To be on the Winning Side

Previous articleNext article No AccessThe Closed Rule and the Paradox of VotingJohn C. BlydenburghJohn C. Blydenburgh Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by The Journal of Politics Volume 33, Number 1Feb., 1971 Sponsored by the Southern Political Science Association Article DOIhttps://doi.org/10.2307/2128532 Views: 16Total views on this site Citations: 23Citations are reported from Crossref Copyright 1971 Southern Political Science AssociationPDF download Crossref reports the following articles citing this article:Valerio Dotti Reaching across the aisle to block reforms, Economic Theory 72, no.22 (Aug 2020): 533–578.https://doi.org/10.1007/s00199-020-01298-6Jim Granato, Melody Lo, M. C. Sunny Wong Empirical Implications of Theoretical Models in Political Science, 1 (May 2021).https://doi.org/10.1017/9781139026819Donald P. Green, Alan S. Gerber Voter Mobilization, Experimentation, and Translational Social Science, Perspectives on Politics 14, no.33 (Aug 2016): 738–749.https://doi.org/10.1017/S1537592716001158Eerik Lagerspetz Social Choice in the Real World, (Jan 2016): 383–430.https://doi.org/10.1007/978-3-319-23261-4_7Adrian Van Deemen On the empirical relevance of Condorcet’s paradox, Public Choice 158, no.3-43-4 (Nov 2013): 311–330.https://doi.org/10.1007/s11127-013-0133-3Jan Skalík Pozměňovací návrh jako indikátor při přijímání české legislativy životního prostředí, Sociální studia / Social Studies 10, no.11 (Jan 2013): 75.https://doi.org/10.5817/SOC2013-1-75William V. Gehrlein, Dominique Lepelley Voting Paradoxes and Their Probabilities, (Jul 2010): 1–47.https://doi.org/10.1007/978-3-642-03107-6_1Gerry Mackie Democracy Defended, 20 (Sep 2009).https://doi.org/10.1017/CBO9780511490293Gary Prevost, Robert Weber The Prospects for the Free Trade Area of the Américas in the Bush Administration, (Jan 2002): 67–106.https://doi.org/10.1057/9780230107434_4John D. Wilkerson “Killer” Amendments in Congress, American Political Science Review 93, no.33 (Aug 2014): 535–552.https://doi.org/10.2307/2585573Ad M. A. Van Deemen, Noël P. Vergunst Empirical evidence of paradoxes of voting in Dutch elections, (Jan 1998): 257–272.https://doi.org/10.1007/978-1-4757-5127-7_11Eerik Lagerspetz Social Choice in the Real World II: Cyclical Preferences and Strategic Voting in the Finnish Presidential Elections, Scandinavian Political Studies 20, no.11 (Mar 1997): 53–67.https://doi.org/10.1111/j.1467-9477.1997.tb00184.xDan S Felsenthal, Moshé Machover Who ought to be elected and who is actually elected? An empirical investigation of 92 elections under three procedures, Electoral Studies 14, no.22 (Jun 1995): 143–169.https://doi.org/10.1016/0261-3794(94)00019-6Dan S. Felsenthal, Zeev Maoz, Amnon Rapoport An Empirical Evaluation of Six Voting Procedures: Do They Really Make Any Difference?, British Journal of Political Science 23, no.11 (Jan 2009): 1–27.https://doi.org/10.1017/S0007123400006542Dan S. Felsenthal, Moshé Machover After two centuries, should condorcet's voting procedure be implemented?, Behavioral Science 37, no.44 (Oct 1992): 250–274.https://doi.org/10.1002/bs.3830370403Arthur Denzau, William Riker, Kenneth Shepsle Farquharson and Fenno: Sophisticated Voting and Home Style, American Political Science Review 79, no.44 (Dec 1985): 1117–1134.https://doi.org/10.2307/1956251 Bibliography, (Jan 1985): 215–224.https://doi.org/10.1016/B978-0-12-125455-1.50016-7William V. Gehrlein Condorcet's paradox, Theory and Decision 15, no.22 (Jun 1983): 161–197.https://doi.org/10.1007/BF00143070E. M. Uslaner Manipulation of the Agenda by Strategic Voting: Separable and Nonseparable Preferences, (Jan 1981): 135–152.https://doi.org/10.1007/978-3-662-00411-1_10John R. Chamberlin, Michael D. Cohen Toward Applicable Social Choice Theory: A Comparison of Social Choice Functions under Spatial Model Assumptions, American Political Science Review 72, no.44 (Aug 2014): 1341–1356.https://doi.org/10.2307/1954543Terry Sullivan Voter's paradox and logrolling, Public Choice 25, no.11 (Mar 1976): 31–44.https://doi.org/10.1007/BF01726329Joe Oppenheimer Some Political Implications of “Vote Trading and the Voting Paradox: A Proof of Logical Equivalence:” A Comment, American Political Science Review 69, no.33 (Aug 2014): 963–966.https://doi.org/10.2307/1958412Nicholas R. Miller Logrolling and the arrow paradox: A note, Public Choice 21, no.11 (Mar 1975): 107–110.https://doi.org/10.1007/BF01705951

We theoretically and experimentally study voter behavior in a setting characterized by plurality rule and mandatory voting, where voters choose from three options. We are interested in the occurrence of strategic voting in an environment where Condorcet cycles may occur. In particular, we focus on how information about the distribution of preferences affects strategic behavior. We also vary the relative importance of the second preferred option to investigate how this affects the strategic vote. Quantal response equilibrium analysis is used to analyze the game and proves to be a good predictor for the experimental data. Our results indeed show that strategic voting arises, the extent of which depends on (i) the availability of information; (ii) the relative importance of the intermediate candidate; (iii) the electorate's relative support for one's preferred candidate; and (iv) the relative position of the plurality-supported candidate in a voter's preference ordering. Our results show that information serves as a coordination device where strategic voting does not harm the plurality-preferred candidate's chances of winning.

Strategic Voting and Coalitions: Condorcet’s Paradox and Ben-Gurion’s Tri-lemma

We theoretically and experimentally study voter behavior in a setting characterized by plurality rule and mandatory voting. Voters choose from three options. We are interested in the occurrence of strategic voting in an environment where Condorcet cycles may occur and focus on how information about the preference distribution affects strategic behavior. We also vary the relative importance of the second preferred option. Quantal response equilibrium analysis is used to analyze the game and derive predictions. Our results indeed show that strategic voting arises. Its extent depends on (i) information availability; (ii) the relative importance of the intermediate candidate; (iii) the electorate’s relative support for one’s preferred candidate; (iv) the relative position of the plurality-supported candidate in one’s preference ordering. Our results show that information serves as a coordination device where strategic voting does not harm the plurality-preferred candidate’s chances of winning.Electronic supplementary materialThe online version of this article (doi:10.1007/s10683-015-9443-2) contains supplementary material, which is available to authorized users.

We study strategic voting in a setting where voters choose from three options and Condorcet cycles may occur. We introduce in the electorate heterogeneity in preference intensity by allowing voters to differ in the extent to which they value the three options. Three information conditions are tested: uninformed, in which voters know only their own preference ordering and the own benefits from each option; aggregate information, in which in addition they know the aggregate realized distribution of the preference orderings and full information, in which they also know how the relative importance attributed to the options are distributed within the electorate. As a general result, heterogeneity seems to decrease the level of strategic voting in our experiment compared to the homogenous preference case that we study in a companion paper. Both theoretically and empirically (with data collected in a laboratory experiment), the main comparative static results obtained for the homogenous case carry over to the present setting with preference heterogeneity. Moreover, information about the realized aggregate distribution of preferences seems to be the element that best explains observed differences in voting behavior. Additional information about the realized distribution of preference intensity does not yield significant further changes.

In a paper entitled "Beyond the Voter's Paradox" (Ethics, October 1977), I outlined a general theory of rationality for social decision procedures according to which rationality consists in procedural determinacy, a condition in which the aggregated desiderative data wholly entail the decision drawn from them, and irrationality consists in procedural indeterminacy, a condition which makes possible the Voter's Paradox and the various other deficiencies of existing voting practices. I also argued that, with a minor modification, C. L. Dodgson's Method of Marks would conform to this criterion of rationality, and, further, that use of this Modified Method of Marks in practice would have the effect of eliminating many cumbersome features of majority rule. In a response to this paper, Elaine Mates Spitz claims, not only that there are defects in the Modified Method of Marks, but also that all formal models of decision theory fail to reflect fully the political, social, and moral complexities of majority rule, and therefore have no place either in justifying or attacking it (Elaine Mates Spitz, "Majority Rule: The Virtue of Numbers," Ethics, vol. 89, no. 1 [October 1978]). My main concern in this paper will be to defend the use of such formal models against this sort of attack. However, because it is made to appear that the attack draws much of its force from its seemingly devastating criticisms of the Modified Method of Marks, I will begin by correcting the distortions of this method which make that sham seem plausible.

‘Condorcet cycles’ (or ‘paradoxes of cyclical majorities’) are an empirically rare phenomenon. A referendum in the Swiss canton of Bern on 28 November 2004 presents a rare occurrence. This study presents a new multi-option referendum procedure that makes Condorcet cycles visible, and it argues that in this case, the paradox might have resulted from strategic voting patterns.

According to the oft-repeated story, the theory of social choice was invented by the eighteenth century French mathematicians: Borda. Condorcet, and Laplace. After their contributions, the subject is said to have fallen into oblivion. The aim of this article is to challenge this narrative by reviewing a nineteenth century discussion on the merits of different voting rules. In that discussion the social choice results had a central role. The participants in the heated dispute were both professors at the University of Helsinki: Lorenz Lindelof (1827–1908) was the Professor of Mathematics, a noted mathematician and statistician, while Johan Wilhelm Snellman (1806–1881) was the Professor of Philosophy and the unofficial intellectual leader of the Finnish national movement. Many of the arguments used by them also appear in modern treatments of social choice theory. Such basic anomalies of social choice as the Borda paradox, the Condorcet paradox, path-dependence, and strategic voting figured in the discussion.

At first glance, digital platforms seem to be an excellent way to strengthen democracy by expanding opportunities for participation. More inclusive by involving all sections of the population and more substantial by the easy availability of information. Unfortunately, the utopia of the digital republic will never be realized. Three theorems show why: First, Condorcet’s “problem of cyclical majorities” (also known as the “Condorcet paradox”), then Kenneth Arrow’s “impossibility theorem,” and finally Allan Gibbard and Mark Satterthwaite’s “manipulation or strategic voting theorem”. However, even if we object to the idea of a digital republic, demonstrating that it is not feasible for systematic reasons and that moving toward it is not desirable, we believe it to be compatible with advocating massive use of the new technological possibilities. While the enrichment of public space through the involvement of as many citizens as possible may not replace democracy it may very well strengthen it.

This chapter begins by assessing the empirical evidence about the social choice paradoxes, especially the evidence about the Condorcet Paradox. I discuss briefly the possible reasons of the paucity of the empirical evidence. Then, I compare two real-life political institutions: the traditional Finnish presidential election system, which was in use from 1925 to 1988, and its US-American counterpart. For several reasons, the two Electoral Colleges provide an interesting subject for applied social choice. By using historical sources I try to show that the history of the Finnish Electoral College exhibits two, perhaps three instances of the Condorcet paradox, and provides dramatic examples of the effects of strategic voting. In contrast, in the US Electoral College there are no instances of the Condorcet paradox, for the unit-rule version of plurality tends to produce unambiguous majorities. This is acquired at a cost: the US system of electing the College violates the Arrovian independence and path-independence conditions far more often than the proportional Finnish system. For this reason, the connection between the distribution of the popular vote and the composition of the College is very weak. Both the US and the Finnish system may exhibit quasi-chaotic behaviour—“chaotic” in the sense that very small, unpredictable perturbations may sometimes change the outcome. This is one consequence of Arrow’s theorem.

This article examines the contributions of formal modeling to the study of American elections and voting behavior. It concentrates on strategic voting and voter competence for which formal models have been used to explain complex, subtle, and important patterns of behavior that other theories did not explain well. It then tries to clarify the broader potential contributions of the method to the study of voting behavior. Moreover, it provides a brief discussion of the likely role of formal modeling in future voting behavior scholarship. In so doing, it presents examples of current scholarly pursuits whose precision and validity could be improved by greater clarity about assumptions and logical transparency in inference. Formal models provide a rigorous means for converting knowledge from fields such as social or cognitive psychology into more effective research designs and stronger conclusions about why voters act as they do.

In this study formal spatial models are applied to cross-sectional analysis of district results on the second ballot of French legislative elections. A model of probabilistic spatial voting better accounts for the data than either standard “ecological” models or a model of deterministic spatial voting. There are three substantive findings concerning voter behavior. First, the adjustment of voters to external information can be largely viewed as a shift in the spatial (Left-Right) distribution of voters. This shift, plus decisions by parties and candidates as to which districts parties will contest, determines the first ballot outcome. In arriving at second ballot choices, voters then appear to utilize decision rules that have a substantial degree of temporal stability. A second and related finding is that the second ballot can be reasonably accounted for by a single Left-Right dimension. Third, in those districts with three or more candidates on the second ballot, there may be substantial strategic voting with voters switching from candidates close to their ideal points but unlikely to win to more distant candidates who are more likely to win. The existence of strategic voting is suggested by the finding that models based solely on spatial preferences perform well for two-candidate districts, but less well for three- or four-candidate districts.

In this study formal spatial models are applied to cross-sectional analysis of district results on the second ballot of French legislative elections. A model of probabilistic spatial voting better accounts for the data than either standard “ecological” models or a model of deterministic spatial voting. There are three substantive findings concerning voter behavior. First, the adjustment of voters to external information can be largely viewed as a shift in the spatial (Left-Right) distribution of voters. This shift, plus decisions by parties and candidates as to which districts parties will contest, determines the first ballot outcome. In arriving at second ballot choices, voters then appear to utilize decision rules that have a substantial degree of temporal stability. A second and related finding is that the second ballot can be reasonably accounted for by a single Left-Right dimension. Third, in those districts with three or more candidates on the second ballot, there may be substantial strategic voting with voters switching from candidates close to their ideal points but unlikely to win to more distant candidates who are more likely to win. The existence of strategic voting is suggested by the finding that models based solely on spatial preferences perform well for two-candidate districts, but less well for three- or four-candidate districts.

This paper investigates the dynamics of the “wasted vote” phenomenon and Duverger's Law. I construct a theoretical model in order to consider how preelection polls serve to inform the electorate about the relative chances of the candidates and how that information acts over time to decrease the support of the trailing candidate. The results shed light on how public opinion polls can aggregate information in the electorate and coordinate voters on the viable candidates in the election. Specifically, I show that in a Bayesian game model of strategic voting there exist non-Duvergerian equilibria in which all three candidates receive votes (in the limit). These equilibria require extreme coordination, however, and any variation in beliefs leads voters away from them to one of the Duvergerian equilibria. Thus, non-Duvergerian equilibria are unstable, while two-party equilibria are not. In addition, I describe how preelection polls provide information to voters about the viability of candidates and can thus be used by voters to coordinate on a Duvergerian outcome.

Research on strategic voting has mainly focused on electoral system effects but largely neglected the impact of different rationales of coalition formation. Based on a formal model of rational party choice and a simulation study, we systematically investigate this impact and explore the implications. We show that the logic of the underlying coalition formation procedure clearly affects the degree to which the electorate is exposed to strategic incentives regarding the vote choice. The key implications are that sincere voting is more often in the voter’s best interest if parties are policy-seeking and if there is increased uncertainty during the stage of coalition formation. Furthermore, we explore how different types of coalition formation affect strategic incentives across the policy space.