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Incentive-compatible voting rules with positively correlated beliefs. (English) Zbl 1395.91153

Theor. Econ. 10, No. 3, 867-885 (2015); correction ibid. 17, No. 2, 929-942 (2022).
Summary: We study the consequences of positive correlation of beliefs in the design of voting rules in a model with an arbitrary number of voters. We propose a notion of positive correlation, based on the likelihood of agreement of the k-best alternatives (for any \(k\)) of two orders called top-set (TS) correlation. We characterize the set of ordinal Bayesian incentive compatible (OBIC) [C. d’Aspremont and B. Peleg, Soc. Choice Welfare 5, No. 4, 261–279 (1988; Zbl 0651.90003)] voting rules with TS-correlated beliefs and additionally satisfy robustness with respect to local perturbations. We provide an example of a voting rule that satisfies OBIC with respect to all TS-correlated beliefs. The generally positive results contrast sharply with the negative results obtained for the independent case by the second and third authors [Econometrica 72, No. 2, 523–540 (2004; Zbl 1130.91324)] and parallel similar results in the auction design model [J. Crémer and R. P. McLean, ibid. 56, No. 6, 1247–1257 (1988; Zbl 0661.90104)].

MSC:

91B12 Voting theory
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