A New Approach to Measure Tactical Voting: Evidence from the British

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Applied Economics Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/raec20 A new approach to measure tactical voting: evidence from the British elections Daniel Mullera & Lionel Pageb a Department of Economics and SFB-884, University of Mannheim, Mannheim, Germany b School of Economics and Finance, Queensland University of Technology, Brisbane, Australia Published online: 18 Mar 2015.

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To cite this article: Daniel Muller & Lionel Page (2015) A new approach to measure tactical voting: evidence from the British elections, Applied Economics, 47:36, 3839-3858, DOI: 10.1080/00036846.2015.1019037 To link to this article: http://dx.doi.org/10.1080/00036846.2015.1019037

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A new approach to measure tactical voting: evidence from the British elections

Daniel Mullera,* and Lionel Pageb aDepartment of Economics and SFB-884, University of Mannheim, Mannheim, Germany bSchool of Economics and Finance, Queensland University of Technology, Brisbane, Australia

Although tactical voting attracts a great deal of attention, it is very hard to measure as it requires knowledge of both individuals’ voting choices as well as their unobserved preferences. In this article, we present a simple empirical strategy to nonparametrically identify tactical voting patterns directly from balloting results. This approach allows us to study the magnitude and direction of strategic voting as well as to verify which information voters and parties take into account to determine marginal constituencies. We show that tactical voting played a signiﬁcant role in the 2010 election, mainly for Liberal–Democratic voters supporting Labour. Moreover, our results suggest that voters seem to form their expectations based on a national swing in vote shares rather than newspaper guides published in the main media outlets or previous election outcomes. We also present some evidence that suggests that campaign spending is not driving tactical voting.

Keywords: tactical voting; British elections; expectations JEL Classiﬁcation: H89; D72; D84

All this talk of tactical voting upsets me though – the expression of their preferences. It has been argued no-one should EVER have to even think about

Downloaded by [Queensland University of Technology] at 18:27 19 May 2015 that, for a democracy to function properly, voters voting tactically – you should be able to vote for should face incentives to truthfully reveal their prefer- the party you want. ences. Tactical or strategic voting, on the other hand, Andrew Whickey, a Liberal Democrats blogger, refers to a situation when voters do not vote according 2010 to their sincere preferences, typically with the inten- tion to inﬂuence the outcome in a preferred way. I. Introduction Tactical voting has long been debated in the political science literature.1 It is typically deﬁned as a Elections are at the very core of democracies. They situation where it is in a voter’s best interest to vote are means to give power to the people by allowing for for a less preferred candidate, or as Fisher (2004) put

*Corresponding author. E-mail: [email protected] 1 See, for example, Galbraith and Rae (1989), Johnston and Pattie (1991) and Fieldhouse et al. (1996).

© 2015 Taylor & Francis 3839 3840 D. Muller and L. Page it, ‘a tactical voter is someone who votes for a party Besides the large attention tactical voting has they believe is more likely to win than their preferred received from experts, layman and the media, there party, to best influence who wins in the constituency’ are considerable difficulties when estimating strate- (Fisher, 2004, p. 157).2 In general, there are at least gic behaviour in elections. These difficulties mainly two ways to vote strategically. First, a voter can vote arise from the fact that in order to study this phenom- for a less preferred candidate because the favourite enon, knowledge of the political preferences as well candidate’s chances of winning are low (which is as of the actual vote cast is necessary. Using survey sometimes called ‘positive strategic voting’). data might be a natural approach but is obviously Second, a voter can decide to vote for a less preferred plagued with several difficulties like recall bias candidate in order to increase the chances of winning (respondents typically have flawed memories about for the preferred candidate (‘negative strategic vot- their past behaviour) and social desirability bias (tac- ing’), see Southwell (1991). tical voting might be seen as socially undesirable and With very close results predicted by the pre-elec- hence it is concealed). A more indirect way used to tion polls, the issue of tactical voting in the British identify strategic voting is to model individual (or elections of 2010 was a more hotly debated topic than constituency) characteristics in order to estimate ever before.3 Key figures in the Labour Party – counterfactual vote choices (or election outcomes) including Alan Johnson (Home Secretary), Ed Balls with and without the possibility to vote tactically. (Children’s Secretary) and Peter Hain (Wales This approach typically employs discrete choice Secretary) – called for backing the best Liberal/ models like probits. A problem with this approach Labour candidate to beat the Conservative candidates is that one needs to make the strong assumption that in marginal (that is, close) constituencies. Compass, a conditional on observables there are no omitted fac- Union organization, supported tactical voting and tors influencing vote choices (or trends in party designed a voting guide for tactical voting in margin- shares respectively). This supposition seems some- als. Numerous left-leaning newspapers advised times hard to justify in reality. voters to vote tactically and many proposed voting In this article, we propose a novel nonparametric guides, for example, the Daily Mirror, the Guardian, strategy to analyse electoral data, which allows us to Independent and New Statesman. Given this specific study tactical voting patterns in the latest British situation, in particular the calls from some well- election. This approach relies on visual inspection known politicians in the Labour Party itself, one of the change in party shares in 2005 versus the 2010 may expect tactical voting to have been significantly elections as a function of the Labour – Conservative, higher than in precedent elections. Liberal Democrats – Conservatives vote share differ- Reducing incentives to tactical voting was also a ences, respectively. While this approach avoids the key argument in the debate surrounding the refer- caveats of the aforementioned strategies, it comes at endum in 2011 to change the voting system in the the cost that the magnitude of tactical voting has to United Kingdom from First-Past-The-Post (FPTP) be ‘eye-balled’ from the plotted data, that is the to alternative voting (AV).4 One of the major approach does not easily deliver precise criticisms made by the opponents of the traditional statistical estimates of the size of tactical voting. voting system used in Britain is that it fosters Nevertheless, it allows us to examine the importance Downloaded by [Queensland University of Technology] at 18:27 19 May 2015 tactical voting to the benefit of the two main parties of the phenomena and additionally we are able to and hence potentially hinders representation study several related questions. It seems that tactical according to the true preferences (Electoral voting played a significant role in the last general Reform Society, 2010). election in the United Kingdom. According to our

2 It has become common to refer to this phenomena as ‘tactical voting’ in the context of the British election and as ‘strategic voting’ in the US elections. Here, we do not make this distinction and use the terms interchangeably. 3 The closeness of the election that year was due to the specific national swing observed which in turn was likely driven by short-term changes in the popularity of the different parties. 4 In alternative voting systems, or instant run-off voting, instead of voting for a single candidate, voters rank the candidates in order of their preferences. The votes are then counted and candidates ranked as a function of the ‘first preferences’, then the lower ranked candidates are eliminated and the votes in their favour are transferred to the next best preferred candidates of their voters. A new approach to measure tactical voting 3841 estimates, mainly former Liberal Democratic voters shows that the search for strategy-proof voting sys- supported Labour in constituencies where a close tems is doomed to fail, some systems may be more or race between Labour and the Conservatives was less prone than other to inducing strategic behaviour. expected.5 In particular, the FPTP system seems to be particularly Moreover, this approach allows us to make three prone to strategic considerations by the voters.6 The further contributions to the tactical voting literature. propensity of the FPTP system to foster tactical voting First, we study the information sets voters use to form has long been suggested (Duverger, 1954). What was expectations about election outcomes, using the 2010 initially a conjecture is now known as ‘Duverger’s general election as an example. We find some evi- law’, see also Riker (1982). Palfrey (1989) proposed dence that voters seem to be more sophisticated than a mathematical proof of this ‘law’, showing that in a voting guides compiled by British newspapers and model with rational voters and three parties, only two based their expectations on a nationwide uniform parties end up having positive vote shares. In this swing assumption (which performed better in pre- setting, non-Duvergean equilibria can appear in rare dicting election outcomes). Second, we discuss the occasions when two parties are tied for second place. relevance of campaign spending in this context and The electoral reality sometimes departs from this pre- present some evidence that it does not seem to have a diction though. Whilst the political history of the major influence on voter’s choices. Third, we test the United Kingdom has shown that the FPTP system is prediction that the propensity to vote tactically clearly associated with a two-party system (Labour increases with the winning margin once the and Conservatives), there is usually a third minor (expected) distance of the third party in the race is party, the Liberal Democrats, which has experienced controlled for, which is what some theoretical evi- significant growth over the recent years. To explain dence is suggesting (Myatt, 2007). We test this pre- such a discrepancy, Myatt (2007) has proposed a diction using a general additive model and, in model where, contrary to Palfrey’s hypothesis, voters contrast to this prediction, we find that tactical voting have imperfect information on the preferences of other seems to be highest in close races even after control- voters, which prevents full coordination of tactical ling for the distance from contention. voters on their best contender. For instance, in a situa- The remainder of the article is organized as fol- tion with two left-wing candidates and one right-wing lows. Section II sets our article in relation to the candidate, some potential left-wing (tactical) voters strategic voting literature. Section III shows that tac- may fail to identify their best strategic option.7 tical voting patterns suggest voters used uniform Besides theoretical attempts to explain the swing models to determine marginal constituencies. observed patterns of tactical voting, there have been Section IV looks at the party spending patterns and numerous empirical studies trying to quantify tactical their influence on vote shares. In Section V we show voting patterns. Naturally most studies look at the that the distance of the third party does not seem to British general elections.8 influence voting behaviour. Section VI discusses the Nevertheless, there are also studies that look at US results and concludes. primaries, see, for example, Abramson et al. (1992) and Cain and Gerber (2002). In general, there are three approaches to estimate tactical voting.9 Downloaded by [Queensland University of Technology] at 18:27 19 May 2015 II. Relation to Literature on Tactical The indirect approach relies on modelling counter- Voting factual voting choices (that is, with and without the opportunity to vote tactically) using observable con- Although the well-known Gibbard–Satterthwaite stituency (or individual) characteristics. Studies theorem (Gibbard, 1973; Satterthwaite, 1975) using this approach typically attempt to estimate the

5 We will discuss later on in more detail how these expectations can be formed. 6 But it is certainly not the only system where strategic voting can be expected. For example, Meffert and Gschwend (2010) and McCuen and Morton (2010) find empirical evidence of tactical coalition voting in a proportional representation system, that is voters might try to vote such that they maximize the winning probability of their preferred coalition. 7 Cox (1997) provides a comprehensive investigation of this topic. 8 See, for example, Niemi et al. (1992), Johnston and Pattie (1991), Lanoue and Bowler (1992), Alvarez and Nagler (2000) and Fisher (2000). 9 Blais et al. (2005) provide a comparison of the two main approaches – the direct and the indirect one. 3842 D. Muller and L. Page impact of perceived closeness of the race in each purposes). Studies using the British Election Survey district on voting choices and then include explana- typically find that around 5% to 10% of voters cast tory variables that are supposed to measure exactly their ballot strategically. Fisher (2000), for example, this. For example, Blais et al. (2005) use a probit estimates that around 5% in 1987, 7.7% in 1992 and model to determine how a vote is cast and include the 8.5% in 1997 voted insincerely. These numbers also perceived probability of a candidate winning in this suggest that tactical voting has slightly increased in model, which is, they argue, indicative for tactical the last decades.12 However, survey studies face voting. Using Canadian elections as an example, they numerous difficulties, which may be particularly pro- find that around 4% of the voters seem to have voted blematic in the study of tactical voting. First, answers insincerely. Cain (1978) suggests that tactical voting to questions on tactical voting may be affected by the is higher in those seats marked as marginals based on well-known recall bias in political surveys, which the results of the previous elections. He also employs systematically advantages the winning parties, see a logit model approach and finds some indications for Himmelweit et al. (1978) and Eubank and Gow tactical voting. Alvarez and Nagler (2000) (and simi- (1983). In a situation with two major parties, this larly, Alvarez et al. (2006)) estimate a multinomial bias could exaggerate the number of tactical voters probit model of voter choices based on survey data in their favour. Second, survey questions on tactical and include a measure of expected closeness of the voting may be affected by a social desirability bias. parties in each district as explanatory variable.10 There is extensive evidence that tactical voting is They interpret this measure as the likelihood that a seen as socially undesirable (or even unethical) by vote is wasted and hence as the potential for strategic some voters. Hence there may be incentives to con- voting. They find that around 8% of voters voted ceal a tactical vote, see Galbraith and Rae (1989). strategically, which is roughly in line with other Finally, if voters cast their vote strategically, they can estimates.11 also be strategic in their answers to political surveys. However, this approach relies on the assumptions Meirowitz (2005) shows that tactical considerations that voting decisions are completely determined by can also lead to misdeclaration of preferences in observables and on the accuracy of the answers when polls. If respondents perceive political surveys in a survey data are exploited. Both suppositions are similar way as polls, they may well choose to answer rather unlikely to be fulfilled in reality. Also, they tactically. They could, for example, hide that they typically rely on a measure of closeness of the elec- voted tactically to prop up the proportion of voters toral race in a constituency, it is however unclear how for their first-choice party. These problems cast doubt voters form expectations. Our article contributes to on the validity of surveys that ask voters to truthfully this problem, as it allows us to make statements about reveal their intentions.13 how sophisticated voters form their expectations. We The third approach infers patterns of strategic vot- find some evidence that they are not purely backing from aggregate level electoral data. Particularly it ward-looking, but more sophisticated. involves estimating vote swings on a district level, The direct approach exploits survey data, mainly for example, using flow-of-the-vote matrices, from the British Election Study, which provides pre- and which tactical voting patterns are deduced.14 post-election survey data, including questions on the Johnston and Pattie (1992) estimate flow-of-the-vote Downloaded by [Queensland University of Technology] at 18:27 19 May 2015 effective vote, the first choice party, or the reason for matrices for the British elections of 1983 and 1987. voting (and whether it was explicitly cast for tactical They find some evidence for tactical voting and that

10 Interestingly, and related to the article at hand, they assume that expectations are formed based on the previous election result. This assumption is strong and is, as we will show later on, empirically most likely not accurate. 11 See also Lanoue and Bowler (1998), Blais and Nadeau (1996), Kim and Fording (2001) and Blais et al. (2001) for studies using the indirect approach of measuring tactical voting. 12 See also Duch and Palmer (2002), Heath and Evans (1994), Niemi et al. (1992) and Niemi et al. (1993) for studies using the direct approach. 13 See also Wright (1990), Wright (1992) and Atkeson (1999) regarding vote misreporting issues and Alvarez and Nagler (2000) who provide a more detailed critique of the empirical tactical voting literature. Blais et al. (2005) discuss advantages and disadvantages of both approaches in more detail. 14 See, for instance, McCarthy and Ryan (1977) and Upton (1978) for early transition probability estimates (although they do not consider tactical voting in particular). A new approach to measure tactical voting 3843 it was strongest in marginal constituencies.15 knowledge and concludes that people mainly form Galbraith and Rae (1989) use electoral results and their expectations about political outcomes using demographic information on the constituencies to heuristics. Hence voters do not seem to be comple- check whether similar electorates voted differently tely sophisticated and forward-looking. Nadeau depending on the relative position of the contenders et al. (1994) provide a study of expectation formation at the last election. They also conclude that there are among British voters. Among other things, they find empirical indications for strategic voting. However, that voters do not seem to be fully sophisticated when this approach naturally runs into the ‘ecological forming their expectation. Looking at the 1988 inference problem’ (King, 1997), which refers to Canadian election, Blais and Bodet (2006) conclude the problem of deducing micro-level behaviour that voters form their expectations based ‘on the basis from macro-level data. In general the usefulness of of both “objective” contextual information and their aggregate level data for individual level inference own personal preferences’ (Blais and Bodet, 2006, seems questionable. p. 488). Lastly, Meffert et al. (2011) look at multi- This article is different from other papers in that it party systems in Germany and Austria to investigate cannot be classified under one of the three cate- which factors determine the quality and precision of gories mentioned above. We do not rely on survey the expectation of the electorate. data but solely on actual vote choices. Moreover, A different but related issue is that of strategic our approach does neither build on modelling vote voter turnout. Before voters decide whether to cast a choices accurately using available observable char- strategicvoteornot,theyhavetodecidewhetherto acteristics nor on ecological regressions. Instead we vote at all or to abstain. One strand of literature has nonparametrically estimate the change in vote emerged that examines the relationship between the shares between two parties as a function of the expected closeness of the electoral race and turnout. previous election result using constituency level Rational choice theory predicts that voters react to data. This technique allows us to avoid all detri- the probability of being pivotal and hence also to the ments of the common three main approaches for expected closeness. While the empirical evidence is measuring tactical voting.16 We see our approach not completely conclusive, it seems that there is by as complimentary and not as a replacement for now a consensus that increased expected closeness of others. It allows us to study expectation formation the electoral race increases voter turnout. For exam- of British voters since we are able to compare the ple, Shachar and Nalebuff (1999) present empirical plotted estimates under different expectation forma- evidence for this relation in the US presidential election assumptions. tions, as predicted by rational choice theory. They Although it has been widely recognized that peo- also provide a theoretical framework that is able to ple’s expectations about election outcomes play a accommodate this observation. Moreover, Endersby vital role in determining strategic behaviour, it has et al. (2002) find a strong and positive relation not been studied more closely until now. Research in between turnout and closeness in Canadian federal this area usually takes past election results as best elections. Looking at the United States, British and guess for future results in order to determine mar- French elections, respectively, Cox and Munger ginal constituencies in the upcoming election.17 It is (1989), Pattie and Johnston (2001) and Fauvelle- Downloaded by [Queensland University of Technology] at 18:27 19 May 2015 however doubtful whether this is in fact the best Aymar and François (2006) also report empirical description of the average voter’s behaviour. We evidence for a positive relation between closeness will discuss that issue in more detail in the next and voter participation. Matsusaka (1993), on the section. One of the few studies that looks more clo- other hand, does not find statistically significant rela- sely into this is Lago (2008). He uses survey data tion between both variables looking at Californian from Spain to retrieve information on political elections and Kirchgässner and Zu Himmern (1997)

15 See also Fieldhouse et al. (1996) and Johnston et al. (1997). 16 As mentioned before, our approach needs a distinct identification assumption and comes at the cost of not allowing for point estimates. Naturally, all empirical strategies come along with some advantages and some drawbacks. 17 See Alvarez and Nagler (2000), for example. 3844 D. Muller and L. Page report only mixed evidence from East and West- to two systems before, there are probably less incen- German elections.18 tives to vote strategically (Ganser and Veuger, 2010). Abramson et al. (2009) however compare strategic Tactical voting worldwide voting under FPTP and PR challenge that conclusion. As mentioned before, tactical voting behaviour is They argue that because there are typically more small overwhelmingly associated with the FPTP system in parties under PR systems there are also more oppor- Great Britain. Nevertheless, it has been shown that no tunities to waste a vote. Looking at elections in electoral system is theoretically immune against stra- Mexico, the United States, Britain, Israel and the tegic considerations and hence tactical voting can be Netherlands they seem to confirm these conclusions. expected to occur in other (democratic) countries as Gschwend et al. (2004) show that strategic voting is well. Here, we briefly summarize the sparse interna- also present in Finland which, they argue, is a parti- tional evidence from other countries on the extent of cularly hard testing ground due to particularities of the tactical voting. We organize the discussion around voting system. In the PR systems, also opportunities four different systems: FPTP, Run-off-, proportional- for strategic coalition voting arise that are not present and AV. An excellent additional source is Cox (1997). under FPTP voting. Bowler et al. (2010) fi nd evidence TheFPTPsystemisalsopartlyusedintheUnited for strategic coalition voting in New Zealand; Meffert States. In such a ‘winner takes all’system, one might be and Gschwend (2010) for Austria. McCuen and tempted to think that all votes for a third party might Morton (2010) present evidence from laboratory elec- mean supporting the winning party. Hence, under tions. Blais (2002) on the other hand finds little evi- FPTP the ‘wasted vote’ logic might be particularly dence for strategic voting in Canadian plurality prevalent and significantly distort the results. One elections. example from the United States is the Gore versus The last system mentioned here in more detail is the Bush presidential election of 2002 where a left-wing AV system as, for instance, used in Australia where candidate impacted on the overall result in favour of there are no ‘wasted votes’ as votes for an eliminated Bush (Burden and Jones, 2009). Nevertheless, there candidate are transferred to the next best preferred does not seem to be a reliable quantification of the candidate on the ballot. This is considered as a factor amount of strategic voting in the United States. limiting the likelihood of tactical voting in this system. Run-off elections (a two-round voting system Gschwend (2004) also argues that the amount of tac- where typically only two candidates proceed to the tical voting is smaller under AVsystems because voting second round) are in general thought of as minimizing strategically under the AV system requires knowledge opportunities to cast a wasted vote. Such a voting of the complete ranking of candidates by other voters. system is, for example, used in France. Nevertheless, opportunities for ‘compromise voting’ (voting for one of the three leading candidates in the first round) and III. A New Approach to Identify Tactical ‘push over’ voting (voting for an unpopular candidate Voting in order to increase the chances that the preferred candidate meets the unpopular one in the second Empirical strategy and voters’ subjective beliefs in round) occur. Again, there does not seem to be reliable election outcomes Downloaded by [Queensland University of Technology] at 18:27 19 May 2015 evidence of amount of tactical voting under run-off Voters willing to consider a tactical vote face a key elections. problem: they have to identify the constituencies The proportional voting (PR) system is currently where switching from a sincere vote to a tactical applied in a majority of countries worldwide. Similar vote is desirable and those where it is not neces- to the run-off voting system mentioned before, scho- sary or even counterproductive. Hence, voters’ lars typically believe that tactical voting is less of a information and beliefs about election outcomes problem relative the FPTP system since the opportu- play a key role. Typically, tactical votes should be nities to cast a wasted votes are rarer. Hence compared concentrated in constituencies identified by voters

18 Additionally, there is a large literature on strategic abstention in elections when voters do not have perfect information about the state of the world. In that case, some voters are potentially better informed than others. This line of research has produced some interesting theoretical and experimental results and is especially connected with the work by Feddersen and Pesendorfer (1996), who show that less informed voters may strictly prefer to abstain even when voting is costless. A new approach to measure tactical voting 3845 as marginal where the effect of a tactical vote for different ways, which can intuitively be understood a better placed party is most likely to have an as nested information sets – from the smallest set to impact. the largest. This fact underlies our empirical strategy. The First of all, tactical voters could be naively back- set of constituencies which are marginal in one ward-looking and simply form their beliefs based on general election is not necessarily the same in the the previous election outcome. In this case, tactical subsequent election. Between two elections, the voting would be worthwhile in constituencies that national variations in popularity of the two main have been closely contested in 2005. Although this parties affect their winning chances in each con- might seem naive initially, the voting guides pub- stituency. When the governing party suffers from lished by the Mirror and the Independent were con- low popularity, previously safe constituencies are structed exactly in this way. in danger of falling to the opposition. This is Second, a more sophisticated technique would indeed the situation which the Labour party faced include some forward-looking information and add in 2010. After 13 years in government, Labour to the previous electoral results a forecast of the party suffered from a drop in popularity with an national vote swing. Such an approach would require expected swing in favour of the Conservative party the inclusion of national opinion polls to make a of around 8%. forecast. Whilst this technique is quite coarse, it When a national swing changes a ‘safe’ seat into a was at the core of the very popular ‘swingometers’ ‘marginal’ seat, one should see stronger tactical vot- on which media and parties extensively relied during ing patterns there relative to the previous general the campaign to forecast the makeup of the next elections. By changing the set of constituencies parliament. For this reason, we can suspect that which are marginal from one election to the other, a many voters who are interested in a tactical ballot national swing entails an exogenous variation in relied on a uniform swing assumption to form their ‘marginality’ which we use to identify tactical voting expectations of the local results. Indeed in the patterns. Section ‘Backward-looking approach and uniform We should observe that new marginal seats exhibit swing pre-diction’, we present empirical support stronger patterns of tactical voting than in previous that voters use the uniform swing prediction and elections, with third-party voters partly opting for not the backward-looking approach to inform them- their second best option. These patterns can be iden- selves about the potential closeness of the electoral tiﬁed by plotting the change in vote shares between race in their corresponding constituency.19 2005 and 2010 as a function of the 2005 Labour/ Third, an even more elaborated voter could add Conservative (Liberal Democratic/Conservative, constituency-speciﬁc information to form expecta- respectively) vote share difference. We use nonpara- tions about election results in her constituency, such metric local polynomial regression to do so. as a scandal affecting the re-election of the incum- Moreover, there may be several ways for voters to bent MP are of course relevant pieces of information. form beliefs about which constituencies are marginal To consider these well-informed voters, we use data or not. Our nonparametric approach allows us to from betting markets. There is clear evidence that examine which ones are considered to be marginals betting markets are very well able to aggregate avail- Downloaded by [Queensland University of Technology] at 18:27 19 May 2015 and which ones not by voters. This information can able information, see Arrow et al. (2008) and Wolfers then be used to test for several layers of sophistica- and Zitzewitz (2004), for instance. This is so because tion of voters when forming beliefs about the likely well-informed market participants have more incen- results of the election in their constituency. tives to bet and therefore will have an impact on the odds. During the campaign, bookmaker offered odds The different types of voter sophistication for all the major parties in each constituency. These A voter willing to know whether his or her constitu- odds aggregate all available (local) information in ency is a marginal one faces a nontrivial problem. addition to the national forecasts. We will use these There are several ways to form beliefs about the odds as a proxy for a well-informed forecast by a marginality of a constituency. We consider four sophisticated voter. Betting is quite popular in the

19 Two swingometers are available at the BBC homepage at and at . 3846 D. Muller and L. Page

Table 1. Actual election results and predictions averaged for three different opinion poll companies (Polls of Polls, ComRes and ICM), published on the election day Conservatives Labour Liberal Democrats Others Results and polls Share Swing Share Swing Share Swing Share Swing 2005 Results 33.2% – 36.1% – 22.6% – 8.0% – Average prediction 36.3% 3.1% 28% −8.1% 27% 4.4% 8.7% 0.7% 2010 Results 36.1% 2.9% 29.0% –7.1% 23% 0.4% 11.9% 3.9%

United Kingdom and it seems reasonable to assume all seats where the corresponding main two parties that a sophisticated voter could use betting odds to are expected to be close according to the opinion form expectations about the likely result in a polls before the election. We also eliminated seats constituency. which could be considered as three-way marginals, Fourth, one could consider the unlikely possibility where the third party was pretty close from the sec- that voters had perfect information – or, alternatively, ond party.20 We are left with 255 Labour/ that they had perfect expectations (Hicks, 1946), Conservatives and 126 Liberal Democrats/ such that they were able to anticipate ex-ante which Conservatives constituencies. Table 1 displays the constituencies would end up being the closest in the changes in party vote shares that could be deduced ﬁnal results. We examine this consideration in from the last opinion polls before election day. Section ‘Perfect predictions: using the 2010 results’. Since there was a change in constituencies Maybe not surprisingly, this does not seem to be a between 2005 and 2010, we use the notional results realistic assumption. of 2005 of the new constituencies, which were estimated for the Press Association, BBC, ITN and Sky Backward-looking approach and uniform swing News by Rallings and Thrasher (2007). All media prediction used these results during the campaign in order to It seems reasonable to assume that voters might use a quantify the evolution of political forces in the uniform swing model to form expectations about the United Kingdom. Those notional results estimated closeness of the race in their constituency, which the shares the different parties would have obtained implies assuming that changes in party vote shares in 2005 in each constituency given the new 2010 will occur homogeneously across the country. boundaries.21 Although this approach might not be completely Our approach to identify tactical voting relies on realistic, it seems at least to be a simple and effective estimating nonparametrically the change in vote way to predict the results. Backward-looking voters shares between 2005 and 2010 for the three parties can be seen as using a speciﬁc case of the uniform for each constituency as a function of the 2005 dif- swing where the expected swing is zero. The seats ference in Labour-Conservative vote shares (Liberal with close results in the previous elections are then Democrat–Conservative, respectively). This will

Downloaded by [Queensland University of Technology] at 18:27 19 May 2015 the ones considered as marginals in the current allow us to study the relation between the (expected) election. tightness of the race and tactical voting behaviour as Most of the discussions about tactical voting were well as to examine which information voters used to aimed at Labour and Liberal Democrat voters aiming form their expectations. We use local linear regres- to vote against the Conservatives. We therefore sions and a bandwidth selected by cross validation restrict our analysis to constituencies where either (Stone, 1974) to estimate this relationship. Figure 1 the Labour or the Liberal Democrats were the displays these estimations with additional 95% con- main opponents of the Conservatives – Labour/ ﬁdence intervals for each party. Conservative and Liberal Democrats/Conservatives There are two variants of the uniform swing seats. In order to study the marginal seats, we select assumption. The ﬁrst one expects marginal

20 Details on the selection of constituencies are provided in the ‘Appendix’. 21 We describe in the ‘Appendix’ how these notional results are built. A new approach to measure tactical voting 3847 10 10 5 5 0 0 −5 −5 −10 −10 −15 −15 −20 −20 −40 −20 0 20 40 60 −40 −20 0 20 40 Labour−Conservatives 2005 vote share difference Liberal Democrats−Conservatives 2005 vote share difference

Cons. change Lab. change Cons. change Lab. change Lib. change Lib. change

Fig. 1. Change in vote shares in the Labour versus Conservatives (left) and Liberal versus Conservatives seats (right), depending on the Labour/Liberal-Conservative 2005 vote share difference. Local linear regression, bandwidth selected by cross validation

constituencies to be those where the Labour party On the other hand, Liberal Democrats seem to wonwitha11.2-pointmarginin2005(fromTable 1, proﬁt in constituencies where they and the the sum of the loss for the Conservatives and the Conservatives have been close in 2005 (right gain from the Labour is: 3.1 − (−8.1) = 11.2). The panel). A uniform swing assumption based on the second method is even more straightforward. Voters polls would have predicted a tight race in constitu- living in a constituency where the race is between encies where the Conservatives had won by a Labour and Conservatives may be concerned with a 1.3-points margin (4.4 − 3.1) in 2005. And in fact, swing from Labour to Conservatives only, that is, there seem to be some indications here that voters they look purely at the swing between those two switched strategically to the Liberals in these consti- parties regardless of the change in the shares of tuencies. However, there is no sign that those who other parties. Therefore voters may apply a symme- voted for Labour in the previous election voted tacti- trical uniform swing to predict the vote shares of the cally to support the Liberal democrats in these seats, two parties. They would then expect Labour to lose but instead the surplus may come from voters who 8.1 points and the Conservatives to exactly gain this otherwise would not have voted. A possible explana- amount, and, therefore, tight races where the Labour tion is that voters in these constituencies did not get wonbya16.2-pointsmarginin2005.Weadded the same amount of information as in Labour/ vertical lines at these values in the left panel of Conservative districts, for example, due to smaller Fig. 1. Strikingly, the extrema of these curves for media coverage. As a result, whilst Liberal voters had Labour and Liberal Democrats are located exactly plenty of opportunities to form expectations about between the two lines, that is, where expectations the marginality of their seat using the uniform swing based on the uniform swing assumption predicted a model, Labour voters in Liberal Democrat– tight race. Conservative seats may have had much less oppor-

Downloaded by [Queensland University of Technology] at 18:27 19 May 2015 For both panels in Fig. 1, the change in the share of tunity to find out in the media whether there was a Conservatives does not seem to depend on the tight- close race expected in their seat. A higher degree of ness of the electoral race, no matter how tight the race uncertainty about the status of their seats may have is expected to be. Instead the Conservatives gained induced Labour voters to keep voting sincerely. around 4−5% irrespective of the 2005 vote share These results suggest two things. First, the sym- difference relative to the other parties. On the other metric evolution of the changes in vote shares of the hand, for the Labour party and Liberal Democrats Labour and the Liberal Democratic party and the fact there are clear indications that the changes in voting that the vote share of the Conservatives seems to be shares strongly depend on the tightness of the elec- unaffected by the expected closeness of the race toral race as predicted by the uniform swing assump- provides strong evidence for the existence of tactical tion. There is a significant change around 10–15% voting. Second, the fact that this pattern appears for points in favour of the Labour party at the costs of the constituencies predicted to be marginal by a uniform liberal parties (left panel). swing method suggests that voters were sophisticated 3848 D. Muller and L. Page enough to do more than just naively use the shares are able to examine the effect of the voting guides from the last general election as such. They published by The Mirror and The Independent in were forward-looking, incorporating predictions on more detail. This is so because these guides relied changes in vote shares to form their expectations. on the 2005 differences in vote shares, but did not This may not appear as a big surprise, but we should recommend to vote tactically in exactly the same remember that both The Mirror and The Independent seats as the uniform swing assumption suggested to published voting guides that pretty much relied on do. The newspaper guides included constituencies such static expectations. Both these voting guides where Labour won by a margin of zero to eight selected seats where the Labour had won by a margin percentage points in 2005 and hence typically failed from 0% to 8% in 2005. Given that the uniform the predict accurately the close constituencies. swing predicted in the media was around 8%, voting If there was any effect of the voting guide, one guides should have focused on seats where the should observe a difference between the constituen- Labour margin was around 8% at the last election. cies that were included and those which were not In practice, many of these voting guides included included. To test this hypothesis, we look at the seats with close results in 2005 and where the results guide published by The Mirror, a newspaper which were very unlikely be close in 2010. has a large distribution (1.2 million copies in 2010). Besides that, the guide was very similar to the ones The impact of newspaper voting guides from The Independent or Compass. The results presented before suggest that the media Figure 2 shows the box plot of the results in the outlets seem to have failed to identify the constitu- seats included in The Mirror’s guide versus those just encies where tactical voting would have been most left out. The constituencies included had Labour effective. For example, out of the 52 Labour/ winning by a margin of 4 to 8 percentage points in Conservatives constituencies where The Mirror 2005, while those not included had the Labour win- guide recommended that Liberal Democratic parti- ning by a margin of 8 to 12. There is no indication of sans should vote for the Labour party, only five were any effect of the guide on this subsample of seats. won by the Labour party. Our analysis above points Labour does not perform better in the seats included in the same direction: it suggests that voting guides in the guide, and Liberal Democrats do not perform were probably not driving the voting decision. In the worse in these seats either. This same result is case of the marginal Labour/Conservatives seats, we observed for The Independent voting guides. (The 10 5 0 Downloaded by [Queensland University of Technology] at 18:27 19 May 2015 −5 −10 Changes in voting share 2005−2010 −15

No advice Tactical advice No advice Tactical advice No advice Tactical advice Labour Liberal Democrats Conservatives

Fig. 2. The absence of an effect of the Mirror’s voting guide. Results in Labour/Conservatives marginals included in the Mirror guide versus marginals not included in the Mirror guide. The guide does not statistically significantly influence the vote share of the Labour party or the Liberal Democrats A new approach to measure tactical voting 3849 Guardian provided an online voting guide, which is the best-forecast predictions among the different not available anymore.) This suggests that voting techniques we have considered. A voter considering guides had no significant effect on the electoral to vote tactically could easily use bookmakers’ odds results.22 to determine marginal seats. These are the constitu- The absence of an effect may be due to a failure to encies where two candidates are close to a 50% reach a large number of voters. In spite of large chance of winning. circulation numbers, the cumulated figures of circu- We employ the same method as before and plot the lation for all the voting guides (1.6 million copies in changes in vote shares between 2005 and 2010 as a 2010) are still small relative to the size of the electo- function of the tightness of the race defined by the rate. Another possible explanation is that the readers winning probabilities implied by the odds. If voters of these guides are not significantly influenced by react tactically to the marginality of a constituency, them because they form their expectations in a more we should observe an increase in the Labour’s vote sophisticated way. share peaking at 50%. The left panel of Fig. 3 displays the corresponding Bookmakers’ predictions results for Labour/Conservative constituencies. The Conservatives’ change in vote share is here again There is a substantial amount of evidence that independent of the winning probability as defined shows that bookmakers typically give very accu- by bookmakers’ odds. Strikingly, we do observe an rate estimates of the probabilities for certain increase in the change in Labour’s and a decrease in future events23 and in particular of election results the Liberal Democrats vote share around the 50% (Rhode and Strumpf, 2004). Bookmakers will try limit. However, the peak and dip are much less pro- to incorporate all available knowledge, like, for nounced than using the uniform swing predictions in example, the relative strength of local candidates, the Section ‘Backward–looking approach and uni- a local political scandal (which might have been form swing pre-diction’. Bookmakers’ predictions particularly relevant given the large number of are however highly correlated with the uniform MPs involved in the expenses scandal in 2010) national swing predicted by the polls and hence the and so on. In that sense, bookmakers’ predictions results might be partly confounded. Interestingly, should be much better on average than the there is no such peak for the Liberal Democratic national swing prediction, which is entirely ignor- votes in Liberal Democrats/Conservatives seats ant of local characteristics.24 (right panel), which seems to support the conclusions We collected odds for each constituency from the from the Section ‘Backward–looking approach and Ladbrokes website preceding the elections, around uniform swing pre-diction’. All in all, this analysis the 30th of April. Out of the 243 Labour/ again not only provides some indications for the Conservatives constituencies for which bookmakers’ presence of tactical voting, but also suggests that data are available, 219 winners have been correctly voters mainly used the uniform swing predictions to predicted (slightly overestimating the performance of determine marginal constituencies. It is mainly the the Conservatives: 22 of these mistakes consisted of Labour party that profits from tactical voting beha- incorrectly announcing a Conservatives victory). In viour and not so much the Liberals.

Downloaded by [Queensland University of Technology] at 18:27 19 May 2015 comparison, over the same 243 seats, static anticipa- tions gave only 161 correct winners, and forecasts Perfect predictions: using the 2010 results based on the uniform swing assumption (translating the shares of all parties) predicted 212 winners cor- Finally, another possibility is that voters form perfect rectly. Book-makers have therefore clearly provided expectations and correctly predict which seats will be

22 This is in line with the study by Lanoue and Bowler (1992), who found that the media did not seem to have a signiﬁcant inﬂuence on tactical voting in 1983 and 1987. 23 See Ali (1979), Pope and Peel (1989), Franck et al. (2010), Wolfers and Zitzewitz (2004) and Arrow et al. (2008). 24 According to the 2010 British Gambling prevalence survey which surveyed a representative sample of the British population, 43% of the respondents had gambled the week before participating in the survey (British Prevalence Survey 2010, p. 23). Additional evidence of the importance of gambling activities in Great Britain comes from Rosenbaum (1999), who states that betting at British General Elections is a popular pastime which ‘involves many members of the general public and large sums of money’ (Rosenbaum, 1999, p. 1). 3850 D. Muller and L. Page 10 10 5 5 0 0 −5 −5 −10 −10 −15 −15 −20 −20 0 .2 .4 .6 .8 1 0 .2 .4 .6 .8 1 Bookies winning probabilities of Labour Bookies winning probabilities of Liberal Democrats Cons. change Lab. change Cons. change Lab. change Lib. change Lib. change

Fig. 3. Change in share in the Labour versus Conservatives seats (left) and Liberal Democrats versus Conservatives seats (right), depending on the winning probability of Labour given by bookmakers. Local linear regression, bandwidth selected by cross validation

the closest. Using the same method as before, it is the reverse from what tactical voting would suggest, possible to look at changes in vote shares as a func- with the Conservatives experiencing a peak relative tion of the 2010 differences between Labour and to 2005 results in precisely those seats that ended up Conservatives (Lib-Dem/Conservatives, respec- being close in 2010. Overall, it is clear that voters do tively). This is problematic in the sense that seats not seem to be characterized by perfect expectations, that happened to experience a positive shock on a result that seems reasonable after all. Labour (or Lib-Dems, respectively) votes will mechanically tend to be higher in the 2010 results. As a consequence, the fitted curve of the changes in IV. Strategic Campaign Spending share for Labour should tend to increase, while the curves from the Conservatives and the Liberal We attributed the increase in votes for the Labour Democrats will tend to decrease. Nevertheless, this party in close constituencies (as predicted by the exercise can still be informative since we are able to uniform swing model) to tactical voting. However, check for peaks or dips in the estimated curves, party spending that is targeted towards close consti- which would be an indication for tactical voting tuencies might be another causal mechanism that is and for the fact that people might do extremely well able to explain the observed patterns. In that case the in predicting election results. The left panel of Fig. 4 data would simply reflect increased (financial) effort shows that there are clearly no signs for such a by the two dominating parties. The literature on behaviour in the data. The right panel – the Liberal campaign spending has made a distinction between Democrats/Conservatives constituencies – exhibits informative and persuasive campaign spending, see some minor variations in close seats, but it is actually Mueller and Stratmann (1994) and Westley and Downloaded by [Queensland University of Technology] at 18:27 19 May 2015 10 10 5 5 0 0 −5 −5 −10 −10 −15 −15 −20 −20 −40 −20 0 20 40 −40 −20 0 20 40 Labour−Conservatives 2010 vote share difference Liberal Democrats−Conservatives 2010 vote share difference Cons. change Lab. change Cons. change Lab. change Lib. change Lib. change

Fig. 4. Changes in the share in Labour versus Conservatives seats (left) and Liberal versus Conservatives seats (right), depending on the Labour/Liberal/Conservative 2010 vote share difference. Local linear regression, bandwidth selected by cross validation A new approach to measure tactical voting 3851 15 000 30 000 10 000 20 000 5000 10 000 0 0

−40 −20 0 20 40 60 −40 −20 0 20 40 60 Labour−Conservatives 2005 vote share difference Labour−Conservatives 2005 vote share difference Cons. short camp. spending Lab. short camp. spending Cons. total spending Lab. total spending Lib. short camp. spending Lib. total spending 15 000 30 000 10 000 20 000 5000 10 000 0 0

0 .2 .4 .6 .8 1 0 .2 .4 .6 .8 1 Bookies winning probabilities of Labour Bookies winning probabilities of Labour

Cons. total spending Lab. total spending Cons. short camp. spending Lab. short camp. spending Lib. total spending Lib. short camp. spending

Fig. 5. Total party spending (left-hand side panels) and spending during the short campaign (right-hand side panels) of Conservatives, Labour and Liberal Democrats in the Labour/Conservatives constituencies, depending on the Labour/Conservatives 2005 vote share difference (top panels), and the winning probability of Labour given by bookmakers (bottom panels). Local linear regression, bandwidth selected by cross validation

Calcagno (2005). The former term is used to denote spending data at the constituency level. Figure 5 dis- spending that aims to inform voters about the candi- plays total party spending during the campaign for a dates’ policy platform. The latter term indicates period from 1 January to 6 May 2010 of spending intended to persuade voters to vote for the Conservatives, Labour and Liberal Democrats in given candidate regardless of the candidates’ policy the marginal Labour/Conservatives seats as function platform.25 of the 2005–2010 vote share difference between Although previous studies have found only limited Labour and Conservatives in the top left panel. The evidence for tactical voting to be induced by party same graphs are depicted in the top right panel spending,26 we examine this potential mechanism whereas campaign spending is restricted to the here more closely. Rather than explaining the short-term period (starting on 13th April). The two

Downloaded by [Queensland University of Technology] at 18:27 19 May 2015 observed pattern with party spending, research on vertical lines indicate the interval in which a uniform that matter has suggested that party spending inter- swing prediction identiﬁed the marginal constituen- acts with tactical voting behaviour, helping to trigger cies to be located. The two bottom panels of Fig. 5 or to moderate it.27 display campaign spending and bookmakers winning We investigate here whether party spending fol- probabilities. lowed the same patterns as the variations in the Spending of both, Labour Party and Conservatives, parties’ shares. We employ detailed data from the peaks in districts where Conservatives gained around British Electoral Commission summarizing party 5% to 10% in the 2010 elections and hence does not

25 Another related but different literature deals with the question how effective campaign spending is and whether there are differences in the effectiveness for incumbents relative to challengers. Among these papers are Levitt (1994), Gerber (1998) and Stratmann (2006). 26 See Galbraith and Rae (1989), Johnston et al. (1997) and Fisher (2001), for example. 27 See Fieldhouse et al. (1996) and Pattie and Johnston (2010). 3852 D. Muller and L. Page exactly fit a uniform swing model. Thus spending is is an increasingly important topic since campaign also not maximal between 10% and 15% where we contributions have been sharply increasing in recent observe tactical voting. years (Stratmann, 2005; Goel, 2014). Note that in the The lower panels in Fig. 5 also clearly show that United Kingdom, the spending of political parties both parties did not opt for spending strategies that represents the bulk of the monetary resources allo- coincide with the bookmakers predictions, as their cated in the campaign in favour of the local candi- total spending peaked for seats where the winning dates. This differs from a country like the United probability for Labour was only estimated at 33% on States where private organizations such as PACs average. Restricting the sample to the short campaign provide additional funding to candidates or to the (lower right panel) tends to make the distribution of causes they defend. spending even uniform across constituencies. Overall, the data suggest that political parties tried to target marginal seats, but did so somewhat imper- V. Controlling for Third Parties’ Distance fi fectly (if we de ne marginals using a uniform from Contention national swing or bookmakers’ odds). In addition, the data does not support the idea that voters simply Conventional wisdom29 suggests that tactical voting ‘follow the money’ of the political parties. is highest in seats that are closely contested. In con- Noticeably, there is no peak for the Conservative trast to that, Myatt (2007) in a recent study puts vote share in the seats where their spending peaks. another argument forward. He argues that once the Overall, the Conservative gains seem to be quite distance from contention of the third party is con- insensitive to the amount of money spent for trolled for, tactical voting should be largest in seats campaigning.28 The absence of an effect could either where the leading party has the greatest advantage mean that Conservatives’ spending had no effect or against the runner-up.30 Myatt’s arguments is that it that it was balanced by Labour’s spending, resulting is not marginality per se that is relevant for tactical in a wasteful ‘arms race’. voting and that it is necessary to control for the role of This does not necessarily imply that party spend- the distance from contention of the third party. ing does not matter for tactical voting. Assuming, for instance, a constituency where Conceptually, the line between the effect of party Conservatives are expected to gain 30% of the spending and tactical voting is a subtle one. First, votes and Labour 28%, tactical voting behaviour of even if campaign spending is unable to change Liberal–Democratic partisans will differ depending voters’ preferences it can play an important role in on whether the Liberal Democrats can expect to signalling the closeness of the race to the voters in gather 10% or 27% of the electoral votes. their constituencies. A large pecuniary effort by a As a third contribution, this article tests the inter- party in one constituency could transmit the infor- esting and somewhat counterintuitive prediction of mation that there is a close race expected, and thus Myatt’s(2007) model regarding the importance of that tactical voting might be worthwhile. In this tactical voting in marginal constituencies.31 Until situation, investments by the Conservative party now, we simply restricted our sample to constituen- could even be counterproductive. Second, a party cies where the third party was sufficiently behind Downloaded by [Queensland University of Technology] at 18:27 19 May 2015 could use its budget to run a political campaign relative to the second party in order to avoid these targeted at promoting tactical voting. problems.32 We estimate a general additive model Our findings also relate to the issue of strategic (Breiman and Friedman, 1985) to control nonpara- campaign contributions, for example, by political metrically for both the closeness of the race and for p action committees (PACs) in the United States. This the distance from contention. The vote share v2010 of

28 This is in line with recent conjectures that the Conservatives are less effective in campaigning, see Pattie and Johnston (2010), for example. 29 But also some empirical studies, see, for example, Cain (1978). 30 See proposition 6 in Myatt (2007). 31 Using a logit model to control for distance from contention of the third party, Fisher (2000) analyses survey data from the British Election study and found some support for Myatt’s prediction for the years 1983 and 1987, but not for 1992 and 1997. 32 Please consult the ‘Appendix’ for more details on the sample selection. A new approach to measure tactical voting 3853 10 5 0 −5 −10 −15 −20 −40 −20 0 20 40 60 Labour−Conservatives 2005 vote share difference

Cons. change Lab. change Lib. change

Fig. 6. Additive model estimation. Change in vote shares as a function of Labour/Conservative vote share differences after controlling for distance from contention

a party P in 2010 is specified as the sum of two VI. Concluding Remarks nonlinear and unknown functions, m1 and m2,of the tightness of the race, t, and the distance from We contribute to the literature on tactical voting in contention of the third party in 2005, c: four different ways. First of all, we propose a novel where ε is a random error term. simple empirical strategy to identify tactical voting. This method is based on the visual inspection of the v p ¼ m ðt Þþm ðc Þþε (1) nonparametrically estimated relationship between 2010 1 2005 2 2005 the change in vote shares between two elections and the difference in vote shares between the two Figure 6 displays the results for the Labour/ major contesters in a certain district. We see our Conservatives constituencies. Visual inspection of method as useful and flexible addition to the exist- the graph indicates that the results are in line with ing methods. As such, this approach is of general those from Section III. Tactical voting still appears to importance and applicable in all similar situations. be prevalent in marginal seats, even after controlling It also avoids the disadvantages of the previous for distance from contention. Beyond the marginals, methods. Applying this approach to the 2010 tactical voting seems to be lower in seats dominated British general election, we find that tactical voting by the Conservatives. This result contradicts the likely played a significant role. Moreover, it seems Downloaded by [Queensland University of Technology] at 18:27 19 May 2015 predictions of the model that tactical voting that mainly those voters who voted for the Liberals should increase with the winning margin of the in the preceding elections are prone to tactical vot- Conservatives. Relative to Fisher’s(2000) empirical ing, but not so much those who voted for the Labour results, our estimation strategy has the advantage that party beforehand. it imposes only minimal identifying assumptions on Secondly, this article sheds new light on how the data-generating process (separable additivity). voters form their expectations about election out- Hence, our results support the commonly held view comes. Our method allows us to compare different that tactical voting is likely to be maximal in seats information acquisition approaches. We find that that are tightly contested. In fact, it is also stronger in voters seem to calculate expected closeness of seats marginals that are defined using a uniform swing mainly using a uniform swing model and not so model. much from newspaper voting guides. Our results 3854 D. Muller and L. Page therefore suggest a ‘partly sophisticated’ voter (as information sets (like the uniform swing mode) to opposed to a ‘sophisticated rational’ voter who make predictions. As an argument in favour of AVis would rather follow bookmakers predictions or made on the ground of its complexity, the degree of even perfect forecasts and opposed to a naive voter sophistication of the electorate matters. With a who is purely backward-looking). ‘somewhat sophisticated’ electorate, for which we Thirdly, we add to the literature on campaign spend- find some empirical evidence here, FPTP may be ing by political parties. We have shown that parties try easy enough for people to use public information to to target marginal constituency with their campaign define a tactical voting strategy. Under the AV sys- spending, but are far from effective in doing so. We tem, such voters may find it too hard to come up with also presented some evidence that the Conservative the right tactical voting strategy. In that sense, our party is particularly inefficient in the use of its money. results suggest that AV could reduce the proportion In general, voters do not seem to be overly influenced of tactical voting by putting such an option out of by campaigning effort of the parties. reach for most voters. Last but not least, we empirically test a prediction Finally, it is important to note that this study is not of the theory of tactical voting as our approach allows able to say anything about the changes in tactical us to test and reject the claim that strategic voting voting over time. This question is important given should be higher in constituencies where the that new information technologies significantly Conservatives have the highest vote edge once dis- reduce the costs of information acquisition and tance from contention is controlled for. We estimated hence facilitate tactical voting for the general a general additive model that explicitly controls for public.33 this distance. This supports our findings from the As a consequence, tactical voting may become sections before – we still find that tactical voting more prevalent over time. Clearly, more research seems to be most likely at close races. remains to be done. What can our results bring to the debate on the electoral reform in Britain? Whilst the Gibbard– Satterthwaite theorem states that there cannot be a Acknowledgements strategy-proof voting system, it is hard in practice to We are particularly indebted to Stéphane Dupraz for compare how different systems would fare in regards his help and assistance. Moreover, we would like to to that matter. The proportion of voters choosing to thank Yola Engler and Gabriele Gratton for helpful vote strategically depends on the distribution of pre- comments and Justus Inhoffen for research ferences and the relative positions of the candidates assistance. in the political space. Empirical comparative research on AV and FPTP is relatively limited. Although tactical voting is gen- Disclosure Statement erally associated with FPTP systems, it is well known fl that tactical voting is also possible with AV No potential con ict of interest was reported by the (Niemi, 1984). However, Bartholdi and authors. Orlin (1991) find that the class of single transferable Downloaded by [Queensland University of Technology] at 18:27 19 May 2015 vote (STV) voting rules, to which AV belongs, should be more resistant to tactical voting as they Funding are characterized by a higher degree of complexity Muller gratefully acknowledges support from the for those voters looking for a tactical vote option. As SFB-884 at the University of Mannheim. it happens, in Australia, a country that uses the alternative vote system, the proportion of tactical votes has been estimated to be much smaller than in Britain References (Gschwend, 2004). Abramson, P., Aldrich, J., Paolino, P. et al. (1992) Related to this debate, our results seem to indicate “Sophisticated” voting in the 1988 presidential pri- that voters (or at least some of them) are sophisti- maries, The American Political Science Review, 86, cated, but that they primarily use rather coarse 55–69. doi:10.2307/1964015

33 We thank a referee for bringing up this important point. A new approach to measure tactical voting 3855

Abramson, P. R., Aldrich, J. H., Blais, A. et al. (2009) Blanket Primary, University of California Press, Comparing strategic voting under FPTP and PR, Berkeley. Comparative Political Studies, 43,61–90. Cox, G. (1997) Making Votes Count: strategic Ali, M. (1979) Some evidence of the efﬁciency of a spec- Coordination in the World’s Electoral Systems, vol. ulative market, Econometrica, 47, 387–92. 7, Cambridge University Press, New York. doi:10.2307/1914189 Cox, G. W. and Munger, M. C. (1989) Closeness, expen- Alvarez, R., Boehmke, F. and Nagler, J. (2006) Strategic ditures, and turnout in the 1982 US House elections, voting in British elections, Electoral Studies, 25,1– The American Political Science Review, 83, 217–31. 19. doi:10.1016/j.electstud.2005.02.008 doi:10.2307/1956441 Alvarez, R. and Nagler, J. (2000) A new approach for Duch, R. M. and Palmer, H. D. (2002) Strategic voting in modelling strategic voting in multiparty elections, post-communist democracy?, British Journal of British Journal of Political Science, 30,57–75. Political Science, 32,63–91. doi:10.1017/ doi:10.1017/S000712340000003X S0007123402000030 Arrow, K., Forsythe, R., Gorham, M. et al. (2008) The Duverger, M. (1954) Political Parties: Their promise of prediction markets, Science, 320, 877–78. Organization and Activity in the Modern State, doi:10.1126/science.1157679 Methuen, London. Atkeson, L. (1999) Sure, I voted for the winner! Electoral Reform Society (2010) What is AV? Available overreport of the primary vote for the party nomi- at http://www.electoral-reform.org.uk/downloads/ nee in the national election studies, What\%20is\%20AVweb.pdf (accessed 7 March Political Behavior, 21, 197–215. doi:10.1023/ 2015). A:1022031432535 Endersby, J. W., Galatas, S. E. and Rackaway, C. B. Bartholdi, J. and Orlin, J. (1991) Single transferable vote (2002) Closeness counts in Canada: voter participa- resists strategic voting, Social Choice and Welfare, 8, tion in the 1993 and 1997 federal elections, The 341–54. doi:10.1007/BF00183045 Journal of Politics, 64, 610–31. doi:10.1111/ Blais, A. (2002) Why is there so little strategic voting in 1468-2508.00143 Canadian plurality rule elections?, Political Studies, Eubank, R. and Gow, D. (1983) The pro-incumbent bias in 50, 445–54. doi:10.1111/1467-9248.00378 the 1978 and 1980 National Election Studies, Blais, A. and Bodet, M. (2006) How do voters form American Journal of Political Science, 27, 122–39. expectations about the parties’ chances of winning doi:10.2307/2111056 the election?, Social Science Quarterly, 87, 477–93. Fauvelle-Aymar, C. and François, A. (2006) The impact of doi:10.1111/j.1540-6237.2006.00392.x closeness on turnout: an empirical relation based on a Blais, A. and Nadeau, R. (1996) Measuring strategic vot- study of a two-round ballot, Public Choice, 127, ing: A two-step procedure, Electoral Studies, 15,39– 461–83. doi:10.1007/s11127-005-9004-x 52. doi:10.1016/0261-3794(94)00014-X Feddersen, T. J. and Pesendorfer, W. (1996) The swing Blais, A., Nadeau, R., Gidengil, E. et al. (2001) Measuring voter’scurse,The American Economic Review, 86, strategic voting in multiparty plurality elections, 404–24. Electoral Studies, 20, 343–52. doi:10.1016/ Fieldhouse, E., Pattie, C. and Johnston, R. (1996) Tactical S0261-3794(00)00017-2 voting and party constituency campaigning at the Blais, A., Young, R. and Turcotte, M. (2005) Direct or 1992 general election in England, British Journal of indirect? Assessing two approaches to the measure- Political Science, 26, 403–18. doi:10.1017/ ment of strategic voting, Electoral Studies, 24, 163– S0007123400007511 76. doi:10.1016/j.electstud.2004.03.001 Fisher, S. D. (2000) Intuition versus formal theory: tactical Bowler, S., Karp, J. A. and Donovan, T. (2010) Strategic voting in England 1987–1997, Paper prepared for coalition voting: evidence from New Zealand, APSA Annual Meeting, Washington, DC, 31 Electoral Studies, 29, 350–57. doi:10.1016/j. August–September. Downloaded by [Queensland University of Technology] at 18:27 19 May 2015 electstud.2010.03.001 Fisher, S. (2001) Extending the rational voter theory of Breiman, L. and Friedman, J. (1985) Estimating optimal tactical voting, Paper presented at the Mid-West transformations for multiple regression and correla- Political Science Association Meeting, Chicago, IL. tion, Journal of the American Statistical Association, Fisher, S. (2004) Deﬁnition and measurement of tactical 80, 580–98. doi:10.1080/01621459.1985.10478157 voting: the role of rational choice, British Journal of Burden, B. C. and Jones, P. E. (2009) Strategic voting in Political Science, 34, 152–66. doi:10.1017/ the US, in Duverger’s Law of Plurality Voting, S0007123403220391 Grofman, B., Blais, A. and Bowler, S. (Eds), Franck, E., Verbeek, E. and Nüesch, S. (2010) Prediction Springer, New York, pp. 47–64. accuracy of different market structures-bookmakers Cain, B. (1978) Strategic voting in Britain, American versus a betting exchange, International Journal of Journal of Political Science, 22, 639–55. Forecasting, 26,448–59. doi:10.1016/j.ijforecast.2010. doi:10.2307/2110465 01.004 Cain, B. E. and Gerber, E. R. (2002) Voting at the Political Galbraith, J. W. and Rae, C. N. (1989) A test of the Fault Line: California’s Experiment with the importance of tactical voting: Great Britain, 1987, 3856 D. Muller and L. Page

British Journal of Political Science, 19, 126–36. Lago, I. (2008) Rational expectations or heuristics?: doi:10.1017/S0007123400005366 strategic voting in proportional representation Ganser, T. and Veuger, S. (2010) Strategic voting in pro- systems, Party Politics, 14,31–49. doi:10.1177/ portional representation systems, AEI Working 1354068807083822 Paper 2014-02. Lanoue, D. and Bowler, S. (1998) Picking the winners: Gerber, A. (1998) Estimating the effect of campaign perceptions of party viability and their impact spending on senate election outcomes using instru- on voting behavior, Social Science Quarterly, 79, mental variables, The American Political Science 361–77. Review, 92, 401–11. doi:10.2307/2585672 Lanoue, D. J. and Bowler, S. (1992) The sources of Gibbard, A. (1973) Manipulation of voting schemes: a tactical voting in British parliamentary elections, general result, Econometrica, 41, 587–601. 1983–1987, Political Behavior, 14, 141–57. doi:10.2307/1914083 doi:10.1007/BF00992239 Goel, R. K. (2014) PACking a punch: Political Action Levitt, S. D. (1994) Using repeat challengers to estimate Committees and corruption, Applied Economics, the effect of campaign spending on election out- 46, 1161–69. doi:10.1080/00036846.2013.868589 comes in the US House, Journal of Political Gschwend, T. (2004) Comparative politics of strategic Economy, 102, 777–98. doi:10.1086/261954 voting: a hierarchy of electoral systems, Paper Matsusaka, J. G. (1993) Election closeness and voter presented at the 2003 annual meeting of the turnout: evidence from California ballot proposi- APSA. tions, Public Choice, 76, 313–34. doi:10.1007/ Gschwend, T., Stoiber, M. and Günther, M. (2004) BF01053302 Strategic voting in proportional systems: the case of McCarthy, C. and Ryan, T. (1977) Estimates of voter Finland, Citeseer. transition probabilities from the British General Heath, A. and Evans, G. (1994) Tactical voting: concepts, Elections of 1974, Journal of the Royal Statistical measurement and ﬁndings, British Journal of Society. Series A (General), 140,78–85. Political Science, 24, 557–61. doi:10.1017/ doi:10.2307/2344518 S0007123400007018 McCuen, B. and Morton, R. (2010) Tactical coalition Hicks, J. R. (1946) Value and Capital, 2nd edn, Oxford voting and information in the laboratory, University Press, Oxford. Electoral Studies, 29, 316–28. doi:10.1016/j. Himmelweit, H., Biberian, M. and Stockdale, J. (1978) electstud.2010.03.009 Memory for past vote: implications of a study of bias Meffert, M. and Gschwend, T. (2010) Strategic coalition in recall, British Journal of Political Science, 8, 365– voting: evidence from Austria, Electoral Studies, 29, 75. doi:10.1017/S0007123400001411 339–49. doi:10.1016/j.electstud.2010.03.005 Johnston, R. and Pattie, C. (1991) Tactical voting in Great Meffert, M., Huber, S., Gschwend, T. et al. (2011) More Britain in 1983 and 1987: an alternative approach, than wishful thinking: Causes and consequences of British Journal of Political Science, 21,95–108. voters electoral expectations about parties and coali- doi:10.1017/S0007123400006049 tions, Electoral Studies, 30, 804–15. doi:10.1016/j. Johnston, R. and Pattie, C. (1992) Using an entropy-max- electstud.2011.08.001 imizing procedure to estimate territorial social indi- Meirowitz, A. (2005) Polling games and information reve- cators: an introduction and illustration, Social lation in the Downsian framework, Games and Indicators Research, 27, 235–56. Economic Behavior, 51, 464–89. doi:10.1016/j. Johnston, R., Pattie, C., MacAllister, I. et al. (1997) geb.2004.09.015 Spatial variations in voter choice: modelling tactical Mueller, D. C. and Stratmann, T. (1994) Informative and voting at the 1997 general election in Great Britain, persuasive campaigning, Public Choice, 81,55–77. Geographical and Environmental Modelling, 1, doi:10.1007/BF01053266 153–78. Myatt, D. (2007) On the theory of strategic voting, Review Downloaded by [Queensland University of Technology] at 18:27 19 May 2015 Kim, H. and Fording, R. (2001) Does tactical voting of Economic Studies, 74, 255–81. doi:10.1111/ matter?: the political impact of tactical voting j.1467-937X.2007.00421.x in recent British elections, Comparative Nadeau, R., Niemi, R. and Amato, T. (1994) Expectations Political Studies, 34, 294–311. doi:10.1177/ and preferences in British general elections, The 0010414001034003003 American Political Science Review, 88, 371–83. King, G. (1997) A Solution to the Ecological Inference doi:10.2307/2944710 Problem: Reconstructing Individual Behavior from Niemi, R. (1984) The problem of strategic behavior under Aggregate Data, Princeton University Press, approval voting, The American Political Science Princeton, NJ. Review, 78, 952–58. doi:10.2307/1955800 Kirchgässner, G. and Zu Himmern, A. M. (1997) Niemi, R., Whitten, G. and Franklin, M. (1993) People Expected closeness and turnout: an empirical who live in glass houses: A response to Evans and analysis for the German General Elections, 1983- Heath’s critique of our note on tactical voting, 1994, Public Choice, 91,3–25. doi:10.1023/ British Journal of Political Science, 23, 549–53. A:1004968816775 doi:10.1017/S0007123400006724 A new approach to measure tactical voting 3857

Niemi, R., Written, G. and Franklin, M. (1992) Journal of Economic Theory, 10, 187–217. Constituency characteristics, individual characteris- doi:10.1016/0022-0531(75)90050-2 tics and tactical voting in the 1987 British general Shachar, R. and Nalebuff, B. (1999) Follow the leader: election, British Journal of Political Science, 22, theory and evidence on political participation, 229–40. doi:10.1017/S0007123400006347 American Economic Review, 89, 525–47. Palfrey, T. (1989) A mathematical proof of Duverger’s doi:10.1257/aer.89.3.525 law, Models of Strategic Choice in Politics, Southwell, P. L. (1991) Open versus closed primaries - the Ordeshook, P. C. (Ed.), University of Michigan effect on strategic voting and candidate fortunes, Press, Ann Arbor. Social Science Quarterly, 72, 788–96. Pattie, C. and Johnston, R. (2001) A low turnout landslide: Stone, M. (1974) Cross-validation and multinomial pre- Abstention at the British general election of 1997, diction, Biometrika, 61, 509–15. doi:10.1093/bio- Political Studies, 49, 286–305. doi:10.1111/ met/61.3.509 1467-9248.00314 Stratmann, T. (2005) Some talk: Money in politics. A Pattie, C. and Johnston, R. (2010) Constituency cam- (partial) review of the literature, Public paigning and local contests at the 2010 UK general Choice, 124, 135–56. doi:10.1007/s11127- election, British Politics, 5, 481–505. doi:10.1057/ 005-4750-3 bp.2010.16 Stratmann, T. (2006) Contribution limits and the effective- Pope, P. and Peel, D. (1989) Information, prices and ness of campaign spending, Public Choice, 129, efﬁciency in a ﬁxedodds betting market, 461–74. doi:10.1007/s11127-006-9066-4 Economica, 56, 323–41. doi:10.2307/2554281 Upton, G. (1978) A note on the estimation of voter transi- Rallings, C. and Thrasher, M. (2007) Media Guide to the tion probabilities, Journal of the Royal Statistical New Parliamentary Constituencies, LGC Elections Society. Series A (General), 141, 507–12. Centre, Plymouth. doi:10.2307/2344485 Rhode, P. and Strumpf, K. (2004) Historical presidential bet- Westley, C. and Calcagno, P. (2005) Incumbent spending ting markets, The Journal of Economic Perspectives, 18, and gubernatorial elections: an investigation of pri- 127–41. doi:10.1257/0895330041371277 mary type and candidate deviation, Journal of Public Riker, W. (1982) The two-party system and Duverger’s Finance and Public Choice, 23,3–18. Law: an essay on the history of political science, The Wolfers, J. and Zitzewitz, E. (2004) Prediction markets, American Political Science Review, 76, 753–66. Journal of Economic Perspectives, 18, 107–26. doi:10.2307/1962968 doi:10.1257/0895330041371321 Rosenbaum, M. (1999) Betting and the 1997 British gen- Wright, G. (1990) Misreports of vote choice in the 1988 eral election, Politics, 19,9–14. doi:10.1111/ NES senate election study, Legislative Studies 1467-9256.00080 Quarterly, 15, 543–63. doi:10.2307/439896 Satterthwaite, M. (1975) Strategy-proofness and arrow’s Wright, G. (1992) Reported versus actual vote: there is conditions: existence and correspondence theorems a difference and it matters, Legislative for voting procedures and social welfare functions, Studies Quarterly, 17,131–42. doi:10.2307/440085

Appendix. Data However, in the British general elections, results are A.1 Redistricting and Notional Results not available on the ward- but only on the constituency-level. This is a direct consequence of how the As mentioned before, between the 2005 and the 2010 ballot papers are counted. The electoral commission elections some constituencies were subject to redis- enforces a system in which all ballot boxes are ﬁrst gathered in a central place in every constituency and

Downloaded by [Queensland University of Technology] at 18:27 19 May 2015 tricting. To adjust for this fact, we employ the widely used notional results by Rallings and are then mixed before they are counted. Thrasher (2007). The notional election result is an Notional results are therefore calculated with the estimate how the previous result would have looked help of election results available on a ward level, like given the new constituency boundaries. primarily local authority elections. Basically, the Nevertheless, those estimates are not perfect since number of votes obtained by party P in the new they neglect tactical voting. In the following, we are constituency C’ is calculated as the sum of votes for going to briefly describe how these results are P at the local elections in all the wards that form the calculated. 2005 constituency C. The vote share of each party at Constituencies are composed of electoral wards, the 2005 national election is then divided by the sum which were almost never cut during the change of of the local election votes in C. This fraction F is used boundaries. Hence, notional results could in theory as a multiplier for each C and P and applied to the be computed by re-assorting electoral wards. party’s vote in each ward that constituted C to obtain 3858 D. Muller and L. Page a notional 2005 general election result in that specific national swing to obtain these expectations. That is, ward. All votes in the wards making up the new given the 2005 election result in a constituency constituency C’ boundaries are then summed to get where Labour and Conservatives came first and sec- the result for the corresponding constituency. In a ond, we drop those constituencies where a national few cases, manual adjustments have been made. vote swing would predict that at least one of the two parties will not be first or runner-up. We are left with 255 Labour/Conservative constituencies. We com- A.2 Selection of the Sample of pile the Liberal Democrats/Conservatives marginals Constituencies accordingly, but since Labour was expected to lose ground and Conservatives and Liberal Democrats to As previously mentioned, we restrict the study to gain votes, we are not dropping any constituencies Labour/Conservatives and Liberal Democrats/ here. That is, with expectations based on a national Conservatives marginal seats. In order to study the vote swing, we will never see a constituency where former for instance, we consider only the constitu- Liberals and Conservatives have been first and sec- encies where Labour and Conservatives arrived first ond, respectively, in 2005 but are not predicted to be and second (or second and first, respectively) in first and second in 2010. As a result, we keep 126 2005. We then drop all seats where those two parties Liberal Democrats/Conservatives marginal constitu- are not expected to remain the two dominating ones encies. Hence, we use information from 381 out of in 2010. We combine the previous result with the 650 constituencies in total. Downloaded by [Queensland University of Technology] at 18:27 19 May 2015