4 November 2016, Computational Social Choice Seminar, Anna Moskalenko
In this work, we aim to get away from the undesirable dictatorial voting rule, motivated by the classical impossibility results of Arrow and Gibbard-Satterthwaite, roughly stating that every voting rule satisfying a subset of reasonable properties leads to dictatorship. We search for the voting rule that could be called "least" dictatorial and ask: if we move away from the "bad" voting rule, will this result in a "good" one? To this end, we define a simple and natural metric between social choice functions, proposing a new alternative to the distance rationalization framework. The concept of distance rationalization of voting rules has been recently investigated as a unifying principle for defining (rationalizing) voting rules. For some notion of consensus (e.g. unanimity or having a Condorcet winner) and a metric (distance function), a voting rule that is rationalizable chooses the alternative that is closest to being a consensus winner. In contrast, instead of minimizing the distance to some plausible criterion, we maximize the distance to the undesirable dictatorial voting rule. The result we obtain is that the antiplurality voting rule is the "least" dictatorial one according to our specifications. From an opposite point of view, we may accept the rules that may allow the voters to feel themselves as a dictator in as many cases as possible, which we call the (subjectively) "most" dictatorial ones. We find that the plurality rule is the "most" dictatorial rule.