A refinement of the uncovered set in tournaments
We introduce a new solution for tournaments called the unsurpassed set. This solution lies between the uncovered set and the Copeland winner set. We show that this solution is more decisive than the uncovered set in discriminating among alternatives, and avoids a deficiency of the Copeland winner set. Moreover, the unsurpassed set is more sensitive than the uncovered set but less sensitive than the Copeland winner set to the reinforcement of the chosen alternatives. Besides, it turns out that this solution violates the other standard properties including independence of unchosen alternatives, stability, composition consistency and indempotency.
KeywordsUncovered set Unsurpassed set Copeland winner set Monotonicity
We would like to thank the anonymous referees and the editor in charge for their excellent comments and insightful remarks. The authors are also grateful to Dr. Jean Derks whose advices and comments improved the paper substantially. Preliminary results of this paper were presented at the 13th Meeting of the Society for Social Choice and Welfare (Lund, Sweden, June 2016). All mistakes are our responsibility. This research was supported by SCNU under the Project No. 508/8S0253.
- Bordes, G. (1979). Some more results on consistency, rationality and collective choice. In J. J. Laffont (Ed.), Aggregation and revelation of preferences, Chap 10, (pp. 175–197). North-Hollabd.Google Scholar
- Copeland, A. H. (1951). A ‘reasonable’ social welfare function. Mimeographed, University of Michigan Seminar on Applications of Mathematics to the Social Sciences.Google Scholar
- Schwartz, T. (1986). The logic of collective choice. New York: Columbia University Press.Google Scholar
- Von Neumann, J., & Morgenstern, O. (1944). Theory of games and economic behavior. Princeton: Princeton University Prress.Google Scholar