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 & Volji in Soc Choice Welfare 51:223–233, 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. In some cases, the voting rules may even lead to the election of a socially unacceptable candidate, that is 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 socially unacceptable candidates is not always guaranteed, we determine the probabilities that such candidates exist given the number of the running candidates and the size of the electorate. Second, 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 simulations under both the Impartial Culture and the Impartial Anonymous Culture, two assumptions which are widely used when studying the likelihood of voting events. Our results show that as the number of candidates increases, it becomes almost assured to have at least one socially unacceptable candidate; in some cases, the probability that half of the candidates in the running are socially unacceptable approaches or even exceeds $$50\%$$ . It also turns out that the extent to which a socially unacceptable candidate is selected depends strongly on the voting rule, the underlying distribution of voters’ preferences, the number of voters and the number of competing candidates.