Coalition in a Plurality System:

Explaining Party System Fragmentation in Britain

Jane Green

Ed Fieldhouse

Chris Prosser

University of Manchester

Paper prepared for the UC Berkeley British Politics Group election conference, 2nd September 2015.

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Abstract

Electoral system theories expect proportional systems to enhance minor

party voting and plurality electoral systems to reduce it. This paper

illustrates how the likelihood of coalition government results in incentives

to vote for minor parties in the absence of proportional representation.

We advance a theory of why expectations of coalition government

enhance strategic and sincere voting for minor parties. We demonstrate

support for our theory using analyses of vote choices in the 2015 British

general election. The findings of this paper are important for electoral

system theories. They reveal that so-called proportional electoral system

effects may arise, in part, due to the presence of coalition government

that so often accompanies proportional representation. The findings also

shed light on an important trend in British politics towards the

fragmentation of the party system and a marked increase in this tendency

in the 2015 British general election.

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The 2015 general election result saw the Conservative party win a majority of seats in the House of

Commons after a period of governing in coalition with the Liberal Democrats. At first glance the

result may look like a return to the classic two-party majoritarian government under a plurality

electoral system. But this conclusion would be wrong. 2015 represents a high watermark for votes

for 'other' parties - those parties challenging the traditional establishment parties in Westminster.

Vote shares for UKIP leapt from 3.1% to 12.6%, the Greens from 1.0% to 3.8%, the SNP leapt from

19.9% to 50% in Scotland and Plaid Cymru saw a small increase from 11.3% to 12.1% in Wales. The

two-party vote share increased by only 2.2% despite the spectacular collapse of the well establish

third party the Liberal Democrats, who lost 15% of the vote. The Conservative majority arose not

because of a surge in popular support (the party gained just 0.8% share of the vote) but because of

the more successful Conservative transmission of votes into parliamentary seats, compared to

Labour. In England the Conservative’s vote gain of 1.4% translated into 21 extra seats, whilst

Labour’s 3.6% gain only resulted in 15. Coupled with its collapse in Scotland, this lead to a net loss of

26 seats for Labour, despite increasing its overall vote share by 1.5%.

The 2015 British election raises a theoretically important question, namely, what can account for the

significant rise in minor party votes in 2015 - votes cast under a plurality electoral system expected

to discourage minor party voting? There are many answers to this question that are specific to the

issues and competition characterising the period of British electoral history: the apparent ideological

convergence of the main parties of government, little differentiation in terms of overall appeal for

Labour, the Liberal Democrats or the Conservatives, a strong anti-Westminster sentiment in Scotland

as well as in other parts of the UK, and the salience of cross-cutting issues (e.g. immigration). In this

paper we diverge from those contemporaneous explanations to offer a theory about the influence of

institutions. Namely, we argue that the experience of coalition government - and the expectation of

coalition government - altered the incentives of voters in a way akin to the apparent incentives

under a proportional representation electoral system. The implication of this argument is that

proportional electoral system is not solely responsible for increasing incentives for minor party

voting under proportional systems. It is the outcome of proportional system - coalition government -

that in part leads to the fragmentation of vote choices spread among a greater number of political

parties, not just the transmission of votes to seats. The British case provides a unique test of this

theory about incentives under different institutional contexts. It allows variation in the governing

system, and perceptions thereof, while holding the electoral system constant, thus moving us

towards the ability to isolate these two institutional effects.

Anticipating different coalition likelihoods, how a local vote might increase the chances of a desired

local and national outcome, knowing which policy combinations different parties may adopt - and

whether they would be able to do so, all introduces a great deal of complexity and uncertainty into

the vote calculus (Hobolt and Karp 2010). This is likely to be especially complex and uncertain in

countries that have recently moved to a proportional system (for example, for Scottish elections to

the Scottish parliament, see Carman and Johns 2010) and where coalition combinations are more

unpredictable, in closely fought elections or where parties might join coalitions with different

ideological alternatives. The 2015 British general election was an extreme case in point. Most Britons

had their first experience of coalition in 2010 but were not operating in an electoral system that was

thought to make them likely. The election campaign was filled with speculation and uncertainty

about the outcome but with a consensus that Labour would be the largest party without an overall

majority. There was a significant surge in SNP support in Scotland which led to a late declared denial

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of a Lab-SNP coalition partnership (which many did not believe) and a greater chance of Labour not

winning a majority. There was speculation over the rise of minor parties such as UKIP, and whether

that would translate into seats, and a declaration by the Liberal Democrats that they would partner

with either major party which had a mandate of the largest number of seats. At the constituency

level, unprecedented churn between 2010 and 2015 made normal assumptions of likely winners less

predictable. In short, this was a highly complex and uncertain election. We therefore ask, if voters

anticipated the hung parliament in 2015, what impact did it have?

Our theory of coalition incentives proposes that coalition government increases the incentives to

vote in ways typically expected under proportional electoral systems. We outline new reasons in

support of this expectation with respect to increasing sincere voting for minor parties, and three

reasons with respect to increasing strategic voting for minor parties drawing on the literature on

coalition voting considerations within proportional electoral systems. We reveal how those strategic

voting expectations relate only to coalitions, not to proportional systems per se. Our sincere voting

incentives relate to a reduction in the degree to which a minor party vote is wasted (because a voter

may wish to signal greater popular support to bolster its mandate in coalition, and because the party

has a greater chance of legislative influence in coalition) and an increase in the degree to which a

major party vote (because a major party cannot deliver its full platform, and ideological blurring

reduces incentives to vote strategically and increases incentives to vote expressively).

The expectation of coalition should not always increase the incentives to vote for minor parties,

however. There is one specific context in which existing theory would expect coalition, or its

expectation, to turn voters back towards a major party, as predicted by Duverger (1954); classic

plurality strategic voting for major parties. It is common in countries where the experience of

coalition government is the norm for voters to choose a party within a party bloc; their preferred

choice-set. If a voter expects a party to govern with ideologically proximate parties, it makes sense

for a voter to choose one of those preferred bloc parties that has the greatest likelihood of winning

in their electoral district, or constituency. For some voters this strategic decision will mean a vote for

a minor party. But for other voters it will mean a vote for a major party - specifically where a major

party has the greatest chance of defeating a less ideologically preferred rival. We currently find no

concrete support for this effect in the 2015 British general election, though we do not rule it out.

In addition to making an argument about electoral systems and strategic voting, this paper brings a

new perspective to bear on the outcome of the 2015 British general election. It suggests that the

Conservative party won in spite of coalition-based incentives to vote against the two largest

Westminster parties. And as we show in this paper, it won in part because of the contextual

dependencies of our theory played out in different constituency contexts.

Coalitions in Plurality Systems: How Might Voters Respond?

Voter decisions in different electoral systems have been thought to exhibit strategic voting under

plurality systems, sincere voting under proportional systems (Duverger 1954; Cox 1997), and latterly

strategic voting under proportional systems also, under conditions of low district magnitude, where

the transfer of votes is less proportional and hence votes might be wasted, as in plurality systems

(Leys 1959; Sartori 1968; Cox and Shugart 1996; Cox 1997). Sincere voting refers to voting simply for

one's preferred party, strategic (or tactical) voting to an instrumentally motivated vote choice for a

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party that has a better chance of influencing government policy than a favoured party (McKelvey

and Ordeshook 1972; Cox and Shugart 1996; Cox 1997; Alvarez and Nagler 2000).

Recent research has begun to illuminate how voters respond to the prospect of coalitions, naturally

exploring this decision-calculus in a proportional system context; where coalition governments arise.

Voting can be strategic in these proportional systems where voters attempt to maximize a preferred

policy outcome by calculating the chances of electing a coalition with policies closest to their

preference, and voting accordingly. Hence, there are two reasons to vote strategically under a

proportional system; one if the transfer of votes is less proportional, where there is low district

magnitude (the number of seats per district), and another where voters vote strategically to

maximize the chances of different coalition outcomes.

Hobolt and Karp (2010) distinguish between three types of policy-maximizing strategic voting in

proportional representation systems. The first is voting as a 'threshold insurance policy'. Voters

increase the likelihood of a preferred coalition by voting for a minor coalition partner rather than

their preferred party, if they think the minor party may be in danger of not getting enough votes to

pass an electoral threshold. This threshold effect has been found in German elections (Gschwend

2007; Shikano et al. 2009) where there is a formal threshold, but the effect could work in any system

in which a preferred coalition can only be formed where a minor party gets 'enough' votes or seats.

The second type is known as 'coalition-targeted Duvergerian voting' (Bargsted and Kedar, 2009). If a

voter's preferred party is unlikely to be part of the governing coalition, voters opt for a second

preference option among those parties likely to be coalition partners. This kind of second preference

voting is similar to strategic voting in plurality systems where a vote for a sincere preference will

result in that vote being 'wasted'. The third kind of policy-maximizing strategic voting is voting as a

'balancing strategy'. Voters opt for a party which, if in the coalition, will move the coalition closer to

their preferred position (Kedar 2005a; 2005b; Austen-Smith and Banks 1988). Note that this

balancing requires that a voter believes their preferred party may be moved away from their own

position (for example, through watering down of policy under coalition negotiations) by another

potential coalition partner.

In our view, neither 'threshold insurance policy' voting, 'coalition-targeted Duvergerian voting' nor

'balancing strategy' voting need be unique to proportional systems. Each of these types of policy-

maximizing strategic voting could also occur in plurality systems if the voter believes a coalition

government is likely. Indeed, given the likelihood of strategic voting under plurality systems, relative

to proportional systems, we expect that in a system that incentivizes strategic voting and where a

coalition is expected, these types of policy-maximizing strategic votes may be especially important.

Note, however, that strategic voting in plurality systems is supposed to favour two-partyism

(Duverger 1954). If coalition expectations are coupled with a plurality system, then coalition-based

policy-maximizing strategic voting might favour multi-partyism in a plurality system. That is to say,

voters may have incentives to vote in ways in plurality systems thought to be consistent with

proportional systems, but both kinds of strategic voting are associated with the common outcomes

of those systems - coalitions - rather than with the electoral systems per se.

The British case study is central to our thinking. The British plurality system delivered the first

coalition government in 2010 since the post-war period, and the first formal five-year coalition in the

majority of British voters' experiences. Not only was this the first experience of coalition, but many

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voters expected the outcome of the 2015 British general election to result in another period of

coalition. This expectation increased significantly throughout the election campaign as the rhetoric,

strategies and the polls all focused on an outcome where neither main party would win a majority.

The result, despite delivering a surprise victory for the Conservatives, also resulted in the largest

ever vote shares gained by minor parties in any British general election. Despite the collapse of the

Liberal Democrat's vote between 2010 and 2015, the two party share increased by only 2.3 points. In

total, the support for minor parties (not including the Liberal Democrats) increased from 9.8% to

22.9% between 2010 and 2015, as shown in the blue line in Figure 1. The Green line is the share for

others if the Liberal Democrats are included in this category. Figure 1 reveals how the 2015 followed

a trend of increasing support for minor parties, but that it also demonstrates a very significant level

change in this trend.

Figure 1 about here

How could a plurality system, thought to lead to strategic desertion of minor parties, result in a

surge in minor party support? Duverger (1954) expected plurality systems to lead to two-partyism

because a voter who might otherwise cast a sincere vote for a minor party would see their vote

wasted. Instead, strategic desertion of minor parties will result in the voter choosing their second (or

third) preference between potential winning parties. Here we argue for the impact of coalition

government increasing sincere voting and strategic voting for minor parties, irrespective of the

electoral system. Since the Liberal Democrats are not one of the two major parties, and they are

expected to be penalised by the plurality system via strategic desertion, we classify the Liberal

Democrats as a minor party in our theory and analysis. To the three types of policy-maximizing

strategic voting listed above - which are not unique to minor parties but which are highly relevant to

their support (especially threshold insurance policy voting) - we add additional coalition

considerations and incentives specific to enhancing sincere voting for minor parties. These incentives

are not unique to plurality systems or indeed to proportional systems. We propose additions to the

emerging literature on coalition voting incentives, most usually analysed under proportionality.

Coalition Enhances Strategic Voting for Minor Parties

'Threshold insurance policy' voting relates specifically to parties that may not get over an electoral

threshold; therefore to minor parties. According to this view of coalition policy-maximizing strategic

voting, a minor party may be supported rather than a preferred party to ensure a preferred

coalition. And as noted above, the logic of this expectation need not be restricted to formal

thresholds but to any situation in which a voter opts to increase the chance of a favoured coalition

by ensuring a minor party is elected. And as also noted above, this logic need not be restricted to

proportional electoral systems. Thus, given the prospects of coalition, a voter may vote strategically

for a minor party to ensure that party joins a coalition with the voter's preferred party.

'Coalition-targeted Duvergerian voting' will result in strategic voting for a second preference minor

party if that minor party has a greater chance of being part of the coalition than the voter's

preferred party. This is made more likely under coalition since coalition enhances the chance a minor

party can form part of any government.

A 'balancing strategy' will lead to greater minor party voting in the event that a voter believes their

preferred party's policies will be altered by a different coalition formation. For example, this

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explanation could apply to Conservatives who vote UKIP to prevent their party from becoming too

moderate in a coalition with the Liberal Democrats, or to Labour supporters who vote SNP in

Scotland to encourage a more pro-austerity Labour party government than if Labour went into

coalition with the Lib Dems. Alternatively, a moderate Conservative could vote Lib Dem to stop their

party being too right-wing, or a Labour voter could vote Lib Dem for the opposite reason.

Each of these incentives could enhance strategic voting for minor parties (i.e. when a voter prefers

another party but votes for a minor party instead), and all are theorised in the presence of coalition

expectations, not in the presence of proportional electoral systems per se.

Coalition Enhances Sincere Voting for Minor Parties

There are additional reasons, we believe, to expect coalition will also enhance sincere voting for

minor parties. That is, the decision to vote for a voter's first minor party preference, rather than to

vote for a major party alternative.

Voters may be more likely to vote sincerely for a minor party if the incentives to vote strategically for

major parties are reduced. This suggests that the presence of coalition may reduce the Duvergerian

incentives of plurality systems. Duverger (1954) expects strategic voting to favour major parties

because a) a vote for a minor party is wasted in plurality systems; and b) voters have incentives to

choose between alternative governments. Coalition alters these incentives.

There are fewer wasted minor party votes under coalition for two reasons. The first is that a minor

party may have greater influence within a coalition government the greater their popular support,

irrespective of where that vote is distributed. Voting for a minor party may offer a different utility

gain for a voter who thinks their preferred party has a chance of being in coalition. The second is

that, whilst the electoral system will still be a barrier to that party winning in a constituency, if the

voter believes the party has a chance of winning locally, the party has a much greater chance under

coalition of having an influence in the legislature. A voter policy-maximizes by voting sincerely.

Conversely, a major party vote might be more wasted under coalition. If a voter strategically deserts

from a minor party in favour of a major party, they do so because that major party is closer to the

voter's preferred policy position than the alternative. But the policy compromise inherent in

coalition negotiations, and the uncertainty regarding which party will form a government when

coalition is more likely (when the race is relatively close) both diminish the incentive to vote

strategically for a major party second preference when a voter expects a coalition.

One further incentive to vote sincerely for a minor party arises when voters face an ambiguous

choice between potential major parties in government. If coalition enhances uncertainty and

ideological blurring between the likely policy platforms of any major party, minor party voters may

be more likely to vote sincerely and expressively, choosing to use their vote as an expression of their

policy beliefs in the context of unclear policy differences between major parties.

Coalition Enhances Plurality Electoral Incentives

Finally, whilst we have highlighted reasons that coalition expectations will increase sincere and

strategic voting for minor parties, even within a plurality system, we do not argue that there are no

'traditional' plurality system effects for some voters, namely, an incentive to increase strategic

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desertion from minor parties in favour of major parties. These incentives still exist, although they

should be less important. Furthermore, for voters anticipating a coalition outcome they least prefer,

we expect people whose first preference is for minor parties to strategically opt for a major second

preference party. Note that the likelihood of coalition can therefore also enhance the impact of

strategic voting for major parties within a plurality system as voters choose a second preference

within their ideological bloc. This expectation is particularly pertinent in an election in which many

commentators believe that the 'threat' of SNP influence in a Labour-led coalition led many voters to

strategically support the Conservatives. If we are to argue that coalition increases support for minor

parties, we need also to weigh up the relative influence of an effect in the opposite direction.

Hypotheses

Coalition hypothesis:

Expectations of a coalition government increases support for minor parties and decreases

support for major parties

Strategic voting hypothesis:

Expectations of a coalition government increases votes for minor parties among existing major

party supporters

Sincere voting hypothesis:

Expectations of coalition government increases votes for minor parties among existing minor

party supporters

Plurality Duvergerian hypothesis:

Expectations of coalition government increases support for major parties and decreases

support for minor parties when a least preferred party may win locally.

Data and Methods

The dependent variables in our analyses are reported vote using the post election wave of the BES

internet panel for each of the major (Conservatives and Labour) and minor parties (UKIP and Greens

in England, SNP in Scotland and Plaid Cymru in Wales).

Our main explanatory variable measures respondents' perceptions of a likely hung parliament, which

denotes whether a coalition government was considered likely. We calculate this variable from

responses to two questions in the BES internet panel; " How likely do you think it is that the

Conservative | Labour party will form a government on its own", each measured on a 0-10 scale

where 0 = very unlikely and 10 = very likely. We then take the mean of each respondent’s answer to

each question and invert the scale, resulting in a variable that ranges from 0 when respondents think

a hung parliament is completely unlikely (both parties are very likely to form a government on their

own) to 10 when a hung parliament is a near certainty (both parties are very unlikely to form

government on their own). We examine the effects both of the expectation of a hung parliament

before the election campaign (in the pre-election wave of the BES internet panel), and whether

respondents thought a hung parliament was more likely (measured as the absolute change in

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likelihood) between the pre-election wave (4) and the campaign wave (5) of the BES internet panel.

The campaign wave randomised survey responses throughout the 38 days of the election campaign.

Our models control for those factors likely to be correlated with coalition expectations and

underlying predisposition to vote for each party; respondent age, their level of interest in the

election, and their like scores for each of the parties (all measured pre-election). The BES internet

panel used a split-sample design asking like-dislike scores for each of the parties (on a 0-10 scale

where 0 = strongly dislike and 10 = strongly like) and 'propensity to vote' questions, asking: 'How

likely is it that you would ever for X party' (0 = very unlikely, 10 = very likely). In order to maximize

the samples, and also following our analyses finding these questions to be functionally equivalent,

these two questions were combined. They allow us to control for partisan bias in coalition

expectations.

The analyses assess whether coalition expectations lead to greater minor party voting (our coalition

hypothesis) using an alternative-specific conditional logit model using our full sample of English

voters. Here we model Liberal Democrat, UKIP, Green, Labour and Conservative vote choice, and

exclude Scotland and Wales as the different choice sets would violate the independence of

irrelevant alternatives assumption of the model. We test two potential causal mechanisms; whether

respondents thought the party had a chance of winning locally, and whether the respondent

thought the party would have influence in the UK government. These mechanisms could increase

strategic voting, but also sincere voting. These are alternative specific variables, alongside party like-

dislike/PTVs. Chance of winning locally was measured in the campaign wave of the survey by a

question which asked ‘How likely is it that each of these parties will win the General Election in your

local constituency?’ Measured on a 0-100 scale for each party. Chance of being in government was

measured by recoding respondent’s answers to ‘Which of these parties do you think has no real

chance of being part of the next UK government (either forming a government by itself or as part of

a coalition)?‘ The variable is coded 1 when a respondent thought a party had a chance of being part

of the next UK government. Choice specific variables are age, election interest, pre-election

expectations of coalition, and change in expectations.

We then assess the effects of coalition expectations upon strategic voting in favour of minor parties.

To do this, we operationalise strategic voting as a minor party vote among respondents whose most

preferred party (measured on the like and propensity to vote scales) is either of the major parties,

Labour or Conservative, excluding those who have a tied preference for the minor party under

examination. Those who did not have a candidate of the minor party in question running in their

constituency are excluded from the analysis. Using stratified logit models, we examine whether

coalition expectations, and change in coalition expectations, increased the likelihood of strategic

defection from the major to each of the minor parties. We also estimate the effects of perceptions

of the likelihood of winning locally and the chance of being part of the UK government upon this

strategic major to minor party desertion, and we add controls.

We assess the effects of coalition expectations upon sincere voting for minor parties by

operationalising sincere voting as a minor party vote among respondents whose most preferred

party (measured on the like and propensity to vote scales) is the minor party in question, including

those who have a tied preference for another party (each model for each party in turn). Again, those

who did not have a candidate of the minor party in question running in their constituency are

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excluded from the analysis. We examine the effects as listed for the stratified strategic voting

models: coalition expectations, change in coalition expectations, likelihood of winning locally and

chance of being part of the UK government.

Finally, we examine whether the 2015 British general election gives support to the classic

Duvergerian expectation (of strategic defection from minor parties to major parties) under an

additional context; whether the respondent thought a rival party had a chance of winning in the

constituency. This is estimated using the stratified models for those who most prefer a minor party

and using a measure of the closeness of the local constituency race between Labour and the

Conservatives, calculated as the absolute difference between how likely a respondent thought each

of the Conservative and Labour candidates were to win in their constituency. This closeness of race

measure is then interacted with expectation of coalition government.

Results

Table 1 presents our tests of the 'Coalition Hypothesis', namely that expectations of coalition will

increase votes for minor parties at the expense of major parties. We also explore the evidence for

two mechanisms; whether respondents believe a party will win in the constituency, and whether

they believe the party has a chance of influencing policy (being part of the government). Both should

increase the incentives to vote for any party. The first rows of Table 1 support those expectations.

Controlling for the strength of feeling towards a party, the belief that party will win locally and the

belief the party will become part of the government has a significant effect on increasing its votes.

The choice-specific models provide the results for expectations of coalition, and changing

expectations of coalition. In each of the minor party reported vote outcomes (Liberal Democrat,

UKIP or Green, in relation to voting Conservative), we find a significant and positive effect of

coalition expectations, as well as a significant and positive effect of an increase in the expectation

that there would be a hung parliament after the election result of May 7th. Table 1 also reveals an

effect of coalition expectations upon a vote for Labour rather than Conservative.

Table 1 about here

These results support our coalition hypothesis. They denote an effect of coalition expectations

within a plurality system, and an effect which increases minor party voting, as we theorised.

Furthermore, across each of our party choices, there is support for the expectation that voters are

more likely to support each party if they think the party can win, and have a chance of being part of

the government. That is to say, it is the perception of likely influence, controlling for the attachment

a respondent feels towards a party, which has a significant effect upon vote choice.

Strategic Voting Hypothesis

If our strategic voting hypothesis is correct, coalition expectations should lead to a greater likelihood

of a strategic vote for a supporter of a major party, in contrast to the usual plurality expectation of

strategic desertion away from minor party voters to major party voters. Table 2 presents the results

of our stratified logit models for each of the minor parties. These models estimate the effects of

coalition expectations for those respondents whose most preferred party is one of the major parties.

It reveals significant and positive effects, as hypothesised, for four out of five of the minor parties

(for the Liberal Democrats, UKIP, Greens and Plaid Cymru), and no significant effects for the SNP. In

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the Liberal Democrat, UKIP and Green party models we find significant effects for coalition

expectations and for changes in coalition expectations, and for Plaid Cymru for change only.

Table 2 about here

The following Figure 2 presents the predicted probability of voting for each of the minor parties

(among major party preferers). Note the Y axis ranges from 0.00 to 0.15.

Figure 2 about here

In addition to the main effects reported in Table 2, we find support for our mechanisms, namely, the

likelihood each party will win in the constituency (significant in the Liberal Democrat, UKIP and

Green models), and the chance the party will be part of the UK government (in the Liberal Democrat,

UKIP, Green and Plaid Cymru models). It is interesting that neither explanation holds for the SNP,

suggesting that desertion to this party was not motivated strategically but via other explanations. It

is notable that we do not find an effect for the SNP in the opposite direction given the political

climate in 2015; that is, we do not find a negative effect of the expectation that the SNP would be

part of the UK government, or whether the party would win locally, on the decision to vote for a

major party rather than the SNP.

Sincere Voting Hypothesis

If we find support for our sincere voting hypothesis, we should find significant effects of coalition

expectations on votes for minor parties among respondents whose most preferred party is the

minor party in question. Table 3 presents the results of the stratified logit models for each party,

respectively. The results confirm our expectations. There is a positive and statistically significant

effect of coalition expectations before the election for each of the minor party models: for the

Liberal Democrats, UKIP, the Greens, SNP and for Plaid Cymru. There are also additional effects for

changes in expectations in the expected direction for the Liberal Democrats, UKIP and Plaid Cymru.

Table 3 about here

It is interesting that the newly theorised sincere voting incentives appear to be somewhat stronger

in the 2015 UK general election than our results for strategic minor party voting. Figure 3 presents

the predicted probabilities of voting for each of the minor parties by coalition expectations. The y

axis, ranging from 0 to 1, reveals much stronger effects than we observed in Figure 2.

Figure 3 about here

Table 3, above, also provides further support for the expected mechanisms. We find significant

effects of expectations the party will win locally in each of the party models, and significant effects

for the expected change of being part of the UK government for the Liberal Democrats, UKIP and the

Greens, controlling for the strength of feeling to each of the parties, respectively.

Plurality Duvergerian Hypothesis

Finally, we test the reverse expectation to our theory, namely the classic Duvergerian prediction that

minor party supporters will defect strategically to major parties in a plurality system. Given the

findings above, we examine whether this occurs within a certain context - namely, when the

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respondent thinks a rival party may win. We estimate this context by the perceived closeness of the

local race, and interacting whether a hung parliament also made it less likely that a respondent

would vote for a minor party when they perceived this 'threat'. For example, were voters more likely

to vote Conservative rather than for a minor party if they thought Labour could win in their

constituency and they thought there could be a coalition? Or were respondents more likely to vote

Labour rather than Green if they thought the Conservatives could win locally and defeat a Labour

candidate (or a Labour candidate could beat a Conservative) under coalition expectations?

The results in Table 4 provide little support for this classic plurality expectation. For most

respondents, the perception of a close race between the two major parties had no effect on their

vote intention. The exception to this were Green Party supporters, for whom the effects of hung

parliament expectations were diminished when they perceived a close race between Labour and the

Conservatives, as illustrated in figure 4.

Table 4 about here

Figure 4 about here

The tests of the Duvergian plurality hypothesis lend further weight to our coalition, strategic voting

and sincere voting hypotheses of increased support for minor parties, since there appears to be

almost no statistical effect of a classic plurality prediction in the opposite direction. In additional

checks for the plurality expectation, and in light of the widely held view that the SNP threat in 2015

handed a victory to the Conservatives, we also modelled whether respondents thought the SNP

could a) have a chance of being part of the UK government, and b) whether respondents disliked the

SNP. These results strengthened the effects for coalition expectations, supporting our coalition,

strategic and sincere voting hypotheses. We found some potential effects of an SNP threat causing

major parties to pick up more votes, but the results were inconclusive. We intend to explore this

further. Another future next step might be to model the likelihood of winning, either locally or

nationally, of a respondents' least preferred party.

Conclusions

We argued that one of the reasons the UK's 2015 general election delivered a step-change in votes

for minor parties is because the 2015 general election was fought in a new context of expectations

of coalition. Our theory of coalition effects predicted that coalition would increase strategic

incentives to vote for minor parties, and would also increase incentives to vote sincerely. These

expectations go against the grain of classic plurality electoral system predictions (Duverger 1954)

which expect minor parties to lose votes due to strategic desertion in favour of major parties, thus

delivering a two-party system, and they also go against the grain of much commentary of the 2015

British general election. There was a great deal of speculation that the likelihood of a hung

parliament - not least an incorrect likelihood of a hung parliament (due to the errors in the opinion

polls which led to an over-estimation of Labour's support and an under-estimation of the

Conservatives') - led voters to support the Conservatives. Our findings challenge both assumptions.

We find that coalition expectations increased the strategic incentives to vote for minor parties, and

they increased the incentives to vote sincerely for minor parties. Whereas the existing literature has

predicted that coalitions would increase strategic voting (Austen-Smith and Banks 1988; Kedar

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2005a; 2005b; Gschwend 2007; Bargsted and Kedar, 2009; Shikano et al. 2009; Hobolt and Karp

2010), they have neither (a) specified those incentives in relation to minor parties, (b) identified that

those incentives could occur in a plurality electoral system as well as under proportional

representation, or (c) considered in any way the effects of coalition upon sincere voting.

Our theory of coalition-induced sincere and strategic voting for minor parties offers three novel

features. First, we add sincere voting incentives to the existing literature pointing to strategic voting

incentives. Second, we argue that none of these incentives need be specific to proportional systems.

This means that those assumptions of the effects of proportionality are effects of the institutions

that arise from proportionality; coalition, rather than from proportionality per se. The third is we

explicitly reveal how incentives arise at the local level and at a national level. This is perhaps implied

in analyses of strategic voting under coalitions, but it has not been stated or tested directly. Our

theory illuminates how the combination of the national level context and the local level context

work to alter voting incentives under the prospects of coalition.

This paper also has important implications for how we understand and interpret the 2015 British

general election and the rising support for minor parties. An interesting paradox emerges. In an

election in which the expectation of a hung parliament was so important, the election resulted in an

unexpected single-party government. Whether this surprise outcome causes voters in future to off-

set their expectations in their voting considerations can only be speculated about. It is certainly the

case that while the UK has delivered a single-party government against prior expectations, the rise in

voting for minor parties continues to contribute to the conditions making coalitions more likely.

14

Bibliography

Alvarez, R. M. and J. Nagler (2000). "A new approach for modelling strategic voting in multiparty elections." British Journal of Political Science 30(01): 57-75. Armstrong Ii, D. A. and R. M. Duch (2010). "Why can voters anticipate post-election coalition formation likelihoods?" Electoral Studies 29(3): 308-315. Austen-Smith, D. and J. Banks (1988). "Elections, coalitions, and legislative outcomes." American Political Science Review 82(02): 405-422. Bargsted, M. A. and O. Kedar (2009). "Coalition‐targeted Duvergerian voting: how expectations affect voter choice under proportional representation." American Journal of Political Science 53(2): 307-323. Bowler, S., et al. (2010). "Strategic coalition voting: Evidence from New Zealand." Electoral Studies 29(3): 350-357. Carman, C. J. and R. Johns (2010). "Linking coalition attitudes and split-ticket voting: The Scottish Parliament elections of 2007." Electoral Studies 29(3): 381-391. Cox, G. W. (1997). Making votes count: strategic coordination in the world's electoral systems, Cambridge Univ Press. Cox, G. W. (1997). Making votes count: strategic coordination in the world's electoral systems, Cambridge Univ Press. Cox, G. W. and M. S. Shugart (1996). "Strategic voting under proportional representation." Journal of Law, Economics, and Organization 12(2): 299-324. Duverger, M. (1959). Political parties: Their organization and activity in the modern state, Methuen. Fisher, S. D. and S. B. Hobolt (2010). "Coalition government and electoral accountability." Electoral Studies 29(3): 358-369. Gschwend, T. (2007). "Ticket‐splitting and strategic voting under mixed electoral rules: Evidence from Germany." European Journal of Political Research 46(1): 1-23. Hobolt, S. B. and J. A. Karp (2010). "Voters and coalition governments." Electoral Studies 29(3): 299-307. Kedar, O. (2005). "How diffusion of power in parliaments affects voter choice." Political Analysis 13(4): 410-429. Kedar, O. (2005). "When moderate voters prefer extreme parties: Policy balancingin parliamentary elections." American Political Science Review 99(02): 185-199. Leys, C. (1959). "Models, theories, and the theory of political parties." Political Studies 7(2): 127-146. McCuen, B. and R. B. Morton (2010). "Tactical coalition voting and information in the laboratory." Electoral Studies 29(3): 316-328.

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McKelvey, R. D. and P. C. Ordeshook (1972). "A general theory of the calculus of voting." Mathematical applications in political science 6: 32-78. Meffert, M. F. and T. Gschwend (2010). "Strategic coalition voting: Evidence from Austria." Electoral Studies 29(3): 339-349. Powell, G. B. (2000). Elections as instruments of democracy: Majoritarian and proportional visions, Yale University Press. Shikano, S., et al. (2009). "Strategic voting under proportional representation: threshold insurance in German elections." West European Politics 32(3): 634-656.

16

Figures

Figure 1: Vote shares for minor parties, 1945-2015

0

5

10

15

20

25

1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

Other Vote Share Other Seat Share

17

Figure 2: Stratified Vote Choice by Hung Parliament Expectation among Major Party Supporters

18

Figure 3: Stratified Vote Choice by Hung Parliament Expectation among Minor Party Supporters

19

Figure 4: Predicted Probabilities of Voting Green by closeness of race and coalition expectations

20

Tables

Table 1: Alternative-Specific Logit Model of 2015 Vote Choice

Party Like/PTV 2.082***

(0.0265)

Win Constituency W5 0.0145***

(0.000587)

Chance Government 0.321***

(0.0609)

Labour Hung Parliament Expectation W4 0.0731***

(0.0215)

Hung Parliament Expectation Change -0.00328

(0.0175)

Age -0.00965***

(0.00236)

Election Interest 0.0792

(0.0515)

Constant -0.140

(0.222)

Liberal Democrat Hung Parliament Expectation W4 0.184***

(0.0253)

Hung Parliament Expectation Change 0.0524**

(0.0208)

Age -0.00235

(0.00275)

Election Interest 0.140**

(0.0619)

Constant -2.725***

(0.271)

UKIP Hung Parliament Expectation W4 0.125***

(0.0221)

Hung Parliament Expectation Change 0.0486***

(0.0175)

Age 0.00206

(0.00273)

Election Interest -0.00616

(0.0536)

Constant -1.994***

(0.246)

Green Party Hung Parliament Expectation W4 0.165***

(0.0310)

Hung Parliament Expectation Change 0.0724***

(0.0264)

Age -0.0230***

(0.00347)

Election Interest 0.168**

(0.0787)

Constant -2.017***

(0.338)

Observations 67202

Cases 13905

Statistical significance: * p<0.05, ** p<0.01, *** p<0.001

21

Table 2: Model of Minor Party Voting in 2015 among Major Party Supporters

Liberal

Democrats UKIP Green Party SNP Plaid Cymru

Hung Parliament Expectation W4 0.182*** 0.174*** 0.101* -0.110 0.141

(0.0285) (0.0400) (0.0573) (0.0782) (0.124)

Hung Parliament Expectation Change 0.0944*** 0.103*** 0.0934** 0.0826 0.233***

(0.0230) (0.0309) (0.0465) (0.0599) (0.0859)

Win Constituency W5 0.0330*** 0.0108*** 0.0128*** -0.000688 0.00978

(0.00177) (0.00276) (0.00426) (0.00510) (0.00663)

Party Like/PTV 0.770*** 1.410*** 1.126*** 1.861*** 0.370

(0.0589) (0.0958) (0.130) (0.196) (0.237)

Age 0.00114 0.00835* -0.0202*** -0.00957 -0.0179

(0.00303) (0.00471) (0.00588) (0.00862) (0.0129)

Election interest 0.0659 -0.479*** -0.0918 -0.459** -0.584**

(0.0803) (0.0948) (0.154) (0.184) (0.268)

Chance Government 0.407** 0.455*** 0.522*** 0.0277 1.102***

(0.163) (0.165) (0.202) (0.359) (0.419)

Constant -6.249*** -4.579*** -4.432*** 0.703 -2.447*

(0.387) (0.467) (0.673) (0.875) (1.277)

N 11755 11075 10173 1405 1018

Pseudo R2 0.1697 0.1814 0.1310 0.2247 0.1156

Statistical significance: * p<0.1, ** p<0.05, *** p<0.01

22

Table 3: Model of Minor Party Voting in 2015 among Minor Party Supporters

Liberal

Democrats UKIP Green Party SNP Plaid Cymru

Hung Parliament Expectation W4 0.164*** 0.202*** 0.0916*** 0.216*** 0.441***

(0.0270) (0.0194) (0.0239) (0.0521) (0.0778)

Hung Parliament Expectation Change 0.0557** 0.0789*** 0.00752 0.0657 0.159***

(0.0221) (0.0158) (0.0210) (0.0439) (0.0581)

Win Constituency W5 0.0218*** 0.0115*** 0.00848*** 0.00895** 0.00872**

(0.00176) (0.00145) (0.00196) (0.00416) (0.00442)

Party Like/PTV 0.605*** 0.984*** 0.754*** 2.468*** 0.840***

(0.0714) (0.0713) (0.0740) (0.226) (0.217)

Age 0.00906*** 0.00568** -0.0152*** -0.0145** -0.0105

(0.00299) (0.00269) (0.00283) (0.00651) (0.00928)

Election interest 0.152** 0.0204 0.0134 -0.0195 0.516**

(0.0682) (0.0526) (0.0688) (0.148) (0.208)

Chance Government 0.462** 0.590*** 0.458*** 0.347 0.449

(0.187) (0.0974) (0.0947) (0.283) (0.280)

Constant -4.241*** -3.830*** -2.338*** -1.219* -5.747***

(0.346) (0.264) (0.295) (0.680) (1.037)

N 2198 3572 2707 1687 329

Pseudo R2 0.1209 0.1120 0.0809 0.2005 0.1845

Statistical significance: * p<0.1, ** p<0.05, *** p<0.01

23

Table 4: Models of Minor Party Voting in 2015 among Minor Party Voters, by Strategic Context

Liberal Democrats UKIP Green Party SNP Plaid Cymru

Hung Parliament Expectation W4 0.173*** 0.190*** 0.000129 0.207** 0.482***

(0.0428) (0.0301) (0.0387) (0.0860) (0.121)

Hung Parliament Expectation Change 0.0415* 0.0803*** -0.00216 0.0649 0.155***

(0.0228) (0.0163) (0.0218) (0.0445) (0.0599)

Win Constituency W5 0.0229*** 0.0120*** 0.00975*** 0.0114*** 0.00883*

(0.00182) (0.00150) (0.00203) (0.00430) (0.00452)

Party Like/PTV 0.594*** 0.985*** 0.729*** 2.384*** 0.834***

(0.0736) (0.0733) (0.0763) (0.229) (0.220)

Age 0.00917*** 0.00559** -0.0135*** -0.0152** -0.0123

(0.00308) (0.00276) (0.00291) (0.00662) (0.00956)

Election interest 0.163** 0.0129 0.00166 0.0274 0.569***

(0.0701) (0.0540) (0.0714) (0.150) (0.217)

Chance Government 0.403** 0.593*** 0.469*** 0.463* 0.398

(0.197) (0.101) (0.0979) (0.281) (0.284)

Local Lab-Con close race 0.0111** -0.00116 -0.00618 -0.00750 0.00598

(0.00471) (0.00322) (0.00413) (0.00995) (0.0124)

Hung Parliament Expectation W4 X -0.000663 0.000319 0.00186*** -0.0000180 -0.000841 Local Lab-Con close race (0.000779) (0.000542) (0.000666) (0.00155) (0.00195) Constant -4.611*** -3.791*** -2.068*** -1.203 -6.080*** (0.402) (0.293) (0.342) (0.772) (1.132)

N 2108 3406 2573 1668 320 Pseudo R

2 0.1306 0.1133 0.0847 0.1961 0.1888

Statistical significance: * p<0.1, ** p<0.05, *** p<0.01