Abstract
How often do events of interest to voting theorists occur in actual elections? For example, what is the probability of observing a voting cycle – an outcome in which no candidate beats all other candidates in pairwise comparison by majority rule? When there is a candidate who beats all others in such pairwise comparisons – a Condorcet winner – what is the probability that a voting method chooses this candidate?What is the probability that voters have an incentive to vote strategically – that is, cast their votes in ways that do not reflect their true preferences? Voting theorists have analyzed these questions in great detail, using a variety of statistical models that describe different distributions of candidate rankings.
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References
Brams, S.J., & Fishburn, P. (2001). A nail-biting election. Social Choice Welfare, 18, 409–414.
Campbell, C., & Tullock, G. (1965). A measure of the importance of cyclical majorities. Economic Journal, 75, 300 & 853–857.
Cervone, D., Gehrlein, W.V., Zwicker, W. (2005). Which scoring rule maximizes Condorcet efficiency under IAC. Theory and Decision, 58 (2), 145–185.
Chamberlin, J.R., & Featherston, F. (1986). Selecting a voting system. Journal of Politics, 48 (2), 347–369.
Condorcet, M.JAN., Marquis de (1785). Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix (Paris).
Conitzer, V., & Sandholm, T. (2005). Common voting rules as maximum likelihood estimators. Proceedings of the 21st Annual Conference on Uncertainty in Artificial Intelligence (UAI-05) (pp. 145–152). UK: Edinburgh.
Davis, O.A., Hinich, M.J., Ordeshook, P.C. (1970). An expository development of a mathematical model of the electoral process. American Political Science Review, 44, 426–448.
DiDonato, A.R., & Hageman, R.K. (1980). Computation of the integral of the bivariate normal distribution over arbitrary polygons. Naval Surface Weapons Center, Government Accession Number ADA102466.
Enelow, J.M., & Hinich, M.J. (1984). The spatial theory of voting: An introduction. Cambridge University Press.
Enelow, J.M., & Hinich, M.J. (1990). Advances in the spatial theory of voting. Cambridge University Press.
Feld, S., & Grofman, B. (1990). Collectivities as actors. Rationality and Society, 2 (4), 429–448.
Feld, S., & Grofman, B. (1992). Who’s afraid of the big bad cycle? Evidence from 36 elections. Journal of Theoretical Politics, 4 (2), 231–237.
Felsenthal, D.S., Maoz, Z., Rapoport, A. (1993). An empirical evaluation of six voting procedures: do they really make any difference? British Journal of Political Science, 23 (1), 1–27.
Felsenthal, D.S., & Machover, M. (1995). Who ought to be elected and who is actually elected? An empirical investigation of 92 Elections under three procedures. Electoral Studies, 14 (2), 143–169.
Gehrlein, W.V., & Fishburn, P.C. (1976). Condorcet’s paradox and anonymous preference profiles. Public Choice, 26, 1–18.
Gehrlein, W.V. (1978). Condorcet winners in dual cultures. Presented at the National Meeting of the Public Choice Society, New Orleans.
Gehrlein, W.V. (2002). Condorcet’s paradox and the likelihood of its occurrence: Different perspectives on balanced preferences. Theory and Decision, 52 (2), 171–199.
Gehrlein, W.V. (2004). Consistency in measures of social homogeneity: A connection with proximity to single-peaked preferences. Quality and Quantity, 38, 147–171.
Gehrlein, W.V. (2006). Condorcet’s paradox. Berlin and Heidelberg: Springer.
Good, I.J., & Tideman, T.N. (1976). From individual to collective ordering through multidimensional attribute space. Proceedings of the Royal Society of London (Series A), 347, 371–385.
Kemeny, J. (1959). Mathematics without numbers. Daedalus, 88, 571–91.
Kendall, M., & Gibbons, J.D. (1990). Rank correlation methods. New York: Oxford University Press.
Kotz, S., Balakrishnan, N., Johnson, N.L. (2000). Continuous multivariate distributions. New York: Wiley.
Kuga, K., & Nagatani, H. (1974). Voter antagonism and the paradox of voting. Econometrica, 42, 1045–1067.
Lepelley, D. (1995). Condorcet efficiency of positional voting rules with single-peaked preferences. Economic Design, 1, 289–299.
Merrill, S. (1984). A comparison of efficiency of multicandidate electoral systems. American Journal of Political Science, 28, 23–48.
Mosimann, J.E. (1962). On the compound multinomial distribution, the multivariate beta distribution, and correlations among proportions. Biometrika, 49, 65–82.
Regenwetter, M., Grofman, B., Marley, A.A.J. (2002). On the model dependence of majority preference relations reconstructed from ballot or survey data. Mathematical Social Sciences, 43, 451–466.
Regenwetter, M., Marley, A.A.J., Grofman, B. (2003). General concepts of value restriction and preference majority. Social Choice Welfare, 21, 149–173.
Regenwetter, M., Grofman, B., Marley, A.A.J., Tsetlin, I.M. (2006). Behavioral social choice: Probabilistic models, statistical inference, and applications. Cambridge University Press.
Saari, D.G. (1990). Susceptibility to manipulation. Public Choice, 64, 21–41.
Saari, D.G. (2001). Analyzing a nail-biting election. Social Choice Welfare, 18, 415–430.
Tideman, T.N., & Richardson, D. (2000). Better voting methods through technology: the refinement-manageability trade-off in the single transferable vote. Public Choice, 103 (1–2), 13–34.
Tideman, T.N. (2006). Collective decisions and voting. Ashgate: Burlington VT.
Truchon, M. (2006). Borda and the maximum likelihood approach to vote aggregation. Mimeo.
Young, H.P. (1988). Condorcet’s theory of voting. American Political Science Review, 82 (4), 1231–1244.
Acknowledgements
We express our gratitude to an anonymous referee, who read our paper with unusual care and pointed out several errors and omissions, as well as to Dan Felsenthal and Moshé Machover for their patience and persistence during the editing process. All remaining errors are ours.
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Tideman, T.N., Plassmann, F. (2012). Modeling the Outcomes of Vote-Casting in Actual Elections. In: Felsenthal, D., Machover, M. (eds) Electoral Systems. Studies in Choice and Welfare. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20441-8_9
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