Abstract (EN)

Voting rules are formal means of aggregating preferences of a group of voters over a set of alternatives into a collective decision. But which rule to use is a difficult question and the answer depends on the conception of justice of the concerned society or committee. Although all voting rules can be seen as a compromise between individuals, some are more so than others. In this manuscript we provide two notions of compromise based on an equal-loss perspective, favoring an outcome where every voter concedes as equally as possible. We study several rules that reflect some idea of compromise and show how, although imposing a willingness to compromise on individuals, they fail to ensure an outcome where everyone has effectively compromised. Moreover, we question the assumption, often made in the classical setting, that the voting rule is fixed beforehand and full information on the preferences of the individuals is provided. Focusing on positional scoring rules, we propose elicitation procedures based on minimax regret, able to interleave questions to the voters and to the entity responsible for designing the voting rule in order to quickly obtain the most relevant information. Considering Majority Judgment rule, we analyze a particular preference elicitation procedure used in real voting scenarios. Given a partial information on individuals preferences, we analyze the probability of selecting a different winner from the one obtained by considering the full profile and study the minimum number of questions to ask voters in order for this probability to be low.