Committee scoring rules form a rich class of aggregators of voters' preferences for the purpose of selecting subsets of objects with desired properties, e.g., a shortlist of candidates for an interview, a representative collective body such as a parliament, or a set of locations for a set of public facilities. In the spirit of celebrated Young's characterization result that axiomatizes single-winner scoring rules, we provide an axiomatic characterization of multiwinner committee scoring rules. We show that committee scoring rules---despite forming a remarkably general class of rules---are characterized by the set of four standard axioms, anonymity, neutrality, consistency and continuity, and by one axiom specific to multiwinner rules which we call committee dominance. In the course of our proof, we develop several new notions and techniques. In particular, we introduce and axiomatically characterize multiwinner decision scoring rules, a class of rules that broadly generalizes the well-known majority relation.
Probabilistic single-winner election rules have also been a subject of axiomatic studies. For instance, Gibbard @cite_3 investigated strategyproofness of probabilistic election systems and blue his result can be seen as an axiomatic characterization of the random dictatorship rule. Brandl et al. @cite_30 , by studying different types of consistency of probabilistic single-winner election rules, characterized the function returning maximal lotteries, first proposed by Fishburn @cite_34 .
@cite_30 @cite_34 @cite_3
2963715374 1966938374 1977126954
Two fundamental axioms in social choice theory are consistency with respect to a variable electorate and consistency with respect to components of similar alternatives. In the context of traditional non‐probabilistic social choice, these axioms are incompatible with each other. We show that in the context of probabilistic social choice, these axioms uniquely characterize a function proposed by Fishburn (1984). Fishburn's function returns so‐called maximal lotteries, that is, lotteries that correspond to optimal mixed strategies in the symmetric zero‐sum game induced by the pairwise majority margins. Maximal lotteries are guaranteed to exist due to von Neumann's Minimax Theorem, are almost always unique, and can be efficiently computed using linear programming. A social choice procedure is developed for selecting an alternative from a finite set on the basis of paired-comparison voting. Ballot data are used to construct a lottery on the alternatives that is socially as preferred as every other lottery. The constructed lottery is then used to select a winner. An axiomatization of social preferences among lotteries that justifies the procedure is included. The procedure will always select a consensus majority alternative when one exists, and it will never select an alternative that is Pareto dominated by another alternative.