Open AccessIncentive‐compatible voting rules with positively correlated beliefs
Author(s) -
Bhargava Mohit,
Majumdar Dipjyoti,
Sen Arunava
Publication year - 2015
Publication title -
theoretical economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.404
H-Index - 32
eISSN - 1555-7561
pISSN - 1933-6837
DOI - 10.3982/te1529
Subject(s) - voting , incentive compatibility , correlation , mathematical economics , approval voting , incentive , anti plurality voting , robustness (evolution) , econometrics , mathematics , set (abstract data type) , bayesian probability , computer science , cardinal voting systems , combinatorics , microeconomics , economics , statistics , political science , biochemistry , chemistry , programming language , geometry , politics , law , gene
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) (d'Aspremont and Peleg 1988) 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 [Majumdar and Sen, 2004] and parallel similar results in the auction design model (Crémer and McLean 1988).