Scoring Rules and Consensus Jos´ e Luis Garc´ ıa-Lapresta, Bonifacio Llamazares and Teresa Pe˜ na Abstract 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. 1 Introduction Some group decision problems are designed for generating an order on the set of feasible alternatives or a set of winning alternatives from the orders that individuals provide on that set of alternatives. Within this approach, it is well-known that there does not exist perfect voting systems (see Arrow [1]). Thus, the problem is to devise group decision procedures satisfying some good properties but not all we may de- sire. In this contribution we focus on scoring rules, a class of voting systems where voters rank order the alternatives from best to worst and they associate a score to Jos´ e Luis Garc´ ıa-Lapresta, Bonifacio Llamazares and Teresa Pe˜ na PRESAD Research Group, Dept. of Applied Economics, University of Valladolid, Spain, e-mail: {lapresta,boni,maitepe}@eco.uva.es 1