A leximin characterization of strategy-proof and non-resolute social choice procedures

Abstract

We characterize strategy-proof social choice procedures when choice sets need not be singletons. Sets are compared by leximin. For a strategy-proof rule g, there is a positive integer k such that either (i) the choice sets g(r) for all profiles r have the same cardinality k and there is an individual i such that g(r) is the set of alternatives that are the k highest ranking in i 's preference ordering, or (ii) all sets of cardinality 1 to k are chosen and there is a coalition L of cardinality k such that g(r) is the union of the tops for the individuals in L. There do not exist any strategy-proof rules such that the choice sets are all of cardinality k * to k where 1 < k * < k .

Manipulability of consular election rules

“…While this is not equivalent to the Duggan-Schwartz conditions, in the case of a rule that elects a pair of alternatives it is strictly narrowerevery lexicographic manipulation is either an optimistic or a pessimistic manipulation. Thus an impossibility result for lexicographic manipulations implies, a fortiori, an impossibility result for pessimistic/optimistic manipulation.Özyurt and Sanver [2009] and Campbell and Kelly [2002] also work in the framework of lexicographic manipulation and their results imply a weakened version of our main theorem -an impossibility result for manipulating an onto selection rule, but do not imply our more general result.…”

Strategyproof Social Choice

“…These works concentrate on the relative size of the subdomains where the rules do satisfy the exact version of strategy-proofness. Another way to measure departures is in Campbell and Kelly (2002. One can also investigate the minimal size of pro…les where manipulation possibilities will arise: Mausa, Peters and Storcken (2007) have established lower bounds on this size.…”

“…As I already mentioned, some authors reject quite explicitly the interpretation that the images of social choice correspondences are the basis for lotteries. Campbell and Kelly (2002 are papers which propose other alternative interpretations and de…ne manipulability under set comparisons which are justi…ed by other means. Speci…cally, leximin orderings of sets are used to establish a number of impossibility results regarding the existence of strategy-proof non-resolute social choice procedures.…”

Choosers as extension axioms

“…Pattanaik and Peleg (1984),Bossert (1995),Campbell and Kelly (2002),Kaymak and Sanver (2003),Dogan and Sanver (2007) explore lexicographic extensions under a variety of definitions.…”