JOURNAL OF ECONOMIC THEORY 4, 63-80 (1988) vering Sets and a New Con Correspondence* BHASKAR DUTTA Indian Statistical Institute. Neul Delhi 110016. India Received May 21, 1985; revised December 17. 1986 Given a finite set A of outcomes and a tournament on A, a new Cocdorcet Choice Correspondence is proposed. The new rule is axiomatically characterised, and its properties are compared with those of the uncovered set and ihe Kemeny rule. Jourttal of Economic Literature Classification Number: 025 :c 1988 Acadenuc Press. Inc. I. INTRODUCTION The notion that an outcome which is better than all other outcomes on the basis of majority voting should be chosen is as old as social choice theory itself. Unfortunately, the knowledge that such an outcome may not always exist is equally ancient. Indeed, one of the more popular pastimes of social choice theorists has been to construct choice rules which satisfy Con- dorcet’s principles, but handle the difficulty posed by the nonexistence of a clear winner in different ways. The present paper follows this distinguished tradition. Given a finite set A of outcomes and a tournament on A which expresses decisive preference judgements for all pairs of outcomes, I propose a new Condorcet choice rule. The new rule has certain similarities with the rule proposed indepen- dently by Fishburn [3] and Miller [7]. In particular, the sense in which the chosen elements “dominate” the rejected elements is closely related to the corresponding notion employed by Fishburn and Miller. The paper also presents an axiomatic characterisation of the new rule. This characterisation highlights the tradeoffs involved between the ability to choose “small” sets of outcomes and consistency conditions which link sets of chosen elements across different choice problems that arise due to changes in the feasible set. I also compare the new rule with the ~ishb~rn-Miller choice rule and the Memeny [4] rule. It is shown that Kemeny’s rule violates seemingly * I am most grateful to Bezalel Peleg for helpful suggestions, and to an anonymous referee for comments on an earlier draft of this paper. 63 os22-0531/m $x0 Copyright 82~ 1988 by Academic Press. ixr All rights of reproductmn m an) form re~ervcd.