THE POLITICAL ECONOMY OFEXTREMISM AND MODERATION

Robert Grafstein

Department of Political Science

University of Georgia

Athens, GA 30602

bobgraf@uga.edu

770.570.8756 (phone) 706.583.0095 (fax)

Abstract

This paper offers a unified political economic explanation of ideological extremismand its complement, moderation. It is unified in the sense that all politicalpreferences are assumed to be rooted in the same fundamental economic preferences,which exhibit nonsatiation. Modern political economy’s understanding of democracyimplicitly limits this "extremism" by imposing exogenous restrictions on the degree ofredistribution self-interested voters can choose. Like the standard spatial model ofvoting generally, it also assumes that ideological location, not "intensity," is all thatdistinguishes moderates and extremists. This paper endogenizes both politicalmoderation and extremism by analyzing democratic voting within an NTUbargaining model based on Aumann and Kurz (1977). The bargaining modelemphasizes the balance of power and threats limiting the extremism of individualsand winning coalitions. It shows why voters with standard utility functions who havevery low or very high incomes are more likely to be political extremists, in the formercase by being bolder in their redistributive demands, in the latter case by being moretenacious in defending their wealth. The model also implies that income changesinduce behavior that is more intense or extremist.

Paper presented at the 7th ECPR General Conference, September 4-7, 2013,Bordeaux, France. I thank Robert Cooper, Keith Dougherty, Gregory Martin, KeithPoole, Joel Simmons, Andrei Zhimov, and members of the audience at the ChineseForeign Affairs University for helpful comments concerning an earlier version of thispaper. The usual absolution applies.

THE POLITICAL ECONOMY OF EXTREMISM AND MODERATION

1 Introduction

What drives ideological extremism in democratic societies? Equally important, when

does the resulting ideological polarization become politically dysfunctional? This paper

offers a unified political economic explanation of ideological extremism and its complement,

moderation. It is unified in the sense that all political preferences are assumed to be rooted

in the same fundamental economic preferences. Extremists are not special types. They are

made, not born. The explanation itself is anchored in Aumann and Kurz’s (1977)

majority-rule bargaining model in which a winning coalition determines the allocation of

society’s total income subject to competing threats and counteroffers from other coalitions.

This framework is used to model the impact of income inequality on ideological

polarization. Unlike other research on extremism, this model explains not only the role of

inequality in creating ideological separation but also why polarized voters at both ends of

the income distribution are more likely to adopt an “extremist”style that inhibits

compromise.

In contrast to the approach taken here, the standard unidimensional spatial model of

voting (e.g., Downs 1957) is not burdened (or enriched) by a commitment to providing

substantive microfoundations for voter preferences. Spatial theory is self-contained,

concentrating on the political consequences of political preferences. According to spatial

analysis, extremists and centrists occupy different locations on an ideological interval.

Extremists stake out the ends of the interval, centrists the middle. Political polarization

occurs when the distribution of political ideal points is fat tailed or, in the extreme case,

bimodal. In all other respects the standard spatial model’s representation of ideology is

homogeneous and therefore surprisingly apolitical. Any and all points on the continuum

1

represent ideologies or ideological positions, and any and all voters are ideological.

Viewed without the blinders of the standard model, however, political extremists seem

to be differentiated from moderates by more than their ideal points. They express and

implement their ideals in distinctive ways compared to run-of-the-mill centrists. As Poole

(2007, 437) notes regarding legislative voting, "The further a legislator is from the center of

the space, the more intense the belief." Those who rely on the standard model tend to

ignore the special ideological intensity extremists introduce into politics. There are

important exceptions such as Rabushka and Shepsle (1972) which will be addressed below.

But overwhelmingly extremism in the standard spatial model is simply a matter of

location, location, location.

So the standard spatial model’s unburdening from microfoundations comes at a price:

its positional understanding of extremism fails to explain the apparent link between

ideological location and political style. The unified explanation presented here

accomplishes this without introducing ad hoc assumptions about extremist personalities.

The advantage of avoiding ad hoc assumptions is partially offset by the explanation’s

fairly narrow economic interpretation of voter preferences. The economic interpretation is a

natural one since political ideology is often economically motivated (e.g., McCarty, Poole,

and Rosenthal 2006). Still, it is restrictive. Therefore I strengthen the motivation for this

approach by considering at greater length the limitations of the standard spatial model’s

alternative, location-based understanding of extremism and the associated problem of

political polarization. Before fixing it, we need to make sure it is broken.

It is also important to recognize that standard models in political economy have the

complementary problem, understanding moderation in democratic settings. Despite a

wide-ranging effort, current models do not adequately explain why majorities of

self-interested voters fail to expropriate minorities. Since the spatial model is the most

widely used framework for understanding political polarization, however, I consider

2

standard spatial theory’s limitations first.

2 Political Polarization

The term ‘polarization’is often used as shorthand for bimodal extremism. In the

spatial model, specifically, descriptive polarization arises when there is a fat tailed or

perhaps bimodal (or multimodal) distribution of political ideal points. However, the

beginning of wisdom here is to recognize that polarization in the descriptive sense does not

necessarily constitute the kind of political problem we associate with extremism. The

convergence result of the classic median voter theorem, for example, is invariant to the

distribution of voter ideal points around the median. If the theorem’s conditions are

satisfied, there is an equilibrium no matter how widely distributed the ideal points. More

important, since utility is measured only up to a positive affi ne transformation, the utility

differential between one extremist voter’s ideal point and the opposite ideal point of her

polarized counterpart provides no basis for saying that their ideal points are far apart

simpliciter. Rescaling can make the utility differential as small or as large as you choose.1

Alternative interpretations of descriptive polarization fare no better. Polarization, for

example, can be defined in terms of a widening gap between ideal points under some metric

1It is worth recalling that some of the great clashes in history, including actual bloodbaths, have

occurred within highly circumscribed ideological groups: think of internecine struggles within communism,

between socialists and communists, or the Night of the Long Knives purge in Nazi Germany (for that

matter, think of fights within families). In any case, the static notion of polarization represents a scaling

judgment. It is not substantively meaningful. This scaling issue also undercuts the idea that polarization

occurs when certain positions are outside a predefined zone of acceptance, an idea used within spatial

theory to rationalize absention due to alienation (Enelow and Hinich 1984). The same idea is associated

with the directional theory of voting (Rabinowitz and MacDonald 1989; see Iverson 1994 for criticism of

this postulate as ad hoc).

3

(e.g., Fiorina, Abrams, and Pope 2011).2 Unfortunately, recognizing the dynamic

dimension of polarization still does not tells us why polarization is a problem. Polarization

eventually leads to a polarized society. Unless the historical contrast is important to voters,

everything that was just said about the meaninglessness of the static notion of polarization

applies to societies we label ‘polarized’. At any point in time they are polarized or not

depending on the magnification of the lens used to examine them.3

The problem of polarization arises when voters with different ideal points find it

particularly diffi cult to resolve their disagreements.4 Polarization, in this view, is not an

increase in the distance between ideal points that otherwise preserves both the shapes of

utility functions and their associated behavioral implications. Something about the

distance itself, the underlying situation of those at the ideological poles, or the sorts of

people who find themselves at such extreme distances, creates political problems:

"Realistically, intensity of belief should itself be a function of the position of the legislator

in the basic space" (Poole 2007, 437).5

The idea that polarization constitutes a threat to political stability or normalcy

responds to an important intuition: those at the political extremes not only have distant

beliefs but especially intense beliefs. According to this interpretation, polarization is a

problem not simply when there is ideological distance between voters but when they

2One can also measure the polarization of parties, rather than voters, by the extent to which the ideal

points of their members do not overlap. This begs the question of why extremism as a distinctive form of

behavior is associated with distance from the center (whether or not other voters happen to overlap).3Whether the increased polarization in the U.S. is primarily an elite phenomenon (see Fiorina, Abrams,

and Pope 2011; Jacoby 2011; Abramowitz 2013) is an important empirical question, but not particularly

relevant to the theoretical issue addressed here.4Descriptive polarization does not have uniformly destabilizing consequences. It can increase political

participation and inclusion (e.g., Crepaz 1990). Of course, other typologies of polarization are possible

(e.g., Serra 2010).5

4

exhibit a psychologically rooted inability to get along politically. Polarization is created by

extremists, defined simply as the kinds of people who do not play politics well with others.

This is one intuition. But we must be careful in translating it into specific conclusions.

Intensity can easily become an ad hoc explanation, a theoretically unmotivated

psychological restatement of unexplained behavior. If it does, ‘polarization’becomes a

synonym for political fractiousness, not an explanation for it.6

It is dangerous, then, to assume that polarization simply reflects psychological

propensities. Moreover, just as spatial position by itself does not adequately explain

extremist intensity, psychological intensity by itself does not adequately explain the

association between extremist intensity and particular spatial positions. In short,

self-contained conceptions of extremism and polarization, whether spatial or psychological,

are insuffi cient. They must be anchored.

An alternative culprit when explaining extremism is institutional structure, which

mediates between polarized voters and polarized politics in the problematic sense. U.S.

institutions, for example, may magnify the impact of polarization (see, e.g., McCarty,

Poole, and Rosenthal 2006, 175-83). This in turn can generate feedback loops in which

policy under political polarization intensifies the economic conditions exacerbating

6Poole (2007, 436-37) associates the ideological melding of belief and passion with the "true believer"

personality analyzed by Hoffer (1951). Similarly, Iyengar, Sood, and Lelkes (2012) focus on affect as a

characteristic of polarization. Roemer (2001, 154-55) rationalizes the "purist" attitude of militants by

attributing to them lower discount rates: over time they hope to win over the electorate to the party’s

"true" position rather than settle for a more immediate but compromised victory. Obviously this too

represents more a characterization of extremism than an explanation. In addition, this rationalization does

not explain the association between ideological position and extremism. Finally, note that Poole and

Rosenthal’s (1997) finding that the U.S. legislature is now unidimensional, which is confirmed for the

general public by Jessee (2012; but cf. Hinich et al. 2013), suggests that extremism cannot be characterized

as a form of resistance to making tradeoffs with respect two or more dimensions.

5

extremism (Bonica, McCarty, Poole, and Rosenthal 2013). Conversely, under some

circumstances proportional representation may attenuate the impact of electoral

polarization because of the pressure to form or preserve coalitions; under other

circumstances it may increase the degree of party-system polarization (see Cox 1997;

Curini and Hino 2012).

In truth, the problem of polarization seems to arise in a variety of institutional

contexts (see, e.g., Dalton 2006), whether as part of the intense politics found in what

Rabushka and Shepsle (1972) call ‘plural societies’or in political systems characterized by

what Sartori (1976; 1994) calls ‘polarized pluralism’. Particular institutions cannot

exculpate the extremist behavior they channel. If polarized parties of the Left and Right

have been able to develop a modus vivendi within capitalist democracies notwithstanding

the enormous ideological distance separating them (Przeworski and Wallerstein 1982), it is

reasonable to ask whether properly motivated legislators with access to side-payments,

logrolling, and the like could overcome the more narrowly structured institutional

impediments found, say, in the U.S.7

Finally, since the standard spatial model has been so central to our understanding of

the impact of economic interests on politics, it is important to clarify why its technique of

isolating political preferences from substantive economic considerations makes this

understanding more diffi cult. From a political economic standpoint, voters choose both

market and public sector goods. The standard spatial model implicitly assumes that voter

utility functions are defined separately over the two sectors, with political ideology

summarizing preferences in one of them. The assumption of a separate Homo politicus

entails serious complications. For even if the underlying utility function encompassing both

types of goods is separable (roughly, utility responses to changes in one set of goods are

7An important underlying issue is the ability of actors within an institution to restructure it. See, e.g.,

McKelvey and Ordeshook (1984) and Shepsle and Weingast (1984).

6

distinct from utility responses to changes in the other set), generally the induced utility

function for those public sector goods is not separable (Denzau and Parks 1977; 1979; see

also Hinich and Munger 1994, 34-36), let alone Euclidean (Milyo 2000).8 The public sector

utility function, therefore, does not inherit the nice properties that have made it such a

workhorse in political science. This makes the spatial model’s isolated focus on political

ideology look all the more artificial.9

8Euclidean preferences and other popular assumptions about public sector preference are discussed by

Merrill and Grofman (1999). Poole and Rosenthal (2007) favor Gaussian utility functions, which likewise

are not induced from an encompassing well-behaved utility function. Hinich and Munger (1994, 115-25)

cleverly confront the separability problem by treating the policy consequences of candidate positions as the

direct source of the voter’s utility and the candidate’s ideological positions as a means to make linear

predictions of those consequences. The voter’s direct preferences, however, are assumed to be ordered by

weighted Euclidean distance. This means interior ideal points, which violate the standard nonsatiation

assumption made about market participants.9The artificial separation of voting analysis from economic interests also underpins the relativity of the

liberal-conservative ideal points assigned by standard estimation techniques (see Poole and Rosenthal

2007). To appreciate the cost of this relativity, an analogy may be helpful. Suppose, says Summers (1985),

there were two sets of researchers concerned with the economics of ketchup. Some study it within the

context of the broader economy to determine the way prices and quantities of ketchup in the market are a

function of tomato prices, wages, etc. Ketchup economists on the other hand are convinced that these

connections are too diffi cult to trace and suffer from serious measurement problems. They focus, therefore,

on what they see as the only hard data available, ketchup transactions prices. The result is an impressive

research program showing that "two quart bottles of ketchup invariably sell for twice as much as one quart

bottles of ketchup except for deviations traceable to transactions costs" (1985, 634). Yet their focus on the

relative prices of ketchup, Summers complains, leads ketchup economists to neglect the more important

question of how the general level of the ketchup price is determined. Similarly, a focus on relative

ideological positions runs the danger of neglecting economic interests that have historically given ideologies

so much of their meaning and importance.

7

Given the strong and, it turns out, heroic assumptions needed for separability, it is

tempting to treat ideological preferences as primitives. To their credit, Hinich and Munger

1994, 232) directly confront this implication: "spatial theories of political choice are not

‘economic’, and are not derivable from economic principles or reasoning." But this

treatment is particularly problematic when ideological preferences have economic

ramifications. If ideology is a primitive, how do economic interests influence political

preferences and how do economic changes cause changes in voting behavior? Answering

these questions is a central task for political economy to which we now turn.

3 The Political Economy of Moderation

The agents populating standard political economic models desire greater and greater

wealth (e.g., Milyo 2000, 287 note 7). To be fair, Homo economicus values wealth only as a

means to increase her consumption, so she is no Scrooge. But her material horizons are

effectively limitless.10 A central challenge facing any economic theory of democracy, then,

is to explain how policy moderation emerges from voters who, in terms of their ideal

points, are economic extremists (see, e.g., Coram 2008).

What happens, in particular, when Homo economicus leaves the market in order to

vote on redistributive taxes? In one sense, what happens according to modern political

economy (e.g., Meltzer and Richard 1981) is just what you would expect. Tax preferences

track income. The poorest voters prefer the tax rate yielding maximum redistribution,

higher income voters prefer lower tax rates, and the richest prefer no redistribution. But

10Strictly speaking, the real issue, we will see, is not nonsatiation (technically, local nonsatiation) but

the assumption that ideal points transcend the aggregate budget. By the same token, those tempted to

dismiss the assumption of infinite financial optima should explain exactly what the finite optimum value is,

the specific value beyond which decision makers would not want one penny more. For evidence in favor of

nonsatiation see Stevenson and Wolfers (2013).

8

because a proportional tax is economically ineffi cient there is an interior solution to the

median income voter’s choice of an optimal rate even when the median voter has

below-average income. Thus the policy determined by this decisive median voter produces

neither complete expropriation nor laissez-faire.11 Political moderation prevails despite

Homo economicus.

When the same story is told in terms of ideology, the lesson from the discussion of

spatial polarization applies. First the translation: the preference for a 0% tax rate is

naturally interpreted as extreme libertarian or anarchist (right-wing extremist), the

preference for a 100% tax rate as socialist (left-wing extremist), and preferences for tax

rates in-between as more moderate positions. In this context, ideological extremism is

entirely a matter of tax preference and, in turn, income. Extremists vote for their preferred

tax and moderates vote for theirs. Otherwise there is no difference between the two types.

The relative intensity of extremists, in other words, plays no role in this analysis. The

median voter is still decisive.

Voters in the canonical political economy model exhibit another kind of political

moderation, but this one is imposed on them. In the canonical model tax revenues are

distributed in equal lump-sum amounts. A winning coalition, therefore, cannot express a

preference for the complete expropriation of the minority’s income even when no effi ciency

losses are involved. Within a model ostensibly focused on self-interested transfers, the most

extreme lower income voter votes merely to share total tax revenue equally with her fellow

11There are many other economic explanations for policy moderation (see Putterman 1997). Bénabou

and Ok (2001), for example, argue that income mobility inhibits the long-term redistributive preferences of

voters with below-mean incomes. Others appeal to a "cross-cutting" noneconomic issue dimension (e.g.,

Roemer 2001). These models also incorporate the exogenous imposition of moderation discussed below.

Baron and Ferejohn (1989) do incorporate voters with increasing (risk-neutral) utility functions typically

leading to "extreme" winner-take-all outcomes, but in an institutionally specific legislative model.

9

voters, including those whom she has expropriated. Similarly the ideal for upper income

voters is to maintain the status quo distribution, not to become even richer.

Thus strong constraints on the range of political outcomes insure that the results of

redistribution are bounded by complete equality on the one end and the status quo on the

other.12 As a result, the standard analysis artificially truncates the political universe and

imposes some moderation by fiat prior to any policy determination. In markets, Homo

economicus’ extremism is constrained by her own budget. In elections, the constraint is

simply imposed on her by assumption.

And this arbitrary political constraint on Homo economicus is binding. For the

unconstrained ideal of a coalition composed of these kinds of voters is to retain all tax

revenue, not to share it with losing coalitions. This is as true for the rich as it is for the

poor: remaining whole is not the highest economic ambition of voters with above-mean

incomes.13 In short, majorities composed of voters whose day job is Homo economicus

desire to expropriate as much of the minority’s income as possible. These voters are even

more extreme than those the standard model labels "political extremists" (Roemer 2001,

73-80).

There are additional problems with the canonical model’s fiscal mechanism for

converting proportional taxes into lump-sum transfers.14 Actual redistribution is effected

12This is even true, say, in Benhabib and Przeworski (2006) who at the same time recognize the

possibility of revolts by either the poor or the rich. The restriction of voting to one dimension, tax rates,

rather than the addition of revenue distribution as a second dimension, is motivated by technical

considerations. But this restriction is a further reason to explore the bargaining model applied here.13As noted above, because Meltzer and Richard’s (1981) model recognizes effi ciency losses, complete

expropriation is precluded endogenously. But the restriction of fiscal policy to equal lump-sum

distributions limits the redistributive preferences of higher income voters: any voter with above mean

income unequivocally prefers a tax rate of zero because the proceeds must be distributed equally.14These lump-sum distributions can be interpreted as modeling pure public goods (see Milyo 2000, 277;

Roemer 2001, 13-72). This formulation precludes simple monetary transfers.

10

through a much more complex set of arrangements than seems necessary for a simple

referendum on public goods (Mueller 2003, 515-19). The resulting tax policy can produce

an elaborate allocation of burdens and benefits violating any notion of horizontal equity or

publicness (see, e.g., Steuerle 2008; Burman and Phaup 2011). More generally, the pattern

of redistribution in modern democratic governments is not necessarily unidirectional. In

principle, winning coalitions can redistribute upward, downward, from the middle to the

ends, or from the ends to the middle (see generally Ward 1961; Tullock 1971; Coram 2008;

Benhabib and Przeworski 2006; Congressional Budget Offi ce 2011; and Stigler 1970 and

Lindbeck and Weibull 1987 on Director’s Law).15 Thus there is little theoretical

justification for the standard assumption that any positive tax rate automatically

redistributes downward.

The implications are wide-ranging: we cannot presume that the winning coalition

corresponds to a clearly defined income interval, that allocations are neatly packaged

according to pre-tax income, and that after-tax income is a simple function of pre-tax

income.16 More important, modern political economy’s standard characterization of the

connection between voters’material interests and their votes fails to establish a fully

coherent connection between self-interest in the market and self-interest in the political

arena. It imposes a degree of political moderation on Homo economicus by artificially

constraining the feasible transfers. Put another way, to the extent political economy has an

explanation of political moderation it comes at the expense of an explanation of political

extremism.15Nonlinear tax schedules can produce an ends-against-the-middle redistributive outcome (Bolton and

Roland 1997, 1062).16An obvious adjustment of possible tax rates would allow negative rates and rates higher than 100%

(Przeworski 2003, 198). Negative rates, coupled with equal lump-sum taxes, imply upward redistribution,

while taxes exceeding 100% imply the taxation of wealth.

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In sum, voters’political economic calculations must be formulated to endogenize the

very different political behavior associated with both types. We cannot understand how

economic preferences map to political preferences for one segment of the ideological interval

if we do not understand the mapping over the rest of the interval. So extremism and

political polarization are not simply important contemporary political phenomena. They

represent a gaping hole in our theory of voting.

4 A Bargaining Model of Democratic Policy

If voters ultimately care only about their incomes, each wants to see total tax revenue

converted into her private property. Selfish or altruistic, she can proceed to dispense her

windfall as she sees fit, including perhaps investments in public goods she privately funds.

Judged by her ideals, then, when Homo economicus votes she still is an extremist in the

purely spatial sense of supporting extreme redistribution. Put less dramatically, if we take

the standard economic utility function seriously, ordinary self-interested voters are satisfied

only at infinity. In net effect at least, ideal points extend to the entire social product.

Voters may have to choose within a politically determined budget, but there is a difference

between constrained choice and the underlying preferences being constrained.

How does the standard economic utility function play out within a democratic setting,

by which I mean a setting in which allocations are determined by a simple voting majority

and only Homo economicus votes?17 One way to address this question without placing

arbitrary restrictions on the majority’s possible choices is to consider the kinds of threats

and counterthreats the ultimate power of the majority engenders. Following Aumann and

Kurz (1977), the situation can be described as follows.18

17Obviously this abstracts from the issue of institutional effects discussed above.18I modify Aumann and Kurz’s original model to include bargaining costs and variable states of ruin.

12

The set V of voters is taken to be a continuum, which means any one voter v has a

negligible impact on policy outcomes. Strictly speaking, a given voter v is considered to be

part of an infinitesimal subset dv of V.19 There is a nonnegative measure µ of the size of

any coalition of voters; µ(V ) = 1 and µ(dv) = 1/V , so the proportion of the electorate in

coalition S is µ(S). Any subset of V is a potential coalition but a coalition S has decisive

redistributive power if and only if µ(S) > 12. A coalition need not be constituted as a

continuous interval, which allows for a rich political structure beyond simple Left and

Right.20

Utility is derived from income and the higher a voter’s income, the greater her utility.

Specifically, the utility function for each voter v is assumed to be three times continuously

differentiable and follow the usual rules: u ′v(·) > 0 and u ′′v(·) < 0.21 This means voters are

risk averse. As a normalization, the utility v derives from complete financial ruin, uv(0), is

set equal to 0; the function is assumed to be continuous at that value.

Each voter v has a finite initial income yv. Bargaining incurs transactions costs which

no voter can avoid, if only because each voter is an interested member of potential

19For an extensive analysis of nonatomic games see Aumann and Shapley (1974). Barlo and Camona

(2011) show how to model individual voters who make meaningful strategic decisions in this environment.20Technically, coalitions within V constitute the measure space isomorphic to the Borel subsets of the

unit interval.21The second-order condition guaranteeing risk aversion thus goes beyond the assumption of

nonsatiation (i.e., u ′v(·) > 0). Another common, alternative assumption is that utility is quasilinear: linear

in private consumption and nonlinear in the public good (e.g., Roemer 2001). This produces separable

political preferences (Diba and Feldman 1984), but it has a number of undesirable properties (Milyo 2000,

283), in addition to risk neutrality. Aumann and Kurz (1977) make the additional technical assumption

that utility is uniformly bounded. They also assume the kind of symmetry built into the standard Nash

bargaining setup, i.e., the assumption that all we need to know about a player is her income and utility

function. This becomes an issue if one thinks that voters are influenced by exogenous factors that are not

fully reflected in their resources.

13

coalitions capable of gaining or losing income. For simplicity I assume this cost is the

uniform value K. Individual income net of K is weakly positive, while total income net of

bargaining costs is strictly positive but finite: inf(y) = K and∫VKµ(dv) = K <

∫Vyvµ(dv)

<∞.22 Designating the time needed to complete a bargain by t = t(K), we will assume

that t′(K), K ′(∫Vyvµ(dv)) > 0: the time needed to complete the bargain is a positive

function of the transactions costs and these, in turn, are a positive function of the size of

the stakes involved. The function t(K) may depend on the particular institutional setting

in which the bargaining takes place.

Aumann and Kurz’s (1977) solution to this game is based on Shapley’s (1953; 1988)

analysis of games of division with non-transferable utility, but embedded in a nonatomic

game (that is, with a continuum of players). The unique solution y∗v for each v, that is,

each v’s post-bargain income, is implicitly given by:

uv(y∗v)− uv(0)u′v(y

∗v)

+ y∗v = uv(y∗v)/u

′v(y∗v) + y∗v =

∫V

[uv(y∗v)/u

′v(y∗v)]µ(dv) + yv. (1)

Defining voter v’s tax by Tv ≡ yv − y∗v , we have

Tv = uv(y∗v)/u

′v(y∗v)−

∫V

[uv(y∗v)/u

′v(y∗v)]µ(dv). (2)

In sum, a bargain balancing majority interests and minority threats produces a distinct tax

amount for each individual. This amount is equivalent to a uniform tax rate with varying

lump-sum distributions. The tax can be positive or negative.

Note the contrast with the standard assumption in the political economy literature

that there is a uniform tax with equal lump-sum distributions. The difference is not merely

technical: taxes in Aumann and Kurz’s model result from a bargain struck by coalitions,

not from a direct vote on a rate. The result is a more "individualized" tax system

22Loosely, inf(y) is the lower bound of income.∫Vrepresents Lebesgue integration over measures of

subsets of V . In the same vein, yv is really shorthand for y(v)µ(dv) with y(v) a density function.

14

consistent with the myriad combinations of tax expenditures and tax rates for different

classes of individuals, businesses, and property found in modern democratic societies.

Whether the resulting tax is progressive, regressive, or neutral depends on voters’

particular utility functions. For voters with the same utility functions, however, post-tax

income is an increasing function of pre-tax income.

The bargaining solution is indeed the product of a bargain, not the simple dictate of a

coalition of size µ(S) > 12. The formal power of majorities notwithstanding, they are

prevented from fully exploiting their power to command the income of others by the

potential power of each voter to make or break majority coalitions.23 Ultimately, majorities

are restrained by the minority’s threat to withdraw its productive endowment rather than

see its proceeds confiscated. In the general spirit of Meltzer and Richard (1981), voters can

go on strike.

In the form presented here, the bargaining model has its share of important

limitations. For example, it leaves implicit both the mechanism by which actual bargaining

proceeds and the process through which the resulting agreement is implemented by elected

representatives and bureaucrats.24 This limitation is formally reflected in the nature of the

solution y∗: even though it is unique, it does double duty as a vector of post-bargain

incomes and as the equilibrium policy emerging from the bargaining process. Other

limitations have already been partially addressed in the literature. The bargaining model

has been refined to recognize the existence of prior group structure (Peck 1986),

23Coram (2008) argues for the core as a solution concept for redistributive games. In contrast to the

core, the bargaining solution considers not only what a coalition can achieve on its own but also the impact

of its threats to diminish the payoffs to others by refusing to cooperate (see Aumann and Kurz 1978, 146).24This approach is consistent with Roemer’s (2001, 26-28) recommended strategy of first assuming

parties to be perfect representatives of underlying economic interests before introducing principal-agent

complications. With regard to actual bargaining, there has been considerable progress in grounding the

bargaining solution in noncooperative game theory (e.g., Binmore, Rubinstein, and Wolinsky 1986).

15

continuously variable labor supply (Peck 1986; see also Coram 2008), and the possibility

that agents do not reveal their true utility (Kurz 1977).25

Yet the unmodified bargaining model has one key redeeming feature. As the next

section shows, Aumann and Kurz’s (1977) model helps us explicitly link the structure of

utility functions and income with both moderation and extremism.

5 Moderation and Extremism

In the bargaining world characterized by Aumann and Kurz (1977), voters do not

surrender their underlying economic motivations: u ′(·) > 0 always. Political moderation

emerges neither from stipulations about the distribution of ideal points nor from an

imposed truncation of the alternatives voters face. Rather, the bargaining solution itself

precludes the complete expropriation of the endowments of others, which provide the

effective boundaries on political choice at every level of income. While the voter’s utility is

increasing over the entire social product, the voter’s political choices, implemented through

a bargain, are constrained by the impact of complete expropriation on incentives. Choices,

not ideals, are tempered by the immediate political-economic reality.

But choices are not tempered equally. Some voters are more extreme than others in

advancing or defending their interests. Using the bargaining model, we will explain this

kind of extremism in terms of incomes and utility functions, specifically in terms of the

25Kurz (1977) finds that declaring a linear utility function is the dominant equilibrium strategy in the

associated "distortion game." But this is true, in part, because his analysis allows only weakly concave

utility functions. Intuitively, if taxes are a positive function of risk aversion, a point discussed in the next

section, then linear functions are simply the least risk averse utility functions among those that are feasible.

Without that restriction, voters would declare incredible strictly convex utility functions. Kurz’s

admissability constraint, then, is a symptom of the general problem with his analysis that declared utility

functions are treated as unquestioned inputs into the calculation of the bargaining solution, so their

credibility is assumed.

16

expression uv(y∗v)/u′v(y∗v), the individually variable component of the tax defined in section

4. This is called the agent’s fear of ruin relative to the allocation y∗v .

To understand this interpretation of the variable component, consider a voter v with

allocation y∗v who faces the prospect of ruin– being taxed y∗v– and the possibility of some

small gain h. Given v’s utility function there exists a probability p that leaves v indifferent

between the bargaining solution allocation and a lottery involving the two outcomes 0 and

y∗v + h:

uv(y∗v) = puv(0) + (1− p)uv(y∗v + h) = (1− p)uv(y∗v + h).

Therefore, per unit of additional income this indifference probability of ruin is

p

h=[uv(y

∗v + h)− uv(y∗v)]/huv(y∗v + h)

.

Using L’Hôpital’s rule, as h→ 0 p/h limits to

u′v(y∗v)

uv(y∗v).

This limiting value of p/h represents v’s boldness: the willingness to risk ruin for the sake

of a small gain. Conversely as h→ 0, h/p limits to

uv(y∗v)

u′v(y∗v),

the variable component of the tax. It represents v’s fear of ruin: the degree to which the

gain h must be assured as compensation for risking ruin. Alternatively, it represents voter’s

willingness to sacrifice h to reduce the probability of ruin. Bearing in mind the

normalization uv(0) = 0, this measure is invariant to positive affi ne transformations of

utility.

Referring back to equation (2), we see that taxes move one-for-one with the voter’s

fear of ruin. The world inherits from the meek. Moreover, since higher incomes produce

17

higher utility and lower marginal utility, increasing income, sensibly enough, leads to

greater fear of ruin: there is greater utility at stake and the "insurance premium" to avoid

risk represents less of a utility loss at the margin. Formally,

∂uv(y∗v)/u

′v(y∗v)

∂y∗v= 1 +

uv(y∗v)

u′v(y∗v)

(−u′′v(y∗v)u′v(y

∗v)

)= 1 +

−u′′v(y∗v)/u′v(y∗v)u′v(y

∗v)/uv(y

∗v)

> 0. (3)

The bargaining outcome exploits this fact via higher taxes. Similarly, a lower income

reduces the fear of ruin. Lower-income individuals are more diffi cult to "exploit" and

therefore the bargaining solution imposes lower taxes on them.

Armed with an interpretation of uv(y∗v)/u′v(y∗v) as fear of ruin, we can also interpret the

threshold for paying positive taxes. From the formula for Tv (equation 2), the bargaining

solution will impose positive taxes on individuals whose utility functions and income are

such that their fear of ruin exceeds the mean fear of ruin in the electorate.26 As a result of

the bargain, their income will decrease. Conversely, the bargaining solution will increase

the incomes of those individuals with below-average fear of ruin.

Fear of ruin and boldness, its inverse, will be our key tools for explaining extremism.

The greater a voter’s fear of ruin, the greater her willingness to expend resources in the

effort to resist catastrophic loss. The greater her boldness, the greater her willingness to

demand gains at the risk of catastrophic loss. Fear of ruin and boldness, then, represent

two extremist tendencies, one conservative, one radical. These are more than preferences or

spatial locations. They indicate the degree to which voters will bear risk to realize their

preferences.

To gain a deeper understanding of fear of ruin and boldness, it is worth considering

how they relate to and improve upon the concept of intensity of preference invoked by

Rabushka and Shepsle (1972) in their seminal attempt to characterize extremism and

26Since fear of ruin is invariant to positive affi ne transformations, calculation of the mean does not

require interpersonal comparisons of utility.

18

explain its destructive impact on democratic stability. They define a quantitative notion of

intensity of preference relative to a choice among a, b, and c, when u(a) > u(b) > u(c), as

the inverse of the probability p that makes a decision maker indifferent between (i)

alternative b for certain, and (ii) a lottery yielding alternative a with probability p and

alternative c with probability 1 - p (1972, 49-52). One contrast with fear of ruin is already

clear: this definition focuses on the decision maker’s relative attraction to a; fear of ruin, in

effect, focuses on the decision maker’s relative repulsion by c.

The focus on attraction reflects Rabushka and Shepsle’s (1972, 73) qualitative

definition of intensity as an individual’s willingness to accept a fair lottery in hopes of

getting alternative a. Individuals who are intense in their sense– also known as risk

acceptant– violate the more standard (economic) assumption about utility made here that

agents are risk averse: for Rabushka and Shepsle’s intense individuals, u ′′v(·) > 0 over the

relevant interval.27 This means that a voter in the bargaining game is not intense in the

qualitative sense no matter how bold or fearful of ruin she may be.

Nevertheless there is a formal relation between Rabushka and Shepsle’s quantitative

measure of intensity and fear of ruin. It can be shown that for small gains the inverse of

their measure is an approximate linear function of the famous Arrow-Pratt measure of

absolute risk aversion, −u′′v(y)/u′v(y) (Arrow 1965, 34; Pratt 1964):

pv ≈1

2+1

4[−u′′v(y)/u′v(y)]h, (4)

27Carroll, Lewis, Lo, and Poole (forthcoming) consider voters with Gaussian random utility functions

characterized by varying degrees of "intensity" measured as greater precision. Intuitively, intensity in their

sense makes it less likely that a random shock will negate the behavioral implications of the deterministic

component of the utility function. This version of intensity is nearly the opposite of Rabushka and

Shepsle’s. ‘Nearly’since their sense reflects the individual’s behavior in the face of risk, whereas Carroll,

Lewis, Lo, and Poole’s is a property of the concave, deterministic component of the utility function.

19

where pv is the probability that voter v will receive the small gain h = a− b.28 The greater

v’s degree of risk aversion, the less intense is her preference for her most preferred

alternative when confronted with a set of three. From equation (3), we see that for a given

level of income y∗v , the greater the income sensitivity of an agent’s fear of ruin the greater

her absolute risk aversion at that income. Thus the agent’s intensity in Rabushka and

Shepsle’s sense is positively related to the sensitivity of her fear of ruin to increases in

income. Put another way, the more the bargaining solution exploits her, the more intense

she is.

We have seen that fear of ruin responds unequivocally to increases in income y∗v . What

about intensity? The response of absolute risk aversion to changes in income is given by

∂[−u′′v(y∗v)/u′v(y∗v)]∂y∗v

=−u′′′v (y∗v)u′v(y

∗v)

+

[u′′v(y

∗v)

u′v(y∗v)

]2. (5)

The second term on the right-hand side of equation (5) is positive, but the first term

cannot be signed a priori without knowing the sign of u′′′v (y∗v).

Fortunately, both issues can be resolved with a very plausible behavioral assumption:

absolute risk aversion decreases with wealth (for an empirical evaluation of this

assumption, see Lengwiler 2004, 87). As Arrow (1965, 35) points out, "If absolute risk

aversion increased with wealth, it would follow that as an individual became wealthier, he

would actually decrease the amount of risky assets held." Given decreasing absolute risk

aversion, −u′′′v (y∗v)/u′v(y∗v) + [u′′v(y∗v)/u′v(y∗v)]2 < 0. This inequality, of course, also signs

u′′′v (y∗v) > 0. By the approximation (4), therefore, intensity increases with wealth, assuming

decreasing absolute risk aversion. This result becomes important in the next section.

28The relation (4) is derived from a Taylor approximation. Here y + h corresponds to alternative a in

the definition of intensity, y corresponds to alternative b, and y − h corresponds to alternative c. Note that

fear of ruin governs a decision between the total loss of wealth and a small gain whereas risk aversion

governs reactions to small changes in wealth relative to the status quo.

20

Thus with plausible empirical restrictions the intensity measure 1/p can be reverse

engineered to determine its relation to the fear of ruin. This reverse engineering exploits

both the relevance of the utility function’s curvature to both measures and the possibility

of judiciously selecting the alternatives anchoring the intensity measure to match

alternatives relevant to calculating the fear of ruin. The resulting connection suggests a

wider application of the fear of ruin measure to plural societies. In particular, by

substituting fear of ruin for intensity, we are no longer restricted to societies offering voters

three discrete ideological alternatives or restricted to voters who are risk acceptant.

In sum, as a tool to explain the difference between moderates and extremists, fear of

ruin dominates intensity. Fear of ruin is defined globally over a utility function’s entire

domain of alternatives, not just for three predetermined alternatives; its response to income

requires weaker empirical assumptions than does intensity; and unlike intensity it can be

ordered qualitatively across different attitudes toward risk: individuals who are risk averse

always exhibit greater fear of ruin than voters who are risk neutral, and risk neutral voters

always exhibit greater fear of ruin than those who are risk acceptant (see Foncel and Treich

2005, 290-91).29

Of more immediate relevance, we have discovered that intensity, which reflects the

agent’s willingness to take (political) risks for the prospect of gain or victory, is associated

with both absolute risk aversion and fear of ruin. This means that what might be loosely

termed ‘extremism’encompasses both a strong resistance to income loss and a willingness

to gamble for large gains. Even though an extremist elite may tenaciously resist even

modest downward redistribution it might also push recklessly for additions to their already

29For a strictly concave function, (recall the normalization u(0) = 0), u(y)y > u′(y) (e.g., Mas-Colell,

Whinston, and Green 1995, 931) and therefore u(y)u′(y) > y; for a strictly convex function, then, u(y)

u′(y) < y; and

for risk neutral utility u(y) = ay and therefore u(y)u′(y) = y. Thus fear of ruin is greater for risk averse utility

than for risk neutral utility and greater for risk neutral utility than for risk acceptant utility.

21

substantial wealth. Extremism is more nuanced than a blanket psychological diagnosis

might suggest.

This understanding of extremism can be extended in still another important direction.

Authoritarian elites facing calls for a democratic transition will take into account what we

can now call the risk of ruin under democratic voting procedures: elites will worry about

complete expropriation under majority rule. However, elites with mobile capital are less

exposed to ruin under democracy than are elites with fixed capital (Boix 2003). This is

because those holding fixed capital cannot make a credible bargaining threat to flee with

their capital. Their fear of the ruin will be correspondingly high since they face

confiscation or high taxation on this inelastically supplied source of income (see also

Acemoglu and Robinson 2006, 300-307; Freeman and Quinn 2012).

Conversely, when an authoritarian elite’s fear of ruin is relatively low, democratic

transitions do not necessarily require its simple surrender. The elite can play an active role

in a transition process by which "the lower, middle and rich classes struck deals purely as a

function of their income" (Boix 2003, 54). To place Boix’s observation about smooth

democratic transitions within the bargaining framework it is helpful to undo the

normalizations used in the preceding analysis. Let yv be v’s income remaining after ruin:

K ≤ yv≤ yv <∞,

so the fear of ruin measure becomes

uv(y∗v)− uv(yv)u′v(y

∗v)

. (6)

When due to capital mobility the income floor for elites engaged in democratic bargaining

is relatively high, which means their utility at that level– uv(yv)– is high as well, their fear

of ruin is reduced as is their anticipated tax burden. In Boix’s (2003) terms, capital

mobility enhances the prospects for elites under democracy and thereby reduces their

22

opposition to it. Specifically, mobility reduces their extremism or tenacity in defending the

status quo as part of any bargaining over a democratic transition.

In other words, the issue for authoritarian elites is not necessarily the binary choice of

whether or not to repress potential challengers. Elites must also make a strategic decision

about what form their repression of non-elites will take. Death squads represent a very

strong form of repression; police raids a somewhat weaker form; tampering with elections

and censorship a still weaker form; and funding a conservative party a particularly mild

form of "repression." Moving beyond Boix (2003), a model of extremism and moderation

can help explain the degree of repression imposed by elites.30

6 Risk and Ideology

Time to take stock of our intermediate conclusions. One, all individuals are

"extremists" when it comes to economic goods and services. Effectively their optima are at

infinity. But politics puts their material well-being at risk and this engenders the kinds of

bargains found in democracies: "The bargaining associated with entry into (or exclusion

from) a ruling coalition is a risky business, as are the threats of the minority and of the

majority once coalitions have been formed" (Aumann and Kurz 1977, 1140).

Two, current spatial models of extremism and political economy models of moderation

fail to ground extremism and moderation in the fundamental interests over which the

participants are polarized.

30Actually, repression in Boix’s (2003) analysis is binary in one sense, but it also encompasses (i) steps

taken by authoritarian elites to prevent challenges to their power, and (ii) reactions to such challenges.

Regarding (i): "In a right-wing authoritarian regime the poor are excluded from the decision-making

process. . . . The imposition of such a regime requires the exercise of repression by the rich" (2003, 26).

Regarding (ii): "Since the wealthy cannot follow a pure dominant strategy, they will simply repress with a

certain probability (or, in game-theoretic terms, follow mixed strategies) . . ." (2003, 34).

23

Three, the bargaining model creates a theoretical bridge between income and two

tendencies we associate with extremists: the willingness to go for broke and to tenaciously

defend the status quo. The risk built into bargaining over redistribution is assessed

differently by those entering the bargaining process with different amounts of initial

income. All else equal, low initial income is associated with greater boldness, high income

is associated with greater fear of ruin. Those with below-average fear of ruin, in turn, can

anticipate higher incomes from the bargaining solution. Those with above-average fear of

ruin can anticipate lower incomes. All voters prefer to redistribute toward themselves, but

in light of their risk environment some are disposed to pursue gain vigorously and others

are disposed to defend their current income tenaciously.

In the bargaining model, then, low-income individuals are more willing to fight for

gains at the risk of complete loss. High-income individuals are less willing to risk

catastrophic loss for the sake of upward redistribution and more inclined to defend their

existing advantages. But while this gives us a sense of the different attitudes the parties

bring to the table, apparently it does not capture the potential for breakdown, disruption,

and disagreement– the problem of polarization– extremism is generally seen to entail. For

the attitudes toward political risk these individuals exhibit determine the character of a

bargaining equilibrium, which is a solution, not a breakdown.

Assuming fixed utility functions, what undermines such an equilibrium and the

attitudes associated with it is an exogenous shock to incomes.31 In the case of the U.S., a

plausible candidate for this kind of bargain-threatening shock is the noteworthy secular

increase in income inequality over the last forty years (see McCarty, Poole, and Rosenthal

31This is the simplest channel within the bargaining model. It is also possible, for example, to

incorporate the historical evolution of income directly into utility functions by allowing voter utility to be

sensitive to changes in the relation between (i) their income, and (ii) income trends at the aggregate level

or with respect to some reference group (see, e.g., Campbell and Cochrane 1999).

24

2006; for evidence concerning U.S. trends in inequality see Congressional Budget Offi ce

2011). The increase in inequality has been generated largely by rapidly increasing income

for the top 1%– even more the top 0.1%– relative to income growth below.32 Again, U.S.

institutions may exacerbate the political impact of these trends, but the model predicts

independent behavioral changes.

As formulated here, the bargaining model builds in a lag between equilibria (remember

t(K)). Formally, the distinction between behavior within the existing bargain and

bargaining over a new bargaining solution is the distinction between behavior guided by a

local risk of loss and behavior guided by a global risk of loss. For intra-bargain decisions,

the Arrow-Pratt measure is an appropriate measure of risk aversion. For inter-bargain

decisions, fear of ruin and boldness are the appropriate measures, since both reflect the

(global) threat of ruin. In actual situations, no doubt, there is an overlay of risks.33

1. Let us start locally by examining the within-bargain effect of changes in the income

distribution. Consider a better-off voter v with allocation y∗vt−1 at time t-1 who

accumulates a substantially higher income yvt � y∗vt−1. If and when a new bargain is

32Transfers reduce inequality but have had a decreasing impact on it (Congressional Budget Offi ce 2011,

19). In terms of the model, this means that the redistribution embodied in the earlier bargaining solution

has not offset income trends. Another potentially confounding factor is the difference between inequality in

consumption and inequality in income (Congressional Budget Offi ce 2011, 4-5; cf. Hagopian and Ohanian

2012). By focusing on utility, the bargaining model clearly is keyed to the former. As for the relation

between growing inequality in the U.S. and its high degree of political polarization, see Atkinson, Piketty,

and Saez (2011) for a comparison of income inequality in the U.S.and in other countries.33The distinction between an equilibrium and out-of-equilibrium political economy is empirically

challenging: "there are innumerable ways for the [political] economy to be out of equilibrium, so we must

expect any treatment of out-of-equilibrium behavior to have considerable arbitrariness" (Lucas 1978, 1437).

Still, it is implausible that the bargain is instantaneously updated in response to a shock. By the same

token, I assume that when their world has suffi ciently changed, voters are eventually induced to address the

change in opportunities available to them.

25

struck, v will pay higher taxes. Until then, at her current offi cial allocation y∗vt−1 v’s

political behavior will reflect uv(yvt). As we will now see, she therefore will act with a

greater degree of risk acceptance relative to y∗vt−1. In other words, when uv(yvt) determines

her behavior at y∗vt−1, it becomes more likely that her expected utility at yvt with respect to

a given risky decision will be greater than the utility of her expected pre-tax income. As a

consequence, risks she was not prepared to bear become attractive: Etuv(yvt) > Etuv(y∗vt−1)

for the same amount of risk.

Figure 1 illustrates a risky decision by the kind of risk-averse voter studied here:

Figure 1 characterizes a lottery giving the voter an even chance of y ± ε, the fair gamble

used by Rabushka and Shepsle (1972) to characterize intensity. The expected income from

the lottery is y and its expected utility is EU, which for this risk-averse decision maker is

less than the utility U(y) of the corresponding income y for certain. Put another way, this

26

voter would derive the same amount of utility from income CE as from the lottery and

therefore would be willing to pay up to y − CE to avoid the lottery.

Now suppose the decision maker’s income has increased to y from an initial allocation

y∗. Figure 2 represents two fair lotteries giving an even chance of y∗± ε and an even chance

of y ± ε, y∗ < y (see Mas-Colell, Whinston, and Green 1995, 190):

In this Figure, the two relevant segments of the utility function in the neighborhood of y

and y∗ are stacked and oriented to equate first derivatives at those incomes. This artifice

makes absolute risk aversion comparable across income levels, since this measure, like fear

of ruin, is scaled by marginal utility in order to make it invariant to positive affi ne

transformations of the utility function. The impact of higher income is that

CE(y∗) < CE(y): at a higher level of income the decision maker is less risk averse (which

echoes an empirical assumption discussed in the preceding section). In other words, the

amount the voter will pay to avoid the risk– the risk premium– is smaller at higher wealth.

27

This is true during the period between bargains even though the correlative increase in the

voter’s fear of ruin implies higher taxes when the new bargain is completed.

As a consequence of the bargaining solution y∗t−1 determined at time t-1, each

individual voter v’s after-tax income is y∗vt−1. When incomes change but the solution does

not, y∗t−1 6= yt. Likewise, until the next bargain is struck each voter’s tax obligation

Tvt = Tvt−1 = yvt−1 − y∗vt−1 is unchanged. For a voter v whose income has increased, votes

related to Tvt will reflect decreased risk aversion. Specifically these voters will accept

gambles they would (or did) reject at their original levels of income. Modulo y∗vt−1 these

voters behave as if they are more intense in Rabushka and Shepsle’s (1972) sense although

they would continue to reject fair gambles. Again, Etuv(yvt) > Etuv(y∗vt−1) for the same

risk.

In short, prior to the new bargain, increases in income shift attitudes toward greater

risk acceptance. Voters behave differently than they had been behaving. They are more

willing to engage in at-risk political behavior. Within the bargaining model, moreover, the

increasing stakes associated with rising per capita income and inequality, as in the U.S.,

lead to longer delays before there is a new bargain determining a new allocation.

2. Turning to global decision making regarding a new prospective bargain, it is

important to recognize that fear of ruin and boldness are defined relative to some y∗v , but

this can be any allocation. When income changes, fear of ruin and boldness are defined

relative to the new status quo. These attitudes determine the voters’stance toward any

future equilibrium.

The particular shape of increasing inequality in the U.S.– increasing incomes at the

top relative to incomes at the bottom–means that (1) high-income voters with increasing

incomes become more fearful of ruin, more fearful of even small probabilities of

expropriation, and (2) low-income voters exhibit relatively constant boldness in the

technical sense of the term, that is, they are not more willing to take risks for increased

28

allocations. It is striking that while in recent decades there has been some polarizing

movement in the U.S. Congress in both directions, the greater movement has indeed been

to the Right (McCarty, Poole, and Rosenthal 2006). This is consistent with the bargaining

model, but inconsistent with standard political economy models of redistribution focusing

on the absolute size of income inequality rather than its source.

To be more precise, in the bargaining model, prospective gains and losses are

conceptualized as changes in net taxes (for this approach to tax distributions see Piketty

and Saez 2007, 5). Much of the usual political dialog about taxes focuses instead on

marginal tax rates. Within the bargaining model, the marginal tax rate, ∂(yv − y∗v)/∂yv,

cannot be signed directly since, as we have seen, y∗v depends on yv. Indeed under the

bargaining solution the marginal rate can increase, decrease, or remain constant with

income.34

In the U.S. effective marginal Federal tax rates for comprehensive household income

are generally progressive, but not uniformly so when the top 0.01 percentile is subsetted

(Congressional Budget Offi ce 2008, Table 1). If in the spirit of the bargaining model we

take into account net changes in income reflecting not only direct tax obligations but tax

expenditures, the U.S. tax system is progressive in cross-national comparison (Prasad and

Deng 2009). Specifically, the share of total Federal taxes paid by the top percentiles,

including the top 0.01 percentile, is disproportionate and in fact experienced a secular

increase from 1979 to 2005 (Congressional Budget Offi ce 2008, Table 5).35 The resulting

distribution of net tax amounts is consistent with the bargaining model in this particular

34The model is relatively indifferent to marginal tax rates in part because it does not incorporate

distortions in labor and capital supply due to taxation.35These facts have no automatic ideological implications. On the one hand, the rich have paid more

both over time and relative to those with lower incomes. On the other hand, absolute amounts are different

than effective tax rates, and the pre-tax incomes of the top percentile and fractions of that percentile

increased dramatically during the 1979-2005 period.

29

sense: individuals whose income has increased, while their utility functions are unchanged,

are predicted to pay higher taxes. The same holds cross-sectionally with respect to

individuals who have different incomes but the same utility function.

It is worth pausing over this general point given political obsessions over marginal tax

rates. Because the bargaining model has no general implications about the progressivity of

marginal rates, it is consistent, for example, with the 2001 and 2003 Bush tax cuts in the

U.S. When effective tax rates are constant, tax liabilities increase when income does.36 And

the downward adjustment of marginal rates in 2001 and 2003 need not have and in fact did

not fully offset those increased liabilities (Congressional Budget Offi ce 2008, Table 2). If

they had, this would pose a puzzle for the bargaining model.

There is a crucial asymmetry among voters approaching a new bargain. Those who

have gained income exhibit an increased fear of ruin, which means they are more defensive

in protecting their current income. Those who have lost income exhibit greater boldness,

which means they are more aggressive in risking ruin for gains. Given increasing concave

utility functions, both phenomena ceteris paribus will tend to be more pronounced at the

extremes of the income distribution.

This is not the typical way of analyzing the political impact of inequality. According

to the typical analysis, insofar as increasing inequality leads to an increase in projected

taxes for voters at the top, the political stakes will be higher for them and for downstream

voters. Voters at both ends of the income ladder will expend more resources to steer the

direction of policy. This is one sense in which the resulting politics can be described as

more intense. But the kind of intensity or extremism defined within the bargaining model

does not revolve simply around the size of utility differences due to the absolute size of

possible transfers. It revolves around a particular kind of behavior associated with these

36In fact, the top 1% income group faced declining effective average tax rates beginning in the

mid-1990s (Congressional Budget Offi ce 2012, Figure 5).

30

transfers, behavior reflecting the extremism of the voters’response to reductions in income

at the bottom or increases in income at the top. To the extent changes in inequality are

accompanied by increases in the fear of ruin or boldness, the link between increasing

inequality and an increasing risk of instability will depend on the sources of increasing

inequality.37 Polarization does have an historic dimension.

By the same token, increases in inequality are often accompanied by increases in per

capita income. When, in contrast to recent U.S. experience, these increases in per capita

income reflect increases for the poor as well as the rich, extremism by the poor– the

willingness to gamble for increased transfers– is tempered by an accompanying increase in

the fear of ruin. Small wonder that democratic stability is positively associated with

national income (e.g., Przeworski 2005).

Thus given constant utility functions, an increase in a voter’s income leads to

increased extremism due to fear of ruin and to decreased extremism due to boldness.38 Out

of an increased fear of ruin the price those with increased incomes are willing to pay to

avoid expropriation increases. Those who experience reductions in incomes exhibit

increased boldness and are more willing to go for broke. Thus the bargaining solution

implies that when the poor become richer their boldness declines, the cost they pay for a

strike increases (see Benhabib and Przeworski 2006), and their redistributive demands

within the bargaining process are moderated.

The message is that changes in income can affect extremism across the income range.

It is not just for the rich and the poor. By the same token, extremism is not equally likely

37For some of the empirical complexities confronting theories postulating a causal link between

inequality and instability see, e.g., Haggard and Kaufman (2012).38Invoking the informal notion of anticipated tax changes due to increases in income as opposed to the

formal notion of expectation avoids careful consideration of the preservation of measures of risk under the

expectation operator (see Nachman 1982).

31

across the income spectrum. Voters approaching the average fear of ruin from below

exhibit decreasing boldness in their demands for higher income. Their demands for

redistribution will be moderated. Voters approaching the average fear of ruin from above,

on the other hand, exhibit declining fear of ruin or defensiveness about their incomes and

increasing boldness in their demands for a reversal of fortune.39

The changing tradeoff between fear of ruin and boldness as income increases maps to a

version of the Left-Right "ideological" continuum. Movement along the income continuum

reduces the voter’s boldness (the willingness to take risks to implement redistributive

preferences) and increases her fear of ruin (the willingness to expend wealth to protect

wealth). Ceteris paribus, a lower income means greater boldness which means more

politically Left in the sense of an increased and increasingly extreme preference for

downward redistribution. A higher income means less boldness and greater fear of ruin

which means more politically Right in the sense of an increased and increasingly extreme

opposition to downward redistribution.

The "moderation" associated with the center of the continuum does not represent a

moderation in underlying preferences. Nonsatiation still rules. But the moderate is

particularly cross-pressured: enough income to be concerned about ruin, not enough

income to be fanatic about protecting it. With respect to ruin, the "middle class" identifies

39This statement requires a technical qualification. Arrow’s (1965, 27) Utility Boundedness Theorem

shows that any utility function satisfying the assumptions needed to order preferences according to

expected utility must be bounded from below and from above. As a consequence, even an otherwise

concave utility function will turn convex near its lower bound. Behavior in this interval will be risk

acceptant or intense according to Rabushka and Shepsle’s (1972) definition. From the perspective of

someone at the absolute bottom, there is no utility to lose and only utility to gain. At the other end, the

bound reinforces risk aversion. Specifically, assuming u′′′(·) 6= 0, both fear of ruin and, by L’Hôpital’s rule,

absolute risk aversion equal infinity at the limit. The bounds, however, are theoretical. No individuals in

any society of interest need be at either of them.

32

with the rich, while with respect to boldness it identifies with the poor.40 Small wonder

this group plays such a pivotal role in democratic transitions (e.g., Acemoglu and Robinson

2006).

The term ‘moderation’, therefore, has two meanings in this analysis. There is

attitudinal moderation reflecting the cross-cutting pressure of boldness and fear of ruin.

There is also ideological moderation: a revealed preference for redistribution constrained by

the political reality that the voter’s ideal point– complete control of the social

product– cannot be achieved through bargaining.

It may seem odd to label as ideologically moderate any result falling short of complete

expropriation. The labeling is not important. What is important for theoretical clarity is

recognition that "extreme" outcomes like equality and laissez faire are more moderate than

the outcomes associated with the unvarnished ideal points of Homo economicus. The

intuitive association between tax rates and ideology may make the imposed restrictions on

redistribution seem less artificial. But as we have seen, this association should not mislead

us into thinking we can explain political moderation simply by invoking the moderating

discipline of political ideologies.

For however easily interpreted politically and however empirically accurate, the

ideological bounds of the voting dimension reflect an artificial restriction on voters’

economic aspirations if not actual results. Until we have derived political moderation from

unrestricted economic extremism, we have not explained it. With apologies to Barry

Goldwater, political moderation in the pursuit of riches is no theoretical virtue.

A moderate ideology, after all, need not reflect moderate preferences. For example, the

canonical political economy model’s truncation of Left political alternatives may be

40The specific point of minimum extremism– when u(y)/u′(y) + u′(y)/u(y), the sum of fear of ruin and

boldness, is minimized– depends on the utility function. For all utility functions, of course, the minimum

point occurs where the marginal increase in the fear of ruin equals the marginal reduction in boldness.

33

empirically realistic only because lower-income voters with bigger ambitions than equality

choose a political agent who publicly promotes an egalitarian ideology like socialism. If so,

socialism is not a true reflection of the principals’optima but represents a concession to the

necessity of forming broader political coalitions or avoiding large effi ciency losses.

Przeworski and Sprague (1986) argue that socialist parties in power typically compromise

their principles due to the realities of governing. Socialist principles themselves may

already constitute such a compromise.

In general, publicly expressed goals and election manifestos falling short of full-scale

extremism may not offer a useful guide to real agendas. Nor are strategic compromises the

same as goals. Hinich and Munger (1994) stress ideology’s important role in selling parties

or candidates, but selling can involve disguising rather than expressing preferences.41

The point is not that no one really believes these formal ideologies. But however

believable to some, ideologies can also serve as coherent summaries or characterizations of

possible prudential compromises, albeit summaries with long historical pedigrees. So there

is nothing surprising about the mass public’s failure to have internalized them.42 From the

narrow perspective of political economy they are not what the mass public is really

interested in. To expect the public to internalize formal ideologies is to expect them to

41Hinich and Munger (1994, 11) define ideology as "an internally consistent set of propositions that

makes proscriptive and prescriptive demands on human behavior" (emphasis deleted) and as such "an

acual ideology implies . . . a complete worldview" (1994, 101). Therefore, there may be a "paucity of

coherent ideologies" (1994, 105). Their formal model, however, implies a continuum of such worldviews

including mixtures of different ideologies. This feature allows Hinich and Munger to define indirect utility

functions over ideologies that reflect restrictions on Homo economicus as well.42Converse (1964) offers the classic skeptical assessment of the public’s ideological sophistication. In

part under his influence, ideology for empirical analysis often means any statistically measurable coherence

in issue positions or beliefs rather than a full world-view (e.g., Hinich and Munger 1994; Baldassarri and

Gelman 2008; Jessee 2012).

34

confuse the effect for the cause, the sales pitch for the merchandise.

7 Concluding Comments

The attempt to understand the economic microfoundations of voter preferences is

part and parcel of the attempt to understand what voters hope to get in the political arena

and therefore the conditions under which extreme or moderate demands make sense to

them. Democratic processes obscure these microfoundations: "Democratic citizens are not

equal but only anonymous, indistinguishable by any traits they may possess" (Przeworski

2009, 281). By detaching political preferences from underlying economic interests, the

standard spatial analysis of voting confirms that anonymity.

Yet if the veil of anonymity disguises profound economic differences, it is partially

pierced by the power of individuals to restrict the democratic agenda. Voters within the

bargaining model cannot vote on all possible allocations since individuals in and outside of

coalitions determine, in part, which allocations are feasible. As a result, the bargaining

model does not represent democracy in the traditional sense as a sequence of direct or

indirect referenda over policy alternatives. It is more concerned with the correlation of

forces within the scheme of majority rights established by majoritarian institutions.

Changes in the economic environment change the correlation of forces. In tracking the

resulting changes in income distribution, the bargaining model maintains a theoretically

motivated link between economic and political preferences. Moderation in voting is

determined by this link, not by arbitrary restrictions on revealed preferences, or on

personalities for that matter.

The same link also determines endogenously whether voters are extremists. In keeping

with conventional wisdom, the lower and upper classes in the bargaining model are more

prone to extremism. But they are not necessarily the only groups that can experience the

35

significant changes in pre-tax income or post-tax prospects capable of motivating strong

political reactions. As evidenced by the role of the middle class in Weimar Germany (e.g.,

Fischer 1996), neither working class authoritarians (Lipset 1960) nor reactionary elites (see,

e.g., Geary 1990) have a monopoly over the kind of extremism that pushes the envelope of

the existing bargain.43 Extremism is a form of behavior, not simply a position on an

ideological scale, let alone a position on an income scale.

Whatever their income, extremists, according to the bargaining model, are not simply

expressing some congenital psychological defect. Still less did they just happen to wake up

on the wrong side of the bed. Call it the banality of extremism: depending on her financial

situation, any voter with a standard utility function can become an extremist. By the same

token, the model shows why voters with standard utility functions who happen to find

themselves at society’s income extremes are likely candidates for extremism.

Without wishing to mistake suffi cient for necessary conditions, in sum, the bargaining

model encourages the presumption that extremism is highly circumstantial. Currently the

bargaining model shines a spotlight on the U.S. due to the dramatic increase in inequality

in income and wealth in that country over a forty year horizon, a central cause of

polarization highlighted by McCarty, Poole, and Rosenthal (2006). Yet the stability of

national income distributions, which is more the norm (e.g., Li, Squire, and Zou 1997),

provides no guarantee against extremism since static distributions can disguise high

mobility. On this account, mobility more than immobility is the source of extremism in

democracies.

Finally, for obvious reasons a political economic bargaining model focuses on the

relation between income and ideology. What about extremism rooted in differences over

43Consistent with the bargaining model, Fischer (1996) and others also argue that the middle class was

not uniquely responsible for the Nazi’s electoral success: generally speaking, if the middle class experiences

relevant economic distress, others more susceptible to extremism will experience it as well.

36

religious or social issues? The simple substitution of these issue dimensions into the

bargaining model would not make sense, if only because the "extremist" utility functions of

the bargaining model no longer apply.

Some social issues like abortion, of course, do have an economic dimension. Moreover,

when they do not, voters desiring to be part of winning coalitions are forced to make

tradeoffs between their material and nonmaterial preferences. These tradeoffs determine a

shadow price even for ideological values ostensibly beyond crude economic measurement.

This is true of the behavior of Bill Gates, who amassed a fortune he is now redistributing,

and Friedrich Engels, who used his wealth to finance Karl Marx. Nevertheless, the

integration of noneconomic considerations into the bargaining model poses a genuine

technical challenge.

37

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