importance of income to correspond to the fall in union-ism It is possible of course that politicians take time to react tosuch changes and therefore that this decline will manifest itselfin political platforms in future election years

VI CONCLUSION

Even in majoritarian systems there are often major differ-ences in policies between political candidates There is rarelycomplete convergence by candidates to the views of the medianvoter In the United States today the gulf between the Republi-can and Democratic parties on religiously oriented issues likeabortion is quite significant In this paper we have explored thereasons why political platforms might be extreme rather thanmoderate

Our model emphasizes the role of the intensive margin ofgetting voters into the voting booth and informational asymme-tries in creating extremism If politicians care only about attract-

19 Our findings in Tables II and III are robust to including dummies forProtestant and Catholic denomination in all models We also obtain similarresults using data on votes for Senate instead of President


ing the median voter and have little interest in inducing theircore supporters to show up then there will be little extremismEven with an important voter turnout margin a second asymme-try is required so that when politicians deviate from the centerthey benefit more from attracting their own supporters than theylose from alienating their opponentrsquos supporters The heart of ourmodel is that when a politician deviates from the center his ownsupporters are more aware of this deviation than his opponentrsquossupporters With a single relevant policy dimension extremism ismore likely when the information asymmetry is more extremeand when informational groupings are more closely tied to po-litical tastes Extremism is also unsurprisingly more commonwhen underlying preferences are more extreme

The model with two issues predicts that the relevance oforganizations to political extremes is nonmonotonic in the sizeof the organization When the organization is quite small it ispolitically irrelevant When the organization is very large (iemore than 50 percent of the population) it no longer createsthe opportunity for the transmission of targeted messagesLooking across countries in the world we confirm this non-monotonicity in the case of religion Countries with either veryhigh or very low levels of church attendance have little con-nection between religiosity and right-wing orientation Ex-treme connections between religion and politics occur only forcountries where church attendance is around 50 percentAcross American states we find a negative relationship wherehigher church attendance decreases the connection betweenreligiosity and voting Republican

In this paper we have avoided discussing institutions thatmight tend to further or modify extremism but this is clearly animportant topic for future research Some of these institutionallinks have already been examined by Cox [1990] and others butthis paper suggests further directions for research on constitu-tional design For example if geography creates a natural abilityfor politicians to target their messages ie if people in your ownarea are more aware of your policies than people elsewhere thennational systems are always at risk of politicians proposing ex-treme regional policies One way to counter this tendency is tohave voting systems like the United Statesrsquo electoral college thatlimit the value of getting extra votes in one particular geographicarea


APPENDIX

Proof of Propositions 1 and 2 Denoting as ( xL x R) theposition of the parties as perceived by a given voter and as ()the distribution of beliefs the margin of victory for party R is

1

1

Z2( xR xL)x xR xL

2 Z2( xR xL)x

xR xL

2 d fx dx

whose derivative with respect to xR is

1

1

2 x xR

z2 ( xR xL)x xR xL

2 xR xR d f x dx

where we denote with the characteristic or indicator functionThus considering the uniform distribution of costs and the

assumptions on the availability of updated information on theparty platform and letting the probability of a voter being anaffiliate be described by the function 13( x) of his ideal policy theoptimal platform choice for the party regardless of initial beliefsand of the opponentrsquos actions is

xR 1

1 x13 x f x dx 1

1 13 x f x dx

Notice that

R 1

1

13 x f x dx 01

equals the size of the group of party affiliates which can also beinterpreted as the unconditional probability of a voter being anaffiliate while the ideal policy of the average party affiliate is

E xR 1

R

1

1

x13 x f x dtx E x 0

where the inequality is derived from the natural assumption that


R-party affiliates are on average more conservative than votersas a whole

Therefore

xR R

RE xR

It follows immediately that when R 0 the median-voterresult obtains in two cases only in the absence of informationalasymmetries or in the absence of any difference in thepreferences of the average affiliate and nonaffiliate E( xR) E( x) 0 Whenever there are both an informational and anideological difference between affiliates and nonaffiliates xR 0

Furthermore the partyrsquos extremism is then monotone in-creasing in its ability to convey information to its affiliates

xR

R

R2 E xR 0

and to withhold it from nonaffiliates

xR

R

R2 ExR 0

as well as increasing in the number of affiliates (keeping theiraverage conservatism constant)

xR

R

R2 E xR 0

and in the average conservatism of affiliates (keeping their num-ber constant)

xR

E xR

R

R 0

If 13( x) ( x 0) R 1frasl2 and E( xR) E(x)

xR

Ex

which immediately shows that extremism is increasing in theheterogeneity of votersrsquo preferences measured by the meandeviation of their distribution

When the distribution of the cost of voting is generalized toinclude a point mass z0 [01] of voters with zero cost of voting


as well as a uniform density of voters z(c) (1 z0)V for all c [0V ] the margin of victory for party R is

1 z0

2 1

1

xR xLx xR xL

2 d f x dx

z01 2

F xR xL

2 d()


1 z0

2 1

1

x xR 13 x f x dx

z0

fxR xL

2 xR xR d

As shown above the first term is a decreasing function of xRthat equals zero when

xR R

RE xR 0

under the weak assumption that R affiliates are on average moreconservative that nonaffiliates The second term instead is al-ways negative Hence the modified distribution generates lessextremism than the uniform

In the limit as z0 3 0 we have our standard result xR ( )RE( xR)( ( )R) and as z0 3 1 convergenceto the mean as a corner solution when votersrsquo beliefs are rational

By the second-order condition the second derivative of themargin of victory with respect to xR is negative since the crossderivative with respect to z0 is negative by inspection

xR

z0 0

Proof of Proposition 3 The margin of victory for party R is

1

1 1

1

Z2ta Z2ta d fta dt da


whose gradient with respect to the platform choice of party R(TR AR) is

2 1

1 11 (t TR) z(2(ta))

TR TR) d() f(ta) dt da2(1 ) 1

1 11 (a AR) z(2(ta))

AR AR) d() f(ta) dt da

Considering our usual assumptions on the distribution ofcosts and preferences and on the informational structure theoptimal platform choice for the party regardless of initial beliefsand of the opponentrsquos actions is

TR R

REtR

AR R

REaR

where

R 1

1 1

1

13ta fta dt da 01

is the size of the group of party affiliates (or the unconditionalprobability of a voter being an affiliate) and by the assumptionthat R-party affiliates are on average at least as conservative asvoters as a whole on each of the two dimensions

EtR 1

R

1

1 1

1

t13ta fta dt da 0

EaR 1

R

1

1 1

1

a13ta fta dt da 0

Mirroring the one-dimensional case this shows that conver-gence to the position of the median voter for a party with apositive mass of affiliates (R 0) requires the absence either ofinformational asymmetries ( ) or of any difference in theaverage preferences of affiliates and nonaffiliates (E(tR) E(t) 0 and E(aR) E(a) 0) The effect of the differentvariables is also identical moreover

TR AR N EtR EaR


which shows that unsurprisingly the divergence of the partyfrom the median-voter position is greater on the issue where thedifference in preferences between affiliates and nonaffiliates is onaverage greater

If 13(ta) (t a 0) considering that by independencef(ta) fT(t) fA(a) and thus by symmetry f(ta) f(ta) f(ta) f(ta)

R 1

1 t

1

fta da dt 1

1

FAt fTt dt 12

and

EtR 2 1

1

t t

1

fAa dafTt dt 2 1

1

tFAt fTt dt

2 0

1

tfTt2FAt 1 dt 0Et

We say that the distribution G( x) is monotonically moreheterogeneous than F( x) if and only if g( x) f( x) is monotonenondecreasing on [01] (and thus monotone nonincreasing on[10]) or equivalently G( x) F( x) is convex on [01] (and thusconcave on [10]) or equivalently (since by symmetry F(0) G(0) 1frasl2 while F(1) G(1) 1) G( x) F( x)x [01] (andthus G( x) F( x)x [10])

Therefore a monotonic increase in the heterogeneity of FT(weakly) increases E(tR) because t(2FA(t) 1) is (weakly)increasing on [01] while it (weakly) reduces E(aR) becausetfT(t) is (weakly) positive on [01]

Proof of Proposition 4 Consider without loss of generalityparty R for which 13R(ta) (a ) we have R 1 F()E(tR) 0 and E(aR) (

1 afA(a) da)(1 FA()) 0 so that

TR 0

AR 1

1 F

1

afAa da 0

Notice that obviously 1 f AR 0 because an


organization comprising everyone or nobody has no relevance asa channel for informational differentiation moreover

AR

fA

1 FA2

1

afA(a) da

1 FA()

so that

AR

0 0

and the maximum effect of the organization on extremism isattained at 0 such that

1

1

FAa da

1

The left-hand side of this equation is an increasing convexfunction L() such that L(1) 1 and L() FA() [1frasl2 1] [01] while the right-hand side is a line through theorigin with slope greater than 1 which ensures uniqueness of themaximum Since FA(0) 1frasl2 f

1 FA(a) da ((1 ) 2)a 0 we also know that

and indeed

1 FA 0

1 FA 0

Proof of Proposition 5 We proved in Proposition 1 that re-gardless of the votersrsquo initial beliefs

xR R

RE xR and xL

L

LE xL

In any rational-expectations equilibrium in which the par-


tiesrsquo positions are symmetric around the origin all voters withpreferences x 0 affiliate with party R and all those withpreferences x 0 affiliate with party L Hence there is a uniquesuch equilibrium

x R xR

Ex xL xL

HARVARD UNIVERSITY AND NBERHARVARD UNIVERSITY

UNIVERSITY OF CHICAGO AND NBER

REFERENCES

Alesina Alberto ldquoCredibility and Policy Convergence in a Two-party System withRational Votersrdquo American Economic Review LXXVIII (1988) 796ndash805

Anonymous ldquoHigh Pitch Low Politicsrdquo The Economist (2005)Becker Gary S ldquoCompetition and Democracyrdquo Journal of Law and Economics I

(1958) 105ndash109mdashmdash ldquoA Theory of Competition among Pressure Groups for Political Influencerdquo

Quarterly Journal of Economics XCVIII (1983) 371ndash400Blanchflower David G ldquoThe Role and Influence of Trade Unions in the OECDrdquo

Report to the Bureau of International Labor Affairs U S Department ofLabor 1996

Borsuk Alan J ldquoBush Kerry Preach to Faithful Non-Supporters Unlikely to GetClose to Candidatesrdquo Milwaukee Journal Sentinel (2004) A1

Calmes Jackie and John Harwood ldquoCampaign rsquo04ndashMobilization Plan Bushrsquos BigPriority Energize Conservative Christian BasendashUnusual Strategy PlaysDown Importance of Swing Vote As Demographics ShiftmdashA Coordinator inEach Churchrdquo Wall Street Journal (2004) A1

Cox Gary W ldquoCentripetal and Centrifugal Incentives in Electoral SystemsrdquoAmerican Journal of Political Science XXXIV (1990) 903ndash935

Davis James A Tom W Smith and Peter V Marsden General Social Surveys1972ndash2002 (Ann Arbor MI ICPSR 2003) Dataset 3728

Dixit Avinash and John Londregan ldquoRedistributive Politics and Economic Effi-ciencyrdquo American Political Science Review LXXXIX (1995) 856ndash866

Downs Anthony ldquoAn Economic Theory of Political Action in a DemocracyrdquoJournal of Political Economy LXV (1957) 135ndash150

Farrell Joseph and Robert Gibbons ldquoCheap Talk with Two Audiencesrdquo AmericanEconomic Review LXXIX (1989) 1214ndash1223

Fiorina Morris P ldquoWhatever Happened to the Median Voterrdquo Stanford Univer-sity mimeograph 1999

Fiorina Morris P Samuel J Abrams and Jeremy C Pope Culture War TheMyth of a Polarized America (New York NY Pearson Longman 2005)

Gentzkow Matthew A and Jesse M Shapiro ldquoMedia Bias and ReputationrdquoHarvard University mimeograph 2005

Gentzkow Matthew Edward L Glaeser and Claudia D Goldin ldquoThe Rise of theFourth Estate How Newspapers Became Informative and Why it MatteredrdquoHarvard University mimeograph 2004

Glaeser Edward L Giacomo A M Ponzetto and Jesse M Shapiro ldquoStrategicExtremism Why Republicans and Democrats Divide on Religious ValuesrdquoNBER Working Paper No 10835 2004

Grossman Gene M and Elhanan Helpman Special Interest Politics (CambridgeMA MIT Press 2002)

Guttman Joel M Naftali Hilger and Yochanan Schachmurove ldquoVoting as In-vestment vs Voting as Consumption New Evidencerdquo Kyklos XLVII (1994)197ndash207


Hotelling Harold ldquoStability in Competitionrdquo Economic Journal XXXIX (1929)41ndash57

Inglehart Ronald and et al World Values Surveys and European Values Surveys1981ndash84 1990ndash93 and 1995ndash97 (Ann Arbor MI ICPSR 2000) Dataset2790

Irmen Andreas and Jean-Francois Thisse ldquoCompetition in Multi-CharacteristicsSpaces Hotelling Was Almost Rightrdquo Journal of Economic Theory LXXVIII(1998) 76ndash102

Kirchgassner Gebhard ldquoAbstention Because of Indifference and Alienation andIts Consequences for Party Competition A Simple Psychological ModelrdquoUniversity of St Gallen Discussion Paper 2003

Kirkpatrick David D ldquoChurches See an Election Role and Spread the Word onBushrdquo New York Times (2004a)

mdashmdash ldquoThe Republicans The Convention in New YorkmdashThe Religion Issuerdquo NewYork Times (2004b) P1

Layman Geoffrey C ldquoReligion and Political Behavior in the United States TheImpact of Beliefs Affiliations and Commitment from 1980 to 1994rdquo PublicOpinion Quarterly LXI (1997) 288ndash316

mdashmdash ldquo ldquoCulture Warsrdquo in the American Party Systemrdquo American Politics Quar-terly XXVII (1999) 89ndash121

mdashmdash The Great Divide Religious and Cultural Conflict in American Party Politics(New York Columbia University Press 2001)

McDonald Michael P ldquoUp Up and Away Voter Participation in the 2004 Presi-dential Electionrdquo The Forum II (2004)

McDonald Michael P and Samuel L Popkin ldquoThe Myth of the Vanishing VoterrdquoAmerican Political Science Review XCV (2001) 963ndash974

Mullainathan Sendhil and Andrei Shleifer ldquoThe Market for Newsrdquo AmericanEconomic Review (2005) forthcoming

Murphy Kevin M and Andrei Shleifer ldquoPersuasion in Politicsrdquo American Eco-nomic Review XCIV (2004) 435ndash439

Norris Pippa and Ronald Inglehart Sacred and Secular Religion and PoliticsWorldwide Cambridge Studies in Social Theory Religion and Politics (Cam-bridge UK Cambridge University Press 2004)

Putnam Robert D Bowling Alone The Collapse and Revival of American Com-munity (New York Simon and Schuster 2000)

Riker William H and Peter C Ordeshook An Introduction to Positive PoliticalTheory Prentice-Hall Contemporary Political Theory Series (EnglewoodCliffs NJ Prentice-Hall 1973)

Rosenstone Steven J and John Mark Hansen Mobilization Participation andDemocracy in America New Topics in Politics (New York Macmillan Pub-lishing Company 1993)

Sapiro Virginia and Steven J Rosenstone American National Election StudiesCumulative Data File Vol 8475 (Ann Arbor MI ICPSR 2002)

Schuessler Alexander A A Logic of Expressive Choice (Princeton NJ PrincetonUniversity Press 2000)


be infringedrdquo while the Democrats in the same year ldquostandproudly for a womanrsquos right to chooserdquo We will refer to suchdivergent party platforms as extremism

Traditional median-voter results (eg Hotelling [1929])make extremism difficult to understand After all vote-maximiz-ing politicians are supposed to cater to the middle not the edgesof the distribution (see Downs [1957] and Becker [1958]) at leastin majoritarian systems [Cox 1990] Political theorists who try toexplain extremism emphasize the primary system or the ideologi-cal preferences of the candidate or party leaders (as in Alesina[1988])2 While the primary system is important and politiciansrsquopreferences certainly matter this paper explains why extremismoccurs for purely strategic ie vote-maximizing reasons in amajoritarian system with only one issue

2 But see Murphy and Shleifer [2004] and Kirchgassner [2003] for recentexceptions Murphy and Shleifer [2004] show that the effects of social networks onbeliefs can lead to an incentive to move away from the political center Fiorina[1999] reviews the political science literature on polarization

FIGURE IIncome and Republicanism in the 2004 Election

Data are from the National Election Pool Exit Poll 2004 Data include votersvoting for Democratic or Republican candidate in the November 2004 presidentialelection Shares are weighted as recommended by the data providers







































































SP B i1

n

iMxiP xi where

i1

n

i 1



L xi ) M(xiR xi )]

i1n i[M(xi

R xi ) M(xiL xi )]




c Vx xL xR




MxiP xi xi

P xi 2









R and xiL will


L) ( xiR)2 ( xi


R 0 xiL then





















ta TR TL t TL TR

2 1 AR ALa

AL AR

2


























JPx i1

n

ix iP xi 2 with

i1

n

i 1

























UPx G i1

n

iLxi xi 1 i1

n

iLxi xiP

where i1

n

i 1






x xP 1 xP














































(1) (2) (3) (4) (5) (6)


01639 00301(00149) (00334)


08215 07965 07748 08321 11488(02105) (01933) (03305) (01761) (03028)


09135 08876 08138 07673 15635(02385) (02140) (04103) (01923) (03255)


13176(04395)



04497 04487 04760 05423 03674(00262) (00228) (00579) (00537) (00549)
































(1) (2) (3) (4) (5)



04888 04214 02698 02279(01139) (01169) (01393) (02087)


05804(02552)




















(1) (2) (3) (4) (5)


01237 02676(00115) (00685)


02954 03419 02841 03820(01402) (01464) (01336) (01756)


07509(04381)







VI CONCLUSION









APPENDIX


1

1

Z2( xR xL)x xR xL

2 Z2( xR xL)x

xR xL

2 d fx dx


1

1

2 x xR

z2 ( xR xL)x xR xL

2 xR xR d f x dx



xR 1

1 x13 x f x dx 1

1 13 x f x dx

Notice that

R 1

1

13 x f x dx 01


E xR 1

R

1

1

x13 x f x dtx E x 0




Therefore

xR R

RE xR



xR

R

R2 E xR 0


xR

R

R2 ExR 0


xR

R

R2 E xR 0


xR

E xR

R

R 0


xR

Ex





1 z0

2 1

1

xR xLx xR xL

2 d f x dx

z01 2

F xR xL

2 d()


1 z0

2 1

1

x xR 13 x f x dx

z0

fxR xL

2 xR xR d


xR R

RE xR 0




xR

z0 0


1

1 1

1




2 1

1 11 (t TR) z(2(ta))


1 11 (a AR) z(2(ta))



TR R

REtR

AR R

REaR

where

R 1

1 1

1

13ta fta dt da 01


EtR 1

R

1

1 1

1

t13ta fta dt da 0

EaR 1

R

1

1 1

1

a13ta fta dt da 0


TR AR N EtR EaR




R 1

1 t

1

fta da dt 1

1

FAt fTt dt 12

and

EtR 2 1

1

t t

1

fAa dafTt dt 2 1

1

tFAt fTt dt

2 0

1

tfTt2FAt 1 dt 0Et





TR 0

AR 1

1 F

1

afAa da 0




AR

fA

1 FA2

1

afA(a) da

1 FA()

so that

AR

0 0


1

1

FAa da

1



and indeed

1 FA 0

1 FA 0


xR R

RE xR and xL

L

LE xL




x R xR

Ex xL xL



REFERENCES














































































































SP B i1

n

iMxiP xi where

i1

n

i 1



L xi ) M(xiR xi )]

i1n i[M(xi

R xi ) M(xiL xi )]




c Vx xL xR




MxiP xi xi

P xi 2









R and xiL will


L) ( xiR)2 ( xi


R 0 xiL then





















ta TR TL t TL TR

2 1 AR ALa

AL AR

2


























JPx i1

n

ix iP xi 2 with

i1

n

i 1

























UPx G i1

n

iLxi xi 1 i1

n

iLxi xiP

where i1

n

i 1






x xP 1 xP














































(1) (2) (3) (4) (5) (6)


01639 00301(00149) (00334)


08215 07965 07748 08321 11488(02105) (01933) (03305) (01761) (03028)


09135 08876 08138 07673 15635(02385) (02140) (04103) (01923) (03255)


13176(04395)



04497 04487 04760 05423 03674(00262) (00228) (00579) (00537) (00549)
































(1) (2) (3) (4) (5)



04888 04214 02698 02279(01139) (01169) (01393) (02087)


05804(02552)




















(1) (2) (3) (4) (5)


01237 02676(00115) (00685)


02954 03419 02841 03820(01402) (01464) (01336) (01756)


07509(04381)







VI CONCLUSION









APPENDIX


1

1

Z2( xR xL)x xR xL

2 Z2( xR xL)x

xR xL

2 d fx dx


1

1

2 x xR

z2 ( xR xL)x xR xL

2 xR xR d f x dx



xR 1

1 x13 x f x dx 1

1 13 x f x dx

Notice that

R 1

1

13 x f x dx 01


E xR 1

R

1

1

x13 x f x dtx E x 0




Therefore

xR R

RE xR



xR

R

R2 E xR 0


xR

R

R2 ExR 0


xR

R

R2 E xR 0


xR

E xR

R

R 0


xR

Ex





1 z0

2 1

1

xR xLx xR xL

2 d f x dx

z01 2

F xR xL

2 d()


1 z0

2 1

1

x xR 13 x f x dx

z0

fxR xL

2 xR xR d


xR R

RE xR 0




xR

z0 0


1

1 1

1




2 1

1 11 (t TR) z(2(ta))


1 11 (a AR) z(2(ta))



TR R

REtR

AR R

REaR

where

R 1

1 1

1

13ta fta dt da 01


EtR 1

R

1

1 1

1

t13ta fta dt da 0

EaR 1

R

1

1 1

1

a13ta fta dt da 0


TR AR N EtR EaR




R 1

1 t

1

fta da dt 1

1

FAt fTt dt 12

and

EtR 2 1

1

t t

1

fAa dafTt dt 2 1

1

tFAt fTt dt

2 0

1

tfTt2FAt 1 dt 0Et





TR 0

AR 1

1 F

1

afAa da 0




AR

fA

1 FA2

1

afA(a) da

1 FA()

so that

AR

0 0


1

1

FAa da

1



and indeed

1 FA 0

1 FA 0


xR R

RE xR and xL

L

LE xL




x R xR

Ex xL xL



REFERENCES










































c Vx xL xR




MxiP xi xi

P xi 2









R and xiL will


L) ( xiR)2 ( xi


R 0 xiL then





















ta TR TL t TL TR

2 1 AR ALa

AL AR

2


























JPx i1

n

ix iP xi 2 with

i1

n

i 1

























UPx G i1

n

iLxi xi 1 i1

n

iLxi xiP

where i1

n

i 1






x xP 1 xP














































(1) (2) (3) (4) (5) (6)


01639 00301(00149) (00334)


08215 07965 07748 08321 11488(02105) (01933) (03305) (01761) (03028)


09135 08876 08138 07673 15635(02385) (02140) (04103) (01923) (03255)


13176(04395)



04497 04487 04760 05423 03674(00262) (00228) (00579) (00537) (00549)
































(1) (2) (3) (4) (5)



04888 04214 02698 02279(01139) (01169) (01393) (02087)


05804(02552)




















(1) (2) (3) (4) (5)


01237 02676(00115) (00685)


02954 03419 02841 03820(01402) (01464) (01336) (01756)


07509(04381)







VI CONCLUSION









APPENDIX


1

1

Z2( xR xL)x xR xL

2 Z2( xR xL)x

xR xL

2 d fx dx


1

1

2 x xR

z2 ( xR xL)x xR xL

2 xR xR d f x dx



xR 1

1 x13 x f x dx 1

1 13 x f x dx

Notice that

R 1

1

13 x f x dx 01


E xR 1

R

1

1

x13 x f x dtx E x 0




Therefore

xR R

RE xR



xR

R

R2 E xR 0


xR

R

R2 ExR 0


xR

R

R2 E xR 0


xR

E xR

R

R 0


xR

Ex





1 z0

2 1

1

xR xLx xR xL

2 d f x dx

z01 2

F xR xL

2 d()


1 z0

2 1

1

x xR 13 x f x dx

z0

fxR xL

2 xR xR d


xR R

RE xR 0




xR

z0 0


1

1 1

1




2 1

1 11 (t TR) z(2(ta))


1 11 (a AR) z(2(ta))



TR R

REtR

AR R

REaR

where

R 1

1 1

1

13ta fta dt da 01


EtR 1

R

1

1 1

1

t13ta fta dt da 0

EaR 1

R

1

1 1

1

a13ta fta dt da 0


TR AR N EtR EaR




R 1

1 t

1

fta da dt 1

1

FAt fTt dt 12

and

EtR 2 1

1

t t

1

fAa dafTt dt 2 1

1

tFAt fTt dt

2 0

1

tfTt2FAt 1 dt 0Et





TR 0

AR 1

1 F

1

afAa da 0




AR

fA

1 FA2

1

afA(a) da

1 FA()

so that

AR

0 0


1

1

FAa da

1



and indeed

1 FA 0

1 FA 0


xR R

RE xR and xL

L

LE xL




x R xR

Ex xL xL



REFERENCES











































R and xiL will


L) ( xiR)2 ( xi


R 0 xiL then





















ta TR TL t TL TR

2 1 AR ALa

AL AR

2


























JPx i1

n

ix iP xi 2 with

i1

n

i 1

























UPx G i1

n

iLxi xi 1 i1

n

iLxi xiP

where i1

n

i 1






x xP 1 xP














































(1) (2) (3) (4) (5) (6)


01639 00301(00149) (00334)


08215 07965 07748 08321 11488(02105) (01933) (03305) (01761) (03028)


09135 08876 08138 07673 15635(02385) (02140) (04103) (01923) (03255)


13176(04395)



04497 04487 04760 05423 03674(00262) (00228) (00579) (00537) (00549)
































(1) (2) (3) (4) (5)



04888 04214 02698 02279(01139) (01169) (01393) (02087)


05804(02552)




















(1) (2) (3) (4) (5)


01237 02676(00115) (00685)


02954 03419 02841 03820(01402) (01464) (01336) (01756)


07509(04381)







VI CONCLUSION









APPENDIX


1

1

Z2( xR xL)x xR xL

2 Z2( xR xL)x

xR xL

2 d fx dx


1

1

2 x xR

z2 ( xR xL)x xR xL

2 xR xR d f x dx



xR 1

1 x13 x f x dx 1

1 13 x f x dx

Notice that

R 1

1

13 x f x dx 01


E xR 1

R

1

1

x13 x f x dtx E x 0




Therefore

xR R

RE xR



xR

R

R2 E xR 0


xR

R

R2 ExR 0


xR

R

R2 E xR 0


xR

E xR

R

R 0


xR

Ex





1 z0

2 1

1

xR xLx xR xL

2 d f x dx

z01 2

F xR xL

2 d()


1 z0

2 1

1

x xR 13 x f x dx

z0

fxR xL

2 xR xR d


xR R

RE xR 0




xR

z0 0


1

1 1

1




2 1

1 11 (t TR) z(2(ta))


1 11 (a AR) z(2(ta))



TR R

REtR

AR R

REaR

where

R 1

1 1

1

13ta fta dt da 01


EtR 1

R

1

1 1

1

t13ta fta dt da 0

EaR 1

R

1

1 1

1

a13ta fta dt da 0


TR AR N EtR EaR




R 1

1 t

1

fta da dt 1

1

FAt fTt dt 12

and

EtR 2 1

1

t t

1

fAa dafTt dt 2 1

1

tFAt fTt dt

2 0

1

tfTt2FAt 1 dt 0Et





TR 0

AR 1

1 F

1

afAa da 0




AR

fA

1 FA2

1

afA(a) da

1 FA()

so that

AR

0 0


1

1

FAa da

1



and indeed

1 FA 0

1 FA 0


xR R

RE xR and xL

L

LE xL




x R xR

Ex xL xL



REFERENCES























































ta TR TL t TL TR

2 1 AR ALa

AL AR

2


























JPx i1

n

ix iP xi 2 with

i1

n

i 1

























UPx G i1

n

iLxi xi 1 i1

n

iLxi xiP

where i1

n

i 1






x xP 1 xP














































(1) (2) (3) (4) (5) (6)


01639 00301(00149) (00334)


08215 07965 07748 08321 11488(02105) (01933) (03305) (01761) (03028)


09135 08876 08138 07673 15635(02385) (02140) (04103) (01923) (03255)


13176(04395)



04497 04487 04760 05423 03674(00262) (00228) (00579) (00537) (00549)
































(1) (2) (3) (4) (5)



04888 04214 02698 02279(01139) (01169) (01393) (02087)


05804(02552)




















(1) (2) (3) (4) (5)


01237 02676(00115) (00685)


02954 03419 02841 03820(01402) (01464) (01336) (01756)


07509(04381)







VI CONCLUSION









APPENDIX


1

1

Z2( xR xL)x xR xL

2 Z2( xR xL)x

xR xL

2 d fx dx


1

1

2 x xR

z2 ( xR xL)x xR xL

2 xR xR d f x dx



xR 1

1 x13 x f x dx 1

1 13 x f x dx

Notice that

R 1

1

13 x f x dx 01


E xR 1

R

1

1

x13 x f x dtx E x 0




Therefore

xR R

RE xR



xR

R

R2 E xR 0


xR

R

R2 ExR 0


xR

R

R2 E xR 0


xR

E xR

R

R 0


xR

Ex





1 z0

2 1

1

xR xLx xR xL

2 d f x dx

z01 2

F xR xL

2 d()


1 z0

2 1

1

x xR 13 x f x dx

z0

fxR xL

2 xR xR d


xR R

RE xR 0




xR

z0 0


1

1 1

1




2 1

1 11 (t TR) z(2(ta))


1 11 (a AR) z(2(ta))



TR R

REtR

AR R

REaR

where

R 1

1 1

1

13ta fta dt da 01


EtR 1

R

1

1 1

1

t13ta fta dt da 0

EaR 1

R

1

1 1

1

a13ta fta dt da 0


TR AR N EtR EaR




R 1

1 t

1

fta da dt 1

1

FAt fTt dt 12

and

EtR 2 1

1

t t

1

fAa dafTt dt 2 1

1

tFAt fTt dt

2 0

1

tfTt2FAt 1 dt 0Et





TR 0

AR 1

1 F

1

afAa da 0




AR

fA

1 FA2

1

afA(a) da

1 FA()

so that

AR

0 0


1

1

FAa da

1



and indeed

1 FA 0

1 FA 0


xR R

RE xR and xL

L

LE xL




x R xR

Ex xL xL



REFERENCES
































































JPx i1

n

ix iP xi 2 with

i1

n

i 1

























UPx G i1

n

iLxi xi 1 i1

n

iLxi xiP

where i1

n

i 1






x xP 1 xP














































(1) (2) (3) (4) (5) (6)


01639 00301(00149) (00334)


08215 07965 07748 08321 11488(02105) (01933) (03305) (01761) (03028)


09135 08876 08138 07673 15635(02385) (02140) (04103) (01923) (03255)


13176(04395)



04497 04487 04760 05423 03674(00262) (00228) (00579) (00537) (00549)
































(1) (2) (3) (4) (5)



04888 04214 02698 02279(01139) (01169) (01393) (02087)


05804(02552)




















(1) (2) (3) (4) (5)


01237 02676(00115) (00685)


02954 03419 02841 03820(01402) (01464) (01336) (01756)


07509(04381)







VI CONCLUSION









APPENDIX


1

1

Z2( xR xL)x xR xL

2 Z2( xR xL)x

xR xL

2 d fx dx


1

1

2 x xR

z2 ( xR xL)x xR xL

2 xR xR d f x dx



xR 1

1 x13 x f x dx 1

1 13 x f x dx

Notice that

R 1

1

13 x f x dx 01


E xR 1

R

1

1

x13 x f x dtx E x 0




Therefore

xR R

RE xR



xR

R

R2 E xR 0


xR

R

R2 ExR 0


xR

R

R2 E xR 0


xR

E xR

R

R 0


xR

Ex





1 z0

2 1

1

xR xLx xR xL

2 d f x dx

z01 2

F xR xL

2 d()


1 z0

2 1

1

x xR 13 x f x dx

z0

fxR xL

2 xR xR d


xR R

RE xR 0




xR

z0 0


1

1 1

1




2 1

1 11 (t TR) z(2(ta))


1 11 (a AR) z(2(ta))



TR R

REtR

AR R

REaR

where

R 1

1 1

1

13ta fta dt da 01


EtR 1

R

1

1 1

1

t13ta fta dt da 0

EaR 1

R

1

1 1

1

a13ta fta dt da 0


TR AR N EtR EaR




R 1

1 t

1

fta da dt 1

1

FAt fTt dt 12

and

EtR 2 1

1

t t

1

fAa dafTt dt 2 1

1

tFAt fTt dt

2 0

1

tfTt2FAt 1 dt 0Et





TR 0

AR 1

1 F

1

afAa da 0




AR

fA

1 FA2

1

afA(a) da

1 FA()

so that

AR

0 0


1

1

FAa da

1



and indeed

1 FA 0

1 FA 0


xR R

RE xR and xL

L

LE xL




x R xR

Ex xL xL



REFERENCES































































UPx G i1

n

iLxi xi 1 i1

n

iLxi xiP

where i1

n

i 1






x xP 1 xP














































(1) (2) (3) (4) (5) (6)


01639 00301(00149) (00334)


08215 07965 07748 08321 11488(02105) (01933) (03305) (01761) (03028)


09135 08876 08138 07673 15635(02385) (02140) (04103) (01923) (03255)


13176(04395)



04497 04487 04760 05423 03674(00262) (00228) (00579) (00537) (00549)
































(1) (2) (3) (4) (5)



04888 04214 02698 02279(01139) (01169) (01393) (02087)


05804(02552)




















(1) (2) (3) (4) (5)


01237 02676(00115) (00685)


02954 03419 02841 03820(01402) (01464) (01336) (01756)


07509(04381)







VI CONCLUSION









APPENDIX


1

1

Z2( xR xL)x xR xL

2 Z2( xR xL)x

xR xL

2 d fx dx


1

1

2 x xR

z2 ( xR xL)x xR xL

2 xR xR d f x dx



xR 1

1 x13 x f x dx 1

1 13 x f x dx

Notice that

R 1

1

13 x f x dx 01


E xR 1

R

1

1

x13 x f x dtx E x 0




Therefore

xR R

RE xR



xR

R

R2 E xR 0


xR

R

R2 ExR 0


xR

R

R2 E xR 0


xR

E xR

R

R 0


xR

Ex





1 z0

2 1

1

xR xLx xR xL

2 d f x dx

z01 2

F xR xL

2 d()


1 z0

2 1

1

x xR 13 x f x dx

z0

fxR xL

2 xR xR d


xR R

RE xR 0




xR

z0 0


1

1 1

1




2 1

1 11 (t TR) z(2(ta))


1 11 (a AR) z(2(ta))



TR R

REtR

AR R

REaR

where

R 1

1 1

1

13ta fta dt da 01


EtR 1

R

1

1 1

1

t13ta fta dt da 0

EaR 1

R

1

1 1

1

a13ta fta dt da 0


TR AR N EtR EaR




R 1

1 t

1

fta da dt 1

1

FAt fTt dt 12

and

EtR 2 1

1

t t

1

fAa dafTt dt 2 1

1

tFAt fTt dt

2 0

1

tfTt2FAt 1 dt 0Et





TR 0

AR 1

1 F

1

afAa da 0




AR

fA

1 FA2

1

afA(a) da

1 FA()

so that

AR

0 0


1

1

FAa da

1



and indeed

1 FA 0

1 FA 0


xR R

RE xR and xL

L

LE xL




x R xR

Ex xL xL



REFERENCES












































x xP 1 xP














































(1) (2) (3) (4) (5) (6)


01639 00301(00149) (00334)


08215 07965 07748 08321 11488(02105) (01933) (03305) (01761) (03028)


09135 08876 08138 07673 15635(02385) (02140) (04103) (01923) (03255)


13176(04395)



04497 04487 04760 05423 03674(00262) (00228) (00579) (00537) (00549)
































(1) (2) (3) (4) (5)



04888 04214 02698 02279(01139) (01169) (01393) (02087)


05804(02552)




















(1) (2) (3) (4) (5)


01237 02676(00115) (00685)


02954 03419 02841 03820(01402) (01464) (01336) (01756)


07509(04381)







VI CONCLUSION









APPENDIX


1

1

Z2( xR xL)x xR xL

2 Z2( xR xL)x

xR xL

2 d fx dx


1

1

2 x xR

z2 ( xR xL)x xR xL

2 xR xR d f x dx



xR 1

1 x13 x f x dx 1

1 13 x f x dx

Notice that

R 1

1

13 x f x dx 01


E xR 1

R

1

1

x13 x f x dtx E x 0




Therefore

xR R

RE xR



xR

R

R2 E xR 0


xR

R

R2 ExR 0


xR

R

R2 E xR 0


xR

E xR

R

R 0


xR

Ex





1 z0

2 1

1

xR xLx xR xL

2 d f x dx

z01 2

F xR xL

2 d()


1 z0

2 1

1

x xR 13 x f x dx

z0

fxR xL

2 xR xR d


xR R

RE xR 0




xR

z0 0


1

1 1

1




2 1

1 11 (t TR) z(2(ta))


1 11 (a AR) z(2(ta))



TR R

REtR

AR R

REaR

where

R 1

1 1

1

13ta fta dt da 01


EtR 1

R

1

1 1

1

t13ta fta dt da 0

EaR 1

R

1

1 1

1

a13ta fta dt da 0


TR AR N EtR EaR




R 1

1 t

1

fta da dt 1

1

FAt fTt dt 12

and

EtR 2 1

1

t t

1

fAa dafTt dt 2 1

1

tFAt fTt dt

2 0

1

tfTt2FAt 1 dt 0Et





TR 0

AR 1

1 F

1

afAa da 0




AR

fA

1 FA2

1

afA(a) da

1 FA()

so that

AR

0 0


1

1

FAa da

1



and indeed

1 FA 0

1 FA 0


xR R

RE xR and xL

L

LE xL




x R xR

Ex xL xL



REFERENCES


















































































(1) (2) (3) (4) (5) (6)


01639 00301(00149) (00334)


08215 07965 07748 08321 11488(02105) (01933) (03305) (01761) (03028)


09135 08876 08138 07673 15635(02385) (02140) (04103) (01923) (03255)


13176(04395)



04497 04487 04760 05423 03674(00262) (00228) (00579) (00537) (00549)
































(1) (2) (3) (4) (5)



04888 04214 02698 02279(01139) (01169) (01393) (02087)


05804(02552)




















(1) (2) (3) (4) (5)


01237 02676(00115) (00685)


02954 03419 02841 03820(01402) (01464) (01336) (01756)


07509(04381)







VI CONCLUSION









APPENDIX


1

1

Z2( xR xL)x xR xL

2 Z2( xR xL)x

xR xL

2 d fx dx


1

1

2 x xR

z2 ( xR xL)x xR xL

2 xR xR d f x dx



xR 1

1 x13 x f x dx 1

1 13 x f x dx

Notice that

R 1

1

13 x f x dx 01


E xR 1

R

1

1

x13 x f x dtx E x 0




Therefore

xR R

RE xR



xR

R

R2 E xR 0


xR

R

R2 ExR 0


xR

R

R2 E xR 0


xR

E xR

R

R 0


xR

Ex





1 z0

2 1

1

xR xLx xR xL

2 d f x dx

z01 2

F xR xL

2 d()


1 z0

2 1

1

x xR 13 x f x dx

z0

fxR xL

2 xR xR d


xR R

RE xR 0




xR

z0 0


1

1 1

1




2 1

1 11 (t TR) z(2(ta))


1 11 (a AR) z(2(ta))



TR R

REtR

AR R

REaR

where

R 1

1 1

1

13ta fta dt da 01


EtR 1

R

1

1 1

1

t13ta fta dt da 0

EaR 1

R

1

1 1

1

a13ta fta dt da 0


TR AR N EtR EaR




R 1

1 t

1

fta da dt 1

1

FAt fTt dt 12

and

EtR 2 1

1

t t

1

fAa dafTt dt 2 1

1

tFAt fTt dt

2 0

1

tfTt2FAt 1 dt 0Et





TR 0

AR 1

1 F

1

afAa da 0




AR

fA

1 FA2

1

afA(a) da

1 FA()

so that

AR

0 0


1

1

FAa da

1



and indeed

1 FA 0

1 FA 0


xR R

RE xR and xL

L

LE xL




x R xR

Ex xL xL



REFERENCES





































































(1) (2) (3) (4) (5)



04888 04214 02698 02279(01139) (01169) (01393) (02087)


05804(02552)




















(1) (2) (3) (4) (5)


01237 02676(00115) (00685)


02954 03419 02841 03820(01402) (01464) (01336) (01756)


07509(04381)







VI CONCLUSION









APPENDIX


1

1

Z2( xR xL)x xR xL

2 Z2( xR xL)x

xR xL

2 d fx dx


1

1

2 x xR

z2 ( xR xL)x xR xL

2 xR xR d f x dx



xR 1

1 x13 x f x dx 1

1 13 x f x dx

Notice that

R 1

1

13 x f x dx 01


E xR 1

R

1

1

x13 x f x dtx E x 0




Therefore

xR R

RE xR



xR

R

R2 E xR 0


xR

R

R2 ExR 0


xR

R

R2 E xR 0


xR

E xR

R

R 0


xR

Ex





1 z0

2 1

1

xR xLx xR xL

2 d f x dx

z01 2

F xR xL

2 d()


1 z0

2 1

1

x xR 13 x f x dx

z0

fxR xL

2 xR xR d


xR R

RE xR 0




xR

z0 0


1

1 1

1




2 1

1 11 (t TR) z(2(ta))


1 11 (a AR) z(2(ta))



TR R

REtR

AR R

REaR

where

R 1

1 1

1

13ta fta dt da 01


EtR 1

R

1

1 1

1

t13ta fta dt da 0

EaR 1

R

1

1 1

1

a13ta fta dt da 0


TR AR N EtR EaR




R 1

1 t

1

fta da dt 1

1

FAt fTt dt 12

and

EtR 2 1

1

t t

1

fAa dafTt dt 2 1

1

tFAt fTt dt

2 0

1

tfTt2FAt 1 dt 0Et





TR 0

AR 1

1 F

1

afAa da 0




AR

fA

1 FA2

1

afA(a) da

1 FA()

so that

AR

0 0


1

1

FAa da

1



and indeed

1 FA 0

1 FA 0


xR R

RE xR and xL

L

LE xL




x R xR

Ex xL xL



REFERENCES

























































(1) (2) (3) (4) (5)


01237 02676(00115) (00685)


02954 03419 02841 03820(01402) (01464) (01336) (01756)


07509(04381)







VI CONCLUSION









APPENDIX


1

1

Z2( xR xL)x xR xL

2 Z2( xR xL)x

xR xL

2 d fx dx


1

1

2 x xR

z2 ( xR xL)x xR xL

2 xR xR d f x dx



xR 1

1 x13 x f x dx 1

1 13 x f x dx

Notice that

R 1

1

13 x f x dx 01


E xR 1

R

1

1

x13 x f x dtx E x 0




Therefore

xR R

RE xR



xR

R

R2 E xR 0


xR

R

R2 ExR 0


xR

R

R2 E xR 0


xR

E xR

R

R 0


xR

Ex





1 z0

2 1

1

xR xLx xR xL

2 d f x dx

z01 2

F xR xL

2 d()


1 z0

2 1

1

x xR 13 x f x dx

z0

fxR xL

2 xR xR d


xR R

RE xR 0




xR

z0 0


1

1 1

1




2 1

1 11 (t TR) z(2(ta))


1 11 (a AR) z(2(ta))



TR R

REtR

AR R

REaR

where

R 1

1 1

1

13ta fta dt da 01


EtR 1

R

1

1 1

1

t13ta fta dt da 0

EaR 1

R

1

1 1

1

a13ta fta dt da 0


TR AR N EtR EaR




R 1

1 t

1

fta da dt 1

1

FAt fTt dt 12

and

EtR 2 1

1

t t

1

fAa dafTt dt 2 1

1

tFAt fTt dt

2 0

1

tfTt2FAt 1 dt 0Et





TR 0

AR 1

1 F

1

afAa da 0




AR

fA

1 FA2

1

afA(a) da

1 FA()

so that

AR

0 0


1

1

FAa da

1



and indeed

1 FA 0

1 FA 0


xR R

RE xR and xL

L

LE xL




x R xR

Ex xL xL



REFERENCES












































VI CONCLUSION









APPENDIX


1

1

Z2( xR xL)x xR xL

2 Z2( xR xL)x

xR xL

2 d fx dx


1

1

2 x xR

z2 ( xR xL)x xR xL

2 xR xR d f x dx



xR 1

1 x13 x f x dx 1

1 13 x f x dx

Notice that

R 1

1

13 x f x dx 01


E xR 1

R

1

1

x13 x f x dtx E x 0




Therefore

xR R

RE xR



xR

R

R2 E xR 0


xR

R

R2 ExR 0


xR

R

R2 E xR 0


xR

E xR

R

R 0


xR

Ex





1 z0

2 1

1

xR xLx xR xL

2 d f x dx

z01 2

F xR xL

2 d()


1 z0

2 1

1

x xR 13 x f x dx

z0

fxR xL

2 xR xR d


xR R

RE xR 0




xR

z0 0


1

1 1

1




2 1

1 11 (t TR) z(2(ta))


1 11 (a AR) z(2(ta))



TR R

REtR

AR R

REaR

where

R 1

1 1

1

13ta fta dt da 01


EtR 1

R

1

1 1

1

t13ta fta dt da 0

EaR 1

R

1

1 1

1

a13ta fta dt da 0


TR AR N EtR EaR




R 1

1 t

1

fta da dt 1

1

FAt fTt dt 12

and

EtR 2 1

1

t t

1

fAa dafTt dt 2 1

1

tFAt fTt dt

2 0

1

tfTt2FAt 1 dt 0Et





TR 0

AR 1

1 F

1

afAa da 0




AR

fA

1 FA2

1

afA(a) da

1 FA()

so that

AR

0 0


1

1

FAa da

1



and indeed

1 FA 0

1 FA 0


xR R

RE xR and xL

L

LE xL




x R xR

Ex xL xL



REFERENCES













































APPENDIX


1

1

Z2( xR xL)x xR xL

2 Z2( xR xL)x

xR xL

2 d fx dx


1

1

2 x xR

z2 ( xR xL)x xR xL

2 xR xR d f x dx



xR 1

1 x13 x f x dx 1

1 13 x f x dx

Notice that

R 1

1

13 x f x dx 01


E xR 1

R

1

1

x13 x f x dtx E x 0




Therefore

xR R

RE xR



xR

R

R2 E xR 0


xR

R

R2 ExR 0


xR

R

R2 E xR 0


xR

E xR

R

R 0


xR

Ex





1 z0

2 1

1

xR xLx xR xL

2 d f x dx

z01 2

F xR xL

2 d()


1 z0

2 1

1

x xR 13 x f x dx

z0

fxR xL

2 xR xR d


xR R

RE xR 0




xR

z0 0


1

1 1

1




2 1

1 11 (t TR) z(2(ta))


1 11 (a AR) z(2(ta))



TR R

REtR

AR R

REaR

where

R 1

1 1

1

13ta fta dt da 01


EtR 1

R

1

1 1

1

t13ta fta dt da 0

EaR 1

R

1

1 1

1

a13ta fta dt da 0


TR AR N EtR EaR




R 1

1 t

1

fta da dt 1

1

FAt fTt dt 12

and

EtR 2 1

1

t t

1

fAa dafTt dt 2 1

1

tFAt fTt dt

2 0

1

tfTt2FAt 1 dt 0Et





TR 0

AR 1

1 F

1

afAa da 0




AR

fA

1 FA2

1

afA(a) da

1 FA()

so that

AR

0 0


1

1

FAa da

1



and indeed

1 FA 0

1 FA 0


xR R

RE xR and xL

L

LE xL




x R xR

Ex xL xL



REFERENCES










































Therefore

xR R

RE xR



xR

R

R2 E xR 0


xR

R

R2 ExR 0


xR

R

R2 E xR 0


xR

E xR

R

R 0


xR

Ex





1 z0

2 1

1

xR xLx xR xL

2 d f x dx

z01 2

F xR xL

2 d()


1 z0

2 1

1

x xR 13 x f x dx

z0

fxR xL

2 xR xR d


xR R

RE xR 0




xR

z0 0


1

1 1

1




2 1

1 11 (t TR) z(2(ta))


1 11 (a AR) z(2(ta))



TR R

REtR

AR R

REaR

where

R 1

1 1

1

13ta fta dt da 01


EtR 1

R

1

1 1

1

t13ta fta dt da 0

EaR 1

R

1

1 1

1

a13ta fta dt da 0


TR AR N EtR EaR




R 1

1 t

1

fta da dt 1

1

FAt fTt dt 12

and

EtR 2 1

1

t t

1

fAa dafTt dt 2 1

1

tFAt fTt dt

2 0

1

tfTt2FAt 1 dt 0Et





TR 0

AR 1

1 F

1

afAa da 0




AR

fA

1 FA2

1

afA(a) da

1 FA()

so that

AR

0 0


1

1

FAa da

1



and indeed

1 FA 0

1 FA 0


xR R

RE xR and xL

L

LE xL




x R xR

Ex xL xL



REFERENCES










































1 z0

2 1

1

xR xLx xR xL

2 d f x dx

z01 2

F xR xL

2 d()


1 z0

2 1

1

x xR 13 x f x dx

z0

fxR xL

2 xR xR d


xR R

RE xR 0




xR

z0 0


1

1 1

1




2 1

1 11 (t TR) z(2(ta))


1 11 (a AR) z(2(ta))



TR R

REtR

AR R

REaR

where

R 1

1 1

1

13ta fta dt da 01


EtR 1

R

1

1 1

1

t13ta fta dt da 0

EaR 1

R

1

1 1

1

a13ta fta dt da 0


TR AR N EtR EaR




R 1

1 t

1

fta da dt 1

1

FAt fTt dt 12

and

EtR 2 1

1

t t

1

fAa dafTt dt 2 1

1

tFAt fTt dt

2 0

1

tfTt2FAt 1 dt 0Et





TR 0

AR 1

1 F

1

afAa da 0




AR

fA

1 FA2

1

afA(a) da

1 FA()

so that

AR

0 0


1

1

FAa da

1



and indeed

1 FA 0

1 FA 0


xR R

RE xR and xL

L

LE xL




x R xR

Ex xL xL



REFERENCES










































2 1

1 11 (t TR) z(2(ta))


1 11 (a AR) z(2(ta))



TR R

REtR

AR R

REaR

where

R 1

1 1

1

13ta fta dt da 01


EtR 1

R

1

1 1

1

t13ta fta dt da 0

EaR 1

R

1

1 1

1

a13ta fta dt da 0


TR AR N EtR EaR




R 1

1 t

1

fta da dt 1

1

FAt fTt dt 12

and

EtR 2 1

1

t t

1

fAa dafTt dt 2 1

1

tFAt fTt dt

2 0

1

tfTt2FAt 1 dt 0Et





TR 0

AR 1

1 F

1

afAa da 0




AR

fA

1 FA2

1

afA(a) da

1 FA()

so that

AR

0 0


1

1

FAa da

1



and indeed

1 FA 0

1 FA 0


xR R

RE xR and xL

L

LE xL




x R xR

Ex xL xL



REFERENCES











































R 1

1 t

1

fta da dt 1

1

FAt fTt dt 12

and

EtR 2 1

1

t t

1

fAa dafTt dt 2 1

1

tFAt fTt dt

2 0

1

tfTt2FAt 1 dt 0Et





TR 0

AR 1

1 F

1

afAa da 0




AR

fA

1 FA2

1

afA(a) da

1 FA()

so that

AR

0 0


1

1

FAa da

1



and indeed

1 FA 0

1 FA 0


xR R

RE xR and xL

L

LE xL




x R xR

Ex xL xL



REFERENCES










































AR

fA

1 FA2

1

afA(a) da

1 FA()

so that

AR

0 0


1

1

FAa da

1



and indeed

1 FA 0

1 FA 0


xR R

RE xR and xL

L

LE xL




x R xR

Ex xL xL



REFERENCES










































x R xR

Ex xL xL



REFERENCES









































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