(2019) Optimal Threshold for Selection of Candidates in Multi-Winner Elections

We devise a method for political and economic decision making that's applicable to the optimal selection of multiple alternatives from a larger set of alternatives. This method could be used, for example, in the selection of a committee or a parliament. The method combines utilitarian voting with approval voting and sets an optimal threshold above which an individual voter's sincere ratings are turned into approval style votes. Those candidates above threshold are chosen in such a way as to maximize the individual's expected utility for the winning set. We generalize range/approval hybrid voting which deals with a single member outcome to the case of multiple outcomes. The political case easily generalizes to the economic case in which a commodity bundle is to be chosen by each individual from an available set which is first chosen from a larger set by the amalgamation of the individual choosers' inputs. As the set made available gets larger, the individual voter or chooser is more likely to gain greater utility or satisfaction because more of their above threshold candidates will be included in the winning set.