Anindya Bhattacharya*, Francesco Ciardiello**
* University of York, Department of Economics and Related Studies, United Kingdom** Internal Speaker

On spatial majority voting with an even (vis-a-vis odd) number of voters: A novel interplay between the uncovered set and the core.

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Abstract

Among the multiple classes of cooperative games, voting games have an appeal for multiple applications to politics, decision making and normative policies. We consider situations of multidimensional spatial majority voting. We explore some possibilities such that under some regularity assumptions usual in this literature, if the number of voters changes from being odd to even then some results may change somewhat drastically. For example, we show that with an even number of voters if the core of the voting situation is singleton and is in the interior of the policy space, then the element in thecore is never externally stable. This is in sharp contrast with what happens with an odd number of voters: in that case, under identical assumptions on the primitives, it is well known that if the core of the voting situation is non-empty then the single element in the core is always externally stable: i.e., the core element majority-dominates every other policy vector. Assuming an even number of voters and the fact that the core is a singleton, we look for further results of core-stability. In fact, under further assumptions, we show that the set of alternatives not dominated by the singleton core - in a neighbourhood of the singleton core- belongs to the Gillies uncovered set. Interestingly, it may not be the case that the whole set of alternatives not dominated by the core is the uncovered set.