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On spatial majority voting with an even (vis-a-vis odd) number of voters: a note

In this note we consider situations of (multidimensional) spatial majority voting. We show that under some assumptions usual in this literature, with an even number of voters if the core of the voting situation is singleton (and in the interior of the policy space) then the element in the core is never a Condorcet winner. This is in sharp contrast with what happens with an odd number of voters: in that case, under identical assumptions, it is well known that if the core of the voting situation is non-empty then the single element in the core is the Condorcet winner as well.