×

A theory of voting in large elections. (English) Zbl 1154.91383

Summary: This paper provides a game-theoretic model of probabilistic voting and then examines the incentives faced by candidates in a spatial model of elections. In our model, voters’ strategies form a Quantal Response Equilibrium (QRE), which merges strategic voting and probabilistic behavior. We first show that a QRE in the voting game exists for all elections with a finite number of candidates, and then proceed to show that, with enough voters and the addition of a regularity condition on voters’ utilities, a Nash equilibrium profile of platforms exists when candidates seek to maximize their expected margin of victory. This equilibrium (1) consists of all candidates converging to the policy that maximizes the expected sum of voters’ utilities, (2) exists even when voters can abstain, and (3) is unique when there are only 2 candidates.

MSC:

91B12 Voting theory
91A80 Applications of game theory
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Alvarez, R. M.; Nagler, J., Economics, issues, and the Perot candidacy: Voter choice in the 1992 presidential election, Amer. J. Polit. Sci., 39, 714-744 (1995)
[2] Alvarez, R. M.; Nagler, J., When politics and models collide: Estimating models of multiparty competition, Amer. J. Polit. Sci., 42, 55-96 (1998)
[3] Alvarez, R.M., Nagler, J., 2001. Correlated disturbances in discrete choice models: A comparison of multinomial probit models and logit models, Mimeo. California Institute of Technology; Alvarez, R.M., Nagler, J., 2001. Correlated disturbances in discrete choice models: A comparison of multinomial probit models and logit models, Mimeo. California Institute of Technology
[4] Alvarez, R. M.; Nagler, J.; Bowler, S., Issues, economics, and the dynamics of multiparty elections: The British 1987 general election, Amer. Polit. Sci. Rev., 94, 131-149 (2000)
[5] Ansolabehere, S.; Snyder, J. M., Valence politics and equilibrium in spatial election models, Public Choice, 103, 3, 327-336 (2000)
[6] Aragones, E.; Palfrey, T., Mixed equilibrium in a Downsian model with a favored candidate, J. Econ. Theory, 103, 1, 131-161 (2002) · Zbl 1050.91028
[7] Austen-Smith, D.; Banks, J. S., Information aggregation, rationality and the Condorcet Jury Theorem, Amer. Polit. Sci. Rev., 90, 3445 (1996)
[8] Banks, J.; Duggan, J., Probabilistic voting in the spatial model of elections: The theory of office-motivated candidates, (Austen-Smith, D.; Duggan, J., Social Choice and Strategic Decisions (2004), Springer: Springer New York, NY) · Zbl 1255.91012
[9] Banks, J.; Duggan, J.; Breton, M. L., Bounds for mixed strategy equilibria and the spatial model of elections, J. Econ. Theory, 103, 88-105 (2002) · Zbl 1022.91001
[10] Bhattacharya, R. N.; Rao, R. R., Normal Approximation and Asymptotic Expansions (1986), Krieger: Krieger Malabar, FL · Zbl 0657.41001
[11] Black, D., On the rationale of group decision-making, J. Polit. Economy, 56, 23-34 (1948)
[12] Brennan, H. G.; Lomasky, L. E., Democracy and Decision (1993), Cambridge Univ. Press: Cambridge Univ. Press Cambridge
[13] Buchanan, J. M., Individual choice in voting and the market, J. Polit. Economy, 62, 334-343 (1954)
[14] Calvert, R., Robustness of the multidimensional voting model: Candidate motivations, uncertainty, and convergence, Amer. J. Polit. Sci., 28, 1, 127-146 (1985)
[15] Coughlin, P. J., Probabilistic Voting Theory (1992), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0601.90011
[16] Coughlin, P. J.; Nitzan, S., Directional and local electoral equilibria with probabilistic voting, J. Econ. Theory, 24, 226-240 (1981) · Zbl 0487.90011
[17] Coughlin, P. J.; Nitzan, S., Electoral outcomes with probabilistic voting and Nash social welfare maxima, J. Public Econ., 15, 113-122 (1981)
[18] Dow, J. K.; Endersby, J. W., Multinomial probit and multinomial logit: A comparison of choice models for voting research, Electoral Stud., 23, 107-122 (2004)
[19] Duggan, J.; Fey, M., Electoral competition with policy-motivated candidates, Games Econ. Behav., 51, 2, 490-522 (2005) · Zbl 1117.91021
[20] Feddersen, T.; Pesendorfer, W., The swing voters curse, Amer. Econ. Rev., 86, 3, 408-424 (1996)
[21] Groseclose, T., A model of candidate location when one candidate has a valence advantage, Amer. J. Polit. Sci., 45, 4, 862-886 (2001)
[22] Hinich, M. J., Equilibrium in spatial voting: The median voter result is an artifact, J. Econ. Theory, 16, 208-219 (1977) · Zbl 0397.90008
[23] Lacy, D.; Burden, B. C., The vote-stealing and turnout effects of Ross Perot in the 1992 US presidential election, Amer. J. Polit. Sci., 43, 233-255 (1999)
[24] Ledyard, J., The pure theory of large two-candidate elections, Public Choice, 44, 7-41 (1984)
[25] Lin, T.-M.; Enelow, J.; Dorussen, H., Equilibrium in multicandidate probabilistic voting, Public Choice, 98, 59-82 (1999)
[26] McKelvey, R., Intransitivities in multidimensional voting models and some implications for agenda control, J. Econ. Theory, 12, 472-484 (1976) · Zbl 0373.90003
[27] McKelvey, R., General conditions for global intransitivities in formal voting games, Econometrica, 47, 1085-1111 (1979) · Zbl 0411.90009
[28] McKelvey, R. D.; Ordeshook, P. C., A general theory of the calculus of voting, (Herndon, J.; Bernd, J., Mathematical Applications in Political Science, vol. VI (1972), Univ. Press of Virginia: Univ. Press of Virginia Charlottesville), 32-78 · Zbl 0419.90008
[29] McKelvey, R. D.; Palfrey, T. R., Quantal response equilibria in normal form games, Games Econ. Behav., 10, 6-38 (1995) · Zbl 0832.90126
[30] McKelvey, R. D.; Palfrey, T. R., Quantal response equilibria in extensive form games, Exper. Econ., 1, 9-41 (1998) · Zbl 0920.90141
[31] McKelvey, R.; Schofield, N., Generalized symmetry conditions at a core point, Econometrica, 55, 923-933 (1987) · Zbl 0617.90004
[32] Meerschaert, M. M.; Schemer, H.-P., Limit Distributions for Sums of Independent Random Vectors (2001), Wiley: Wiley New York · Zbl 0990.60003
[33] Milgrom, P.; Weber, R., Distributional strategies for games with incomplete information, Math. Operations Res., 10, 619-632 (1985) · Zbl 0582.90106
[34] Myerson, R., Large Poisson games, J. Econ. Theory, 94, 7-45 (2000) · Zbl 1044.91004
[35] Myerson, R.; Weber, R., A theory of voting equilibria, Amer. Polit. Sci. Rev., 87, 102-114 (1993)
[36] Patty, J. W., Equivalence of objectives in two-candidate elections, Public Choice, 112, 1, 151-166 (2002)
[37] Patty, J. W., Local equilibrium equivalence in probabilistic voting models, Games Econ. Behav., 51, 2, 523-536 (2005) · Zbl 1099.91040
[38] Patty, J.W., 2006. Generic difference of expected vote share and probability of victory maximization in simple plurality elections with probabilistic voters. Soc. Choice Welfare. In press; Patty, J.W., 2006. Generic difference of expected vote share and probability of victory maximization in simple plurality elections with probabilistic voters. Soc. Choice Welfare. In press · Zbl 1133.91012
[39] Quinn, K. M.; Martin, A. D.; Whitford, A. B., Voter Choice in multiparty democracies: A test of competing theories and models, Amer. J. Polit. Sci., 43, 1231-1247 (1999)
[40] Schofield, N., Local political equilibria, (Austen-Smith, D.; Duggan, J., Social Choice and Strategic Decisions (2004), Springer: Springer Heidelberg) · Zbl 1255.91017
[41] Schofield, N., A valence model of political competition in Britain, 1992-1997, Electoral Stud., 24, 3, 347-370 (2005)
[42] Schofield, N.; Sened, I., Modeling the interaction of parties, activists and voters: Why is the political center so empty?, Europ. J. Polit. Res., 44, 3, 355-390 (2005)
[43] Schofield, N.; Martin, A. D.; Quinn, K. M.; Whitford, A. B., Multiparty electoral competition in Netherlands and Germany: A model based on multinomial probit, Public Choice, 97, 257-293 (1998)
[44] Schuessler, A. A., A Logic of Expressive Choice (2000), Princeton Univ. Press: Princeton Univ. Press Princeton
[45] Tullock, G., The charity of the uncharitable, Western Econ. J., 9, 379-392 (1971)
[46] Wittman, D. A., Candidate motivation: A synthesis of alternative theories, Amer. Polit. Sci. Rev., 77, 142-157 (1983)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.