An extension of the Moulin No Show Paradox for voting correspondences

Abstract

In this article, we analyse the possibility of extending the Moulin theorem to Condorcet voting correspondences. Moulin (1988) established that every Condorcet voting function suffers from the No Show Paradox, or Abstention Paradox, which means that in some voting situations some voters would achieve a better result by abstaining (in other words, could manipulate the election by abstaining). This problem is similar to that of extending the Gibbard–Satterthwaite theorem on voting manipulation through casting an insincere ballot to voting correspondences. The main result of the paper states that for every Condorcet voting correspondence there are situations in which every optimistic or pessimistic voter with some preferences could manipulate the election by abstaining. Another result states, by counterexample, that some Condorcet voting correspondences are free from the Abstention Paradox from the point of view of other types of voters.