Scoring Rules, Ballot Truncation, and the Truncation Paradox

Abstract

International audience ; A voting rule that permits some voters to favor a candidate by providing only the initial segment of their sincere rankings is said to be vulnerable to the truncation paradox. In this paper, we consider four models for counting truncated ballots, optimistic, pessimistic (the most common), averaged, and round-down. Under the impartial anonymous culture assumption, the choice of model generally has a real impact on truncation-paradox vulnerability, but there are exceptions. When the election is decided by a one-shot scoring rule, the optimistic model is invulnerable to the truncation paradox, but all other models are vulnerable. We identify new voting rules immune to the truncation paradox, such as the Modified Borda Count. To obtain a more complete picture of the impact of processing model, we assess the likelihood of the truncation paradox in three-candidate elections with large electorates, focusing not only on oneshot scoring rules but also scoring rules with one-by-one or below-average elimination. Our assessment confirms that the processing model for truncated ballots may really matter.