Preventing Social Disappointment in Elections (1801.05911v4)

Abstract: Mechanism design is concerned with settings where a policymaker (or social planner) faces the problem of aggregating the announced preferences of multiple agents into a collective (or social), system-wide decision. One of the most important ways for aggregating preference that has been used in multi-agent systems is election. In an election, the aim is to select the candidate who reflects the common will of society. Despite the importance of this subject, in some situations, the result of the election does not respect the purpose of those who execute it and the election leads to dissatisfaction of a large amount of people and in some cases causes polarization in societies. To analyze these situations, we introduce a new notion called social disappointment and we show which voting rules can prevent it in elections. In addition, we propose new protocols to prevent social disappointment in elections. A version of the impossibility theorem is proved regarding social disappointment in elections, showing that there is no voting rule for four or more candidates that simultaneously satisfies avoiding social disappointment and Condorcet winner criteria. We give conditions under which one of our new protocols always selects the Condorcet winner under the assumption of single peakedness. We empirically compare our protocols with seven well-known other voting protocols and observe that our protocols are capable of preventing social disappointment and are more robust against manipulations.