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**Electoral competition with policy-motivated candidates.**
*(English)*
Zbl 1117.91021

Summary: In the multi-dimensional spatial model of elections with two policy-motivated candidates, we prove that the candidates must adopt the same policy platform in equilibrium. Moreover, when the number of voters is odd, if the gradients of the candidates’ utility functions point in different directions, then they must locate at some voter’s ideal point and a strong symmetry condition must be satisfied: in particular, it must be possible to pair some voters so that their gradients point in exactly opposite directions. If the number of dimensions is more than two, then our condition is knife-edge. When the number of voters is even, the situation is worse: such equilibria never exist, regardless of the dimensionality of the policy space.

### References:

[1] | Banks, J.S., Duggan, J., 2000. A multidimensional model of repeated elections. University of Rochester; Banks, J.S., Duggan, J., 2000. A multidimensional model of repeated elections. University of Rochester |

[2] | Banks, J. S.; 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: Essays in Honor of Jeffrey S. Banks (2005), Springer: Springer New York), 15-56 · Zbl 1255.91012 |

[3] | Besley, T.; Coate, S., An economic model of representative democracy, Quart. J. Econ., 112, 85-114 (1997) · Zbl 0882.90001 |

[4] | Besley, T.; Coate, S., Sources of inefficiency in a representative democracy: A dynamic analysis, Amer. Econ. Rev., 88, 139-156 (1998) |

[5] | Black, D., The Theory of Committees and Elections (1958), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0091.15706 |

[6] | Calvert, R. L., Robustness of the multidimensional voting model: Candidate motivations, uncertainty, and convergence, Amer. J. Polit. Sci., 29, 69-95 (1985) |

[7] | Cox, G. W., Non-collegial simple games and the nowhere denseness of the set of preferences profiles having a core, Soc. Choice Welfare, 1, 159-164 (1984) · Zbl 0587.90105 |

[8] | Davis, O. A.; DeGroot, M. H.; Hinich, M. J., Social preference orderings and majority rule, Econometrica, 40, 147-157 (1972) · Zbl 0261.90006 |

[9] | Downs, A., An Economic Theory of Democracy (1957), Harper and Row: Harper and Row New York |

[10] | Duggan, J., Repeated elections with asymmetric information, Econ. Politics, 12, 109-136 (2000) |

[11] | Duggan, J., Fey, M., 2001. Electoral competition with policy-motivated candidates. University of Rochester; Duggan, J., Fey, M., 2001. Electoral competition with policy-motivated candidates. University of Rochester · Zbl 1117.91021 |

[12] | Lagerlöf, J., Policy-motivated candidates, noisy platforms, and non-robustness, Public Choice, 114, 319-347 (2003) |

[13] | Le Breton, M., On the core of voting games, Soc. Choice Welfare, 4, 295-305 (1987) · Zbl 0636.90099 |

[14] | McKelvey, R. D., Covering, dominance, and institution-free properties of social choice, Amer. J. Polit. Sci., 30, 283-314 (1986) |

[15] | McKelvey, R.D., Patty, J., 2003. A theory of voting in large elections. Carnegie Mellon University; McKelvey, R.D., Patty, J., 2003. A theory of voting in large elections. Carnegie Mellon University · Zbl 1154.91383 |

[16] | McKelvey, R. D.; Schofield, N., Generalized symmetry conditions at a core point, Econometrica, 55, 923-933 (1987) · Zbl 0617.90004 |

[17] | Osborne, M. J., Spatial models of political competition under plurality rule: A survey of some explanations of the number of candidates and the positions they take, Can. J. Econ., 28, 261-301 (1995) |

[18] | Osborne, M. J.; Slivinski, A., A model of political competition with citizen-candidates, Quart. J. Econ., 111, 65-96 (1996) · Zbl 0870.90041 |

[19] | Plott, C. R., A notion of equilibrium and its possibility under majority rule, Amer. Econ. Rev., 57, 787-806 (1967) |

[20] | Rubinstein, A., A note about the ‘nowhere denseness’ of societies having an equilibrium under majority rule, Econometrica, 47, 511-514 (1979) · Zbl 0416.90006 |

[21] | Schofield, N., Generic instability of majority rule, Rev. Econ. Stud., 50, 695-705 (1983) · Zbl 0521.90011 |

[22] | Shepsle, K. A., Models of Multiparty Electoral Competition, vol. 45 (1991), Harwood Academic Publishers: Harwood Academic Publishers Chur, Switzerland |

[23] | Simon, L. K.; Zame, W. R., Discontinuous games and endogenous sharing rules, Econometrica, 58, 861-872 (1990) · Zbl 0729.90098 |

[24] | Wittman, D., Candidates with policy preferences: A dynamic model, J. Econ. Theory, 14, 180-189 (1977) · Zbl 0357.90088 |

[25] | Wittman, D., Candidate motivation: A synthesis of alternative theories, Amer. Polit. Sci. Rev., 77, 142-157 (1983) |

[26] | Wittman, D., Spatial strategies when candidates have policy preferences, (Enelow, J. M.; Hinich, M. J., Advances in the Spatial Theory of Voting (1990), Cambridge Univ. Press: Cambridge Univ. Press Cambridge), 66-98 · Zbl 1156.91303 |

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