Abstract
In a voting context, when the preferences of voters are described by linear orderings over a finite set of alternatives, the Maximin rule orders the alternatives according to their minimal rank in the voters’ preferences. It is equivalent to the Fallback bargaining process described by Brams and Kilgour (Group Decision and Negotiation 10:287–316, 2001). This article proposes a characterization of the Maximin rule as a social welfare function (SWF) based upon five conditions: Neutrality, Duplication, Unanimity, Top Invariance, and Weak Separability. In a similar way, we obtain a characterization for the Maximax SWF by using Bottom Invariance instead of Top Invariance. Then, these results are compared to the axiomatic characterizations of two famous scoring rules, the Plurality rule and the Antiplurality rule.
Similar content being viewed by others
References
Aleskerov, F., Vyacheslav, V., Chistyakov, V., & Kaliyagin, V. (2010). Social threshold aggregations. Social Choice and Welfare, forthcoming.
Arrow K. J., Hurwicz L. (1972) An optimality criterion for decision-making under ignorance. In: Carter C. F., Ford J. L. (eds) Uncertainty and expectations in economics. Basil Blackwell & Mott Ltd, Oxford, pp 1–11
Barberà S., Dutta B. (1982) Implementability via protective equilibria. Journal of Mathematical Economics 10: 49–65
Barberà S., Dutta B. (1986) General, direct and self-implementation of social choice functions via protective equilibria. Mathematical Social Sciences 11: 109–127
Brams S. J., Kilgour D. M. (2001) Fallback bargaining. Group Decision and Negotiation 10: 287–316
Brams S. J., Kilgour D. M., Sanver R. (2004) A minimax procedure for negotiating multilateral treaties. In: Wiberg Matti (eds) Reasoned choices: Essays in honor of Hannu Nurmi. Finnish Political Science Association, Turku, Finland, pp 108–139
Luce, D. R., & Raiffa, H. (1957). Games and decisions: Introduction and critical survey (Chap. 13). New York: Wiley.
Maniquet, F., & Sen, A. (2001). An axiomatic characterization of Leximin Voting. (Unpublished manuscript).
May K. (1952) A set of independent, necessary and sufficient conditions for simple majority decision. Econometrica 20: 680–684
Merlin, V. (1996). L’agrégation des préférences individuelles: les règles positionnelles itératives et la méthode de Copeland. (PhD dissertation, Université de Caen, 1996).
Milnor J. (1954) Games against nature. In: Thrall R. M., Coombs C. H., Davis R. L. (eds) Decision processes. Wiley, New York, pp 49–59
Moulin H. (1981) Prudence vs. sophistication in voting strategy. Journal of Economic Theory 24: 398–412
Moulin H. (1988) Axioms of cooperative decision making. Cambridge University Press, Cambridge
Muller E., Satterthwaite M. A. (1977) The equivalence of strong positive association and strategy-proofness. Journal of Economic Theory 14: 412–418
Saari D. G. (1991) Consistency of decision processes. Annals of Operation Research 23: 103–137
Sertel, M. R. (1986). Lectures notes in microeconomics, Bogazici University. (Unpublished manuscript).
Sertel M. R., Yilmaz B. (1999) The majoritarian compromise is majoritarian optimal and subgame perfect implementable. Social Choice and Welfare 16: 615–627
Smith J. H. (1973) Aggregation of preferences with variable electorate. Econometrica 41: 1027–1041
Yokoo M., Sakurai Y., Matsubara B. (2005) The effect of false-name bids in combinatorial auctions: New frauds in internet auctions. Games and Economic Behavior 46: 174–188
Young H. P. (1974) An axiomatization of Borda’s rule. Journal of Economic Theory 9: 43–52
Young H. P. (1975) Social choice scoring functions. SIAM Journal of Applied Mathematics 28: 824–838
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Congar, R., Merlin, V. A characterization of the maximin rule in the context of voting. Theory Decis 72, 131–147 (2012). https://doi.org/10.1007/s11238-010-9229-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11238-010-9229-0