Extended Preferences in Voting

Abstract

Extended preferences (preferences over sets of alternatives) are considered. Known main conditions of the relationship between preferences over alternatives and extended preferences over outcomes (sets of alternatives) are studied. Several concepts of extended preferences are elaborated. Known and new schemes of constructing extended preferences over sets of alternatives are described and suggested. Three groups of schemes are defined: lexicographic, probabilistic and average rank methods of preferences extending. While lexicographic and probabilistic algorithms allow comparison of all sets of alternatives, average rank method need additional restrictions. Lexicographic, probabilistic, and cardinality restrictions, as well as attitude to risk restrictions, are introduced and then properties of extended preferences are studied.