Kumabe, Masahiro and Mihara, H. Reiju (2008): Preference aggregation theory without acyclicity: The core without majority dissatisfaction.
Download (285Kb) | Preview
Acyclicity of individual preferences is a minimal assumption in social choice theory. We replace that assumption by the direct assumption that preferences have maximal elements on a fixed agenda. We show that the core of a simple game is nonempty for all profiles of such preferences if and only if the number of alternatives in the agenda is less than the Nakamura number of the game. The same is true if we replace the core by the core without majority dissatisfaction, obtained by deleting from the agenda all the alternatives that are non-maximal for all players in a winning coalition. Unlike the core, the core without majority dissatisfaction depends only onthe players' sets of maximal elements and is included in the union of such sets. A result for an extended framework gives another sense in which the core without majority dissatisfaction behaves better than the core.
|Item Type:||MPRA Paper|
|Original Title:||Preference aggregation theory without acyclicity: The core without majority dissatisfaction|
|Keywords:||Core; Nakamura number; kappa number; simple games; voting games; maximal elements; acyclic preferences; limit ordinals|
|Subjects:||D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice; Clubs; Committees; Associations
C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games
C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods
|Depositing User:||H. Reiju Mihara|
|Date Deposited:||24. Nov 2008 00:27|
|Last Modified:||28. Feb 2013 17:02|
Ambrus, A., Rozen, K., Jul. 2008. Revealed conﬂicting preferences. Discus- sion Paper 1670, Cowles Foundation, Yale University, New Haven.
Andjiga, N. G., Mbih, B., 2000. A note on the core of voting games. Journal of Mathematical Economics 33, 367–372.
Andjiga, N. G., Moyouwou, I., 2006. A note on the non-emptiness of the stability set when individual preferences are weak orders. Mathematical Social Sciences 52, 67–76.
Arrow, K. J., 1963. Social Choice and Individual Values, 2nd Edition. Yale University Press, New Haven.
Austen-Smith, D., Banks, J. S., 1999. Positive Political Theory I: Collective Preference. University of Michigan Press, Ann Arbor.
Banks, J. S., 1985. Sophisticated voting outcomes and agenda control. Social Choice and Welfare 1, 295–306.
Banks, J. S., 1995. Acyclic social choice from ﬁnite sets. Social Choice and Welfare 12, 293–310.
Banks, J. S., Duggan, J., Le Breton, M., 2006. Social choice and electoral competition in the general spatial model. Journal of Economic Theory 126, 194–234.
Dasgupta, P., Maskin, E., 2008. On the robustness of ma jority rule. Journal of the European Economic Association 6, 949–973.
Duggan, J., 2007. A systematic approach to the construction of non-empty choice sets. Social Choice and Welfare 28, 491–506.
Fishburn, P. C., 1970. Arrow’s Impossibility Theorem: Concise proof and inﬁnite voters. Journal of Economic Theory 2, 103–6.
Friedberg, R. M., 1958. Three theorems on recursive enumeration. I. decom- position, II. maximal set, III. enumeration without duplication. Journal of Symbolic Logic 23, 309–316.
Hrbacek, K., Jech, T., 1984. Introduction to Set Theory, second, revised and expanded edition. Marcel Dekker, New York.
Kalai, G., Rubinstein, A., Spiegler, R., 2002. Rationalizing choice functions by multiple rationales. Econometrica 70, 2481–2488.
Kreps, D. M., 1979. A representation theorem for “preference for ﬂexibility”. Econometrica 47, 565–577.
Kumabe, M., Mihara, H. R., 2008a. Computability of simple games: A characterization and application to the core. Journal of Mathematical Economics 44, 348–366.
Kumabe, M., Mihara, H. R., 2008b. The Nakamura numbers for computable simple games. Social Choice and Welfare 31, 621–640.
Le Breton, M., Salles, M., 1990. The stability set of voting games: Classi- ﬁcation and genericity results. International Journal of Game Theory 19, 111–127.
Lipman, B. L., 1991. How to decide how to decide how to . . . : Modeling limited rationality. Econometrica 59, 1105–1125.
Martin, M., Merlin, V., 2006. On the characteristic numbers of voting games. International Game Theory Review 8, 643–654.
Mihara, H. R., 1997. Arrow’s Theorem and Turing computability. Economic Theory 10, 257–76.
Mihara, H. R., 1999. Arrow’s theorem, countably many agents, and more visible invisible dictators. Journal of Mathematical Economics 32, 267– 287.
Mihara, H. R., 2000. Coalitionally strategyproof functions depend only on the most-preferred alternatives. Social Choice and Welfare 17, 393–402.
Nakamura, K., 1979. The vetoers in a simple game with ordinal preferences. International Journal of Game Theory 8, 55–61.
Odifreddi, P., 1992. Classical Recursion Theory: The Theory of Functions and Sets of Natural Numbers. Elsevier, Amsterdam.
Penn, E. M., 2006. The Banks set in inﬁnite spaces. Social Choice and Welfare 27, 531–543.
Royden, H. L., 1988. Real Analysis, 3rd Edition. Macmillan, New York.
Rubinstein, A., 1980. Stability of decision systems under ma jority rule. Jour- nal of Economic Theory 23, 150–159.
Truchon, M., 1995. Voting games and acyclic collective choice rules. Math- ematical Social Sciences 29, 165–179.
Available Versions of this Item
- Preference aggregation theory without acyclicity: The core without majority dissatisfaction. (deposited 24. Nov 2008 00:27) [Currently Displayed]