How Safe are Safe Seats? A Comparison of Voluntary and Compulsory Voting Systems*

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1 brazilianpoliticalciencereview ArtiCLE How Safe are Safe Seat? A Comparion of Voluntary and Compulory Voting Sytem* Tim R. L. Fry RMIT Univerity, Autralia Keith Jakee Florida Atlantic Univerity, USA Martin Kenneally Univerity College Cork, Ireland Many oberver have expreed concern that low voter turnout reflect an acute hortcoming in democratic politic. One propoed remedy, making voting compulory, ha garnered increaing attention among academic over recent year. Our article focue on ome of the technical propertie of compulory voting rule (CVR) while ignoring the philoophical debate over whether voting hould be an obligation or a right. Uing baic probability analyi, we compare a voluntary voting rule (VVR) to a compulory one. We how that, under certain condition, an electoral eat or ditrict can become afer - or le competitive - with the impoition of a CVR. We alo dicu ome political implication of our analyi. For example, when generalized to, ay, the national political ytem, thi reult implie fewer competitive eat in a CVR compared to a VVR, everything ele equal. We contend that, becaue fewer eat will be in play in a CVR, CVR hould exhibit lower turnover of eat. Alo, political upplier can be expected to more narrowly focu their attention - and reource - on thi maller et of competitive eat than we would expect under a VVR. Keyword: Compulory voting and wing eat; Competitivene of electoral eat; Standard deviation of expected electoral reult; arrowing of political upplier focu. *The author would like to thank everal anonymou referee for their effort at improving the paper. Tim Fry acknowledge upport by Autralian Reearch Council Dicovery Project DP : Economic reform and Autralian electoral deciion making. The view expreed, however, are thoe of the author who take reponibility for all remaining error. 93

2 Tim R. L. Fry, Keith Jakee, Martin Kenneally Introduction While voting i not compulory in mot countrie, it i more common than many think: almot 30% of democracie (18 in total) make voting compulory (Maicotte et al. 2003). Depite it widepread implementation (epecially when we include countrie that have relied on compulory voting at ome point in the pat), mot cholarhip on the topic ha focued on it normative apect. The argument for compelling citizen to vote tend to centre on the low and often falling rate of voter turnout around the world. It i argued that highly variable voter participation in voluntary ytem weaken the legitimacy of democratic intitution and therefore weaken democracy itelf. Lijphart (1997, 2), among other, contend that one way to make voting more equal, and hence more democratic, i to aim for a maximization of turnout. A cloe line of argument ugget that voting i really a civic duty which hould be erved by each citizen in return for enjoying the benefit of democracy (Lijphart 1997; Wertheimer 1975). Thoe arguing againt compulion take iue with the view that voting i a duty and challenge the ue of coercion by the tate to enforce what they conider to be a democratic right (Abraham 1955; Jone 1954). They quetion the right of the tate to compel a citizen to vote for a candidate with whom that citizen doe not agree, or in whom he doe not believe. They are alo upiciou of the quality of a democratic outcome if it i baed, at leat in part, upon the opinion of an ill-informed, or apathetic ection of elector who are compelled by law to vote (Hughe 1966, 83). The more analytical exception to thee normative approache are largely empirical tudie that examine the following: how compulory voting rule (CVR) affect voter turnout (ee, inter alia, Jackman 1987; Maicotte et al. 2003; McAlliter 1986): whether compulory voting favour certain partie in Autralia (Jackman 1999; Mackerra and McAlliter 1999); and whether the relatively high level of invalid vote in Autralia i attributable to compulory voting (McAlliter and Makkai 1993). There alo exit a cholarly exchange over compulory voting effect on the growth of government (Crain and Leonard 1993; Yeret 1995; O Toole and Strobl 1995; Crain 1995). Crain and Leonard find that CVR low government growth and poit that thi negative relationhip upport an interet group theory of government a oppoed to a median voter theory of government. Jakee and Sun (2006) conider the likely effect of the role of information (including cot) on the deciion to vote and, taking an expreive view of voting, invetigate two unexamined claim by CVR advocate: (i) that individual are tranformed by forcing them to vote, and (ii) that a compulory electoral outcome i a more accurate reflection of community preference. Uing a formal model, they conclude that compelling thoe who are not particularly intereted 94

3 How Safe are Safe Seat? A Comparion of Voluntary and Compulory Voting Sytem in, or informed about, the political proce to vote increae the proportion of random vote and they how that under imple majority rule, compulory voting may violate the Pareto principle; in other word, the le popular candidate i more likely to be elected (a a random reult) under a CVR. Thi article aim to expand upon our technical undertanding of compulory voting rule and ignore the philoophical debate over whether voting hould be an obligation or a right. In the analyi that follow, we focu on the tatitical propertie aociated with a hift from a voluntary voting rule (VVR) to a CVR. We how that, under certain aumption, an electoral eat or ditrict can become afer or le competitive with the impoition of a CVR. When generalized to an entire political ytem, ay the national one, thi reult implie fewer competitive eat in a CVR compared to a VVR. We then argue that becaue fewer eat will be in play in a CVR, political partie (and incumbent government) will more narrowly focu their attention - and reource - on thi maller et of competitive eat than we would expect under a VVR. Our next ection preent our probability analyi, while the one following dicue ome political implication of our analyi. The penultimate ection raie an important caveat to our reult. The Diperion of Expected Reult under a CVR and a VVR We begin our analyi by noting that real-world CVR tend to regiter higher turnout than voluntary ytem, although they do not typically regiter a full 100% turnout. Turnout in Autralia i, for example, approximately 95% (Autralian Electoral Commiion 2002). While our model and the analytical reult are ufficiently general to encompa CVR turnout that i le than 100%, we tend to dicu our model, below, a if CVR deliver 100% turnout. We do thi for eae of expoition: it i imply more traightforward to illutrate example uing, ay, 100 voter repreenting the entire eligible voting population (i.e., 100% turnout under a CVR) and compare thi etting to ome maller turnout, ay, 64, under a VVR. The VVR turnout can then be eaily calculated a a percentage (i.e., 64%) of the total CVR turnout. Throughout our analyi we aume that there are only two candidate (repreenting two partie), denoted 1 and 2, and that thee candidate run for office in a ingle-member ditrict uing imple majority voting. Imagine a cenario under a VVR in which we know the percentage of the vote that i expected to go to each candidate. Thee expectation are typically formed through pre-election attempt to predict the election outcome uing a variety of mean, uch a opinion poll, previou election reult, and more recently even Internet-baed betting market. For example of the latter in the United State, ee Intrade (n.d.), or the Univerity of Iowa Iowa Electronic Market (n.d.). 95

4 Tim R. L. Fry, Keith Jakee, Martin Kenneally We introduce everal variable and their definition: p 1 p 2 expected percentage of vote for candidate 1 (from among thoe citizen who are expected to vote); expected percentage of vote for candidate 2 (from among thoe citizen who are expected to vote (p2 = 1 p1)); n number of citizen who vote under a VVR; number of citizen who vote under CVR; * number of all citizen eligible to vote; n * * V C percentage of citizen who vote in a VVR, i.e., percentage VVR turnout ; percentage of citizen who vote in a CVR, i.e., percentage CVR turnout ; tandard deviation of the expected vote hare for candidate 1 under VVR and tandard deviation of the expected vote hare for candidate 1 under CVR. For clarity of expoition, we will aume throughout our analyi that candidate 1 i the leading candidate (i.e., p 1 > p 2 ) unle the candidate are tied (i.e., p 1 = p 2 ). We can therefore characterie candidate 2 a the trailing or underdog candidate. Standard deviation and variance are ued in the conventional ene of meauring the variability or diperion of a reult. Specifically, we focu on tandard deviation to meaure the variability of the expected reult p 1. In other word, we are intereted in comparing the variability of the expected vote hare (a percentage) for the winning candidate, candidate 1, under a VVR and a CVR. Formally, thee tandard deviation (of proportion) are defined a: V C p (1 p ) n 1 1 =, and (1) p (1 p ) 1 1 =. (2) The difference between σv and σc lie in the aumption that all eligible citizen, *, are legally obliged to vote under a CVR (i.e., * ), wherea only ome fraction of thee, n/, do o under a voluntary ytem. By definition, then, n <. A noted above, we aume hereafter for expoitory clarity (but without lo of generality) that * =, i.e., that 100% of the electorate vote under CVR. Taking the ratio of σ V to σ C allow u to directly compare the tandard deviation under each rule regime: 96

5 How Safe are Safe Seat? A Comparion of Voluntary and Compulory Voting Sytem V C = p1(1 p1) n p1(1 p1). (3) After rearranging term, we arrive at an expreion for the tandard deviation of p 1 under the CVR in term of the VVR one: C n = ( V). (4) Thi i a reaonably trong reult that tell u that the tandard deviation of the vote hare of candidate 1 will be lower under a CVR than it will under a VVR, a long a turnout i maller in a VVR than a CVR (i.e., that i n< ). Employing value that are eaily calculated, we can imagine the number of all eligible citizen, = 100, and the number who actually turn out in a VVR, n = 64; then n The reulting diperion = = in the CVR, σ C, would be 4/5 the value of the diperion of p 1, σ V, under a VVR. Thi reult can be readily een in Figure 1, which plot the probability ditribution repreenting each of our two example under VVR and a CVR. 1 f(p 1) Tied Election, where (actual p 1 = actual p 2 = 0.5) Voluntary Voting Compulory Voting A B 0,3 0,35 0,4 0,45 0,5 0,55 0,6 0,65 0,7 0,75 0,8 0,85 0,9 0,95 1 Expected Vote Share for Candidate 1 = p 1 Figure 1 Probability ditribution under VVR and CVR (p1 = 0.60, σc, = 4/5(σV), n = 64, = 100) 1 97

6 Tim R. L. Fry, Keith Jakee, Martin Kenneally ote, moreover, that in addition to the lower diperion for the CVR, Figure 1 illutrate that the probability of candidate 1 loing the election ha fallen. Thi reult follow from the fact that the area under either frequency ditribution to the left of any value of p 1 meaure the probability aociated with that value of p 1. Thu, the area under each curve to the left of the vertical line drawn through p 1 = 0.5 meaure the probability that candidate 1 will loe the election, or receive le than 50% of the vote. Under a VVR, Figure 1 how that the probability of candidate 1 actually loing the election i the area A + B. On the other hand, the area under a CVR i only B, which clearly illutrate that the probability that candidate 1 will loe the election under the CVR ha fallen. We can alo characterie the relationhip between the two ytem in term of the likelihood that candidate 2 might catch up with candidate 1 in order to tie the election. Thi can be formalied in the following manner: (0.5 p2). (5) i The numerator in equation (5) i imply the percentage candidate 2 need to tie with candidate 1 and the denominator i the relevant meaure of diperion under each rule regime (i.e., σ i = σ V, or σ i = σ C ). Thi ratio yield the ditance candidate 2 i from tying the election reult in tandard deviation. To take an example, imagine that p 1 = 60% and therefore p 2 = 40% under a VVR. Suppoe further that σ V = 5%. Inerting thee value into equation (5) ugget that 0.10/0.05 = 2. In other word, candidate 2 i 2 tandard deviation away from tying; making up 2 tandard deviation of ditance between himelf and candidate 1 i highly unlikely ince value at 2 tandard deviation and beyond are commonly conidered outide the normal range. ow, conider the ame example under a CVR; we expect C < V, a demontrated in equation (4). In thi cae, the 10% numerator, (0.5 p2), i divided by the CVR maller tandard deviation (i.e., 4/5(σ V ) = 4%) and the entire ratio mut therefore increae. Thu, 0.10/0.04 = 2.5, implying that candidate 2 now ha to make up 2.5 tandard deviation of ditance to tie the race under the CVR. The ditance needed for the loing candidate to tie the race ha increaed under the CVR by 25% (i.e., 0.5 tandard deviation increae under CVR divided by the 2.0 tandard deviation under the VVR). Political Implication The forgoing analyi how that, other thing contant, the certainty of the expected reult of a typical eat or electorate will increae under a CVR. Thi i a key inight becaue reducing the uncertainty (viz. tandard deviation) aociated with the outcome of a given eat mut be valued by political upplier a it allow them to ditinguih between race 98

7 How Safe are Safe Seat? A Comparion of Voluntary and Compulory Voting Sytem that matter veru thoe that do not. In other word, while the competitivene of eat i typically defined in term of the (mall) difference between candidate 1 and candidate 2 expected vote, i.e., p1 p2 0, our reult emphaie the certainty of that difference. 2 For example, the increae in certainty that a CVR can potentially deliver mean that even p a cloe or competitive race under a VVR, in which 1 p2 wa mall, might not be conidered cloe under a CVR if the tandard deviation fell ufficiently to increae the certainty of the outcome, regardle of the proximity of p 1 to p 2. Moreover, the degree of afene will increae under a CVR when the ditance between VVR turnout and CVR turnout i larger, everything ele contant. For example, compare p p two different electorate, each with identically mall ( 1 2 ); uppoe the difference between p 1 and p 2 i 5%. Further uppoe that VVR turnout in eat A i low, wherea VVR turnout in eat B i very high. From equation (4), it can be verified that the CVR make both eat afer, but it ha only a mall effect on eat B compared to a larger effect in eat A. The reult i that all eat become afer under a CVR, but le o for high turnout VVR marginal eat. If we ue our reult to generalie to all electorate within a given regime, ay at the national level, we contend that the number of competitive electorate, when defined in p p term of both ( 1 2 ) and certainty of the expected reult, will fall under a CVR. Put differently, we expect the percentage of afe eat to increae a we move from a VVR to a CVR. Holding everything ele contant, election hould therefore be decided by fewer competitive eat in a CVR. One empirically tetable implication of thi reult i that we would expect CVR to be more table than VVR. By tability, we mean, pecifically that, other thing contant, (i) CVR are expected to have a maller turnover of eat, and (ii) the eat that do wing p p are thoe that would have had a mall ( 1 2 ) under high VVR turnout (recall that cloe race under a VVR with high turnout are expected to remain the cloet when converted to a CVR). The increae in the percentage of afe electorate acro the political ytem raie a final implication of our analyi. A many oberver have noted, an important electoral trategy for political partie and incumbent government i to focu reource on the mot competitive eat. See, for example, Fleck (1999), Levitt and Snyder (1997), or Wright (1974) for empirical analye uing U.S. data, or Denemark (1998) uing Autralian data. Thi hypothei i alo conitent with what Dixit and Londregan (1996) call the wing voter outcome. Our reult ugget that while both ytem generate incentive for political upplier to concentrate on the mot competitive eat, the focu of that concentration will be narrower in a CVR becaue of the fewer number of truly competitive eat. Thi ugget 2 99

8 Tim R. L. Fry, Keith Jakee, Martin Kenneally a greater concentration of political reource, both financial and non-financial, on the relatively maller number of cloe race. Thi aertion applie, of coure, to the activity of incumbent government, ince they have control of the public pure, or what ha been called pork. Indeed, one of the mot well recognized advantage of incumbent i their potential to direct government reource in way that may affect voting outcome. Limitation of our Analyi: IIA Our analyi make a key aumption concerning thoe voter who abtain under a VVR, but are compelled to vote under a CVR, namely that they will vote for candidate 1 and 2 in the ame percentage a the voter do who turnout under a VVR. In other word, our reult depend on the common tatitical aumption, independence from irrelevant alternative (iia). Given that we do not have any a priori ground for auming the voting intention of abtainer differ from thoe who vote, we do not regard thi a an unreaonable working hypothei. On the other hand, if the latent political preference of abtainer differ ubtantially from thoe preference exhibited by voluntary voter, then our analytical framework, which focue on how turnout relate V to C, would have to be broadened to incorporate how turnout might effect ( p 1 p 2 ) under a CVR. Concluion We employed ome baic probability analyi in order to compare the degree of certainty in the ex ante probabilitie aociated with two candidate in voluntary and compulory voting regime. Uing the definition of the tandard deviation of the proportion who are expected to vote for candidate 1, p 1, we howed that, other thing contant, the expected reult for a typical eat or electorate become more certain under a CVR. Thi finding i noteworthy becaue reducing the uncertainty of electoral outcome mut be valuable to political upplier: it allow them to better determine which race matter. Thi certainty of electoral outcome allow u to broaden the definition of a competitive eat, which i typically thought of only in term of a mall difference between candidate 1 and candidate 2 expected vote, i.e., p1 p2 0. Our reult emphaie that the certainty of that difference might be equally valuable to knowing the repective probabilitie for each candidate. A we noted, thi certainty value implie that even a cloe or competitive race p under a VVR (i.e., one in which 1 p2 wa mall) might not be conidered a cloe under a CVR if the tandard deviation fell ufficiently to increae the certainty of the outcome, regardle of the proximity of p 1 to p

9 How Safe are Safe Seat? A Comparion of Voluntary and Compulory Voting Sytem We alo argued that if we generalie our reult to all electorate within, ay, a national electoral ytem, that the number of competitive electorate, when defined in term of both ( p 1 p 2 ) and certainty of the expected reult, will fall under a CVR (and thu the percentage of afe eat will increae). A a reult, we can infer that election might be decided by fewer competitive eat in a CVR. If political upplier focu reource on the more competitive eat, a many oberver have uggeted, we can expect that they will more narrowly focu their attention and reource on a maller ubet of the citizenry in a CVR than they would have to in a VVR. An empirically tetable implication of our analyi i that CVR are expected to be more table than VVR. We define tability in the ene that CVR hould have a maller turnover of eat, and that the eat that do change are expected to be the one p p that would have been cloe (i.e., a mall ( 1 2 )) under high VVR turnout. Finally, we noted that our analyi depend on a common aumption in tatitical inference, the independence of irrelevant alternative. That i, we aume that the abtainer in a VVR who are forced to vote in a CVR would vote in the ame percentage a do the p p elector who vote voluntarily under the VVR. The opinion poll from which ( 1 2 ) i often etablihed typically urvey random electoral ample of thoe who vote and thoe who abtain o thi aumption eem reaonable a an initial hypothei. However, thi aumption doe warrant further theoretical and empirical analyi. Submitted in ovember, 2008 Accepted in June, 2009 ote 1 Our Figure 1 employ the normal ditribution even though our example i that of a binomial ditribution. The normal ditribution i viually eaier to comprehend and ufficiently approximate the binomial when n i large. 2 Beide being decribed a cloe, competitive eat are alo commonly referred to a wing or marginal eat. ote alo that the tandard definition of competitivene (p 1 p 2 ) i related to the numerator in equation (5) by a factor of 2; pecifically, (p 1 p 2 ) = 2(0.5 p 2 ). Bibliographical Reference Abraham, Henry Compulory voting. Wahington DC: Public Affair Pre. Autralian Electoral Commiion (AEC) Voter turnout (ational Summary). 101

10 Tim R. L. Fry, Keith Jakee, Martin Kenneally (acceed ovember, 2009). Crain, W. Mark The right veru the obligation to vote: Rejoinder to Yeret, and O Toole and Strobl. Economic and Politic 7 (3): Crain, W. Mark and Mary Leonard The right veru the obligation to vote: Effect on cro-country government growth. Economic and Politic 5 (1): Denemark, David Buying vote: Parliamentary ytem and pork barrel politic. Autralian Quarterly 70 (6): 37. Dixit, Avinah and John Londregan The determinant of ucce of pecial interet in reditributive politic. The Journal of Politic 58 (4): Fleck, Robert Electoral incentive, public policy, and the new deal realignment. Southern Economic Journal 65 (3): Hughe, Colin Compulory Voting. Politic 1 (2): Intrade. n.d. Intrade: The prediction market. Dublin, Ireland. (acceed ovember, 2009). Iowa Electronic Market. n.d. What i the IEM? Iowa City, Iowa: Univerity of Iowa. biz.uiowa.edu/iem/index.cfm (acceed ovember, 2009). Jackman, Robert Political intitution and voter turnout in the indutrial democracie. American Political Science Review 81 (2): Jackman, Simon on-compulory voting in Autralia? What urvey can (and can t) tell u. Electoral Studie 18: Jakee, Keith, and Guang-Zhen Sun I compulory voting more democratic? Public Choice 129 (1): Jone, W. H. Morri In defence of apathy: Some doubt on the duty to vote. Political Studie 2(1): Levitt, Steven, and Jame Snyder The impact of federal pending on houe election outcome. Journal of Political Economy 105 (1): Lijphart, Arend Unequal participation: Democracy unreolved dilemma. American Political Science Review 91 (1): Mackerra, Malcolm and Ian McAlliter Compulory voting, party tability and electoral advantage in Autralia. Electoral Studie 18 (2): Maicotte, Loui, Andre Blai, and Antoine Yohinaka Etablihing the rule of the game: Election law in democracie. Toronto: Univerity of Toronto Pre. McAlliter, Ian Compulory voting, turnout and party advantage in Autralia. Politic, 21 (1): McAlliter, Ian, and Toni Makkai Intitution, ociety or protet? Explaining invalid vote in autralian election. Electoral Studie 12 (1):

11 How Safe are Safe Seat? A Comparion of Voluntary and Compulory Voting Sytem O Toole, Franci, and Eric Strobl Compulory voting and government pending. Economic and Politic 7 (3): Wertheimer, Alan In defene of Compulory Voting. In Participation in Politic, ed. J. Roland Pennock and John Chapman. ew York: Lieber-Atherton. Wright, Gavin The political economy of new deal pending: An econometric analyi. Review of Economic and Statitic 56 (1): Yeret, Eliyahu Dictator, democracie, and voter: A Comment on the right veru the obligation to vote. Economic and Politic 7 (3):

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