Robust incentive compatibility of voting rules with positively correlated beliefs

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We investigate a voting model where each voter’s beliefs are positively correlated. We show that requiring a social choice function to be Ordinally Bayesian Incentive-Compatible (d’Aspremont and Peleg in Soc Choice Welf 5:261–280, 1988) with respect to all such beliefs is not equivalent to requiring it to be strategy-proof. However, if the social choice function is also required to be efficient, it must be strategy-proof and hence, dictatorial.