Scoring Rules and Consensus

In this paper we consider that voters rank order a set of alternatives and a scoring rule is used for obtaining a set of winning alternatives. The scoring rule we use is not previously fixed, but we analyze how to select one of them in such a way that the collective utility is maximized. In order to generate that collective utility, we ask voters for additional information: agents declare which alternatives are good and their degree of optimism.With that information and a satisfaction function, for each scoring rule we generate individual utility functions. The utility an alternative has for a voter should depend on whether this alternative is a winner for that scoring rule and on the position this alternative has in the individual ranking. Taking into account all these individual utilities, we aggregate them by means of an OWA operator and we generate a collective utility for each scoring rule. By maximizing the collective utility, we obtain the set of scoring rules that maximizes consensus among voters. Then, applying one of these scoring rules we obtain a collective weak order on the set of alternatives, thus a set of winning alternatives.