Social unacceptability for simple voting procedures

A candidate is said to be socially acceptable if the number of voters who rank her among the most preferred half of the candidates is at least as large as the number of voters who rank her among the least preferred half (Mahajne and Volij, 2018). For every voting profile, there always exists at least one socially acceptable candidate. This candidate may not be elected by some well-known voting rules, which may even lead in some cases to the election of a socially unacceptable candidate, the latter being a candidate such that the number of voters who rank her among the most preferred half of the candidates is strictly less than the number of voters who rank her among the least preferred half. In this paper, our contribution is twofold. First, since the existence of a socially unacceptable candidate is not always guaranteed, we determine the probabilities of the existence of such a candidate. Then, we evaluate how often the Plurality rule, the Negative Plurality rule, the Borda rule and their two-round versions can elect a socially unacceptable candidate. We perform our calculations under both the Impartial Culture and the Impartial Anonymous Culture