Abstract.
We consider voting games induced by anonymous and top-unanimous social choice functions. The class of such social choice functions is quite broad, including every “t-refinement” of the Plurality Rule, Plurality with a Runoff, the Majoritarian Compromise and the Single Transferable Vote, i.e., any selection from either of these social choice rules which is obtained via tie-breaking among candidates according to any total order t on the set of alternatives. As announced in our title, the strong equilibrium outcomes of the voting games determined by such social choice functions turn out to be nothing but generalized Condorcet winners, namely the “(n,q)-Condorcet winners”. In the case of social choice functions (such as those just listed) which are furthermore “top-majoritarian”, they coincide with the classical Condorcet winners.
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The non-alphabetic ordering of names has a reason deserving to be explained. Murat R. Sertel, this man from the Bosphorus whose contributions put Turkey on the academic map of Economic Theory, passed away on January 25, 2003, while this paper was in print. His untimely death was met with deep sorrow by his colleagues, friends and students all over the world. Murat R. Sertel was one of the forerunners of the Age of Economic Design. He was a genuine scholar, brilliant intellectual, excellent teacher, beloved friend, a wonderful company, a devoted son and an affectionate father. May he rest in peace.¶The authors thank Semih Koray, Ipek Sanver, Fuad Aleskerov, Ahmet Alkan, Hakan Inal, Hervé Moulin, Bezalel Peleg, Robert Wilson, Muhamet Yıldız and two anonymous referees for their helpful comments. Remzi Sanver gratefully acknowledges partial support from Istanbul Bilgi University, BÜVAK (Boğaziçi University Foundation) and Serem Ltd.1999), Danilov (1992) for Nash implementation; Maskin (1979), Dutta and Sen (1991) for strong implementation; Moore and Repullo (1988), Abreu and Sen (1990) for subgame perfect implementation; Palfrey and Srivastava (1991), Jackson, Palfrey and Srivastava (1994) for undominated Nash implementation; Jackson (1991), Dutta and Sen (1994) for Bayesian implementation. So we know a lot about what is implementable, and what is not, via various solution concepts. In particular, Maskin (1979) shows that strong implementability of a social choice correspondence is inconsistent with the weak no veto power condition. ysis regarding the Nash equilibrium allocations of an allocation rule with wealth-regressive tax rates.
The authors thank Semih Koray, Ipek Sanver, Fuad Aleskerov, Ahmet Alkan, Hakan Inal, Hervé Moulin, Bezalel Peleg, Robert Wilson, Muhamet Yıldız and two anonymous referees for their helpful comments. Remzi Sanver gratefully acknowledges partial support from Istanbul Bilgi University, BÜVAK (Boğaziçi University Foundation) and Serem Ltd.
3 December 2001
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Sertel, M., Sanver, M. Strong equilibrium outcomes of voting games ¶are the generalized Condorcet winners. Soc Choice Welfare 22, 331–347 (2004). https://doi.org/10.1007/s00355-003-0218-x
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DOI: https://doi.org/10.1007/s00355-003-0218-x