Counting Combinatorial Choice Rules
I count the number of combinatorial choice rules that satisfy certain properties: Kelso-Crawford substitutability, and independence of irrelevant alternatives. The results are important for two-sided matching theory, where agents are modeled by combinatorial choice rules with these properties. The rules are a small, and asymptotically vanishing, fraction of all choice rules. But they are still exponentially more than the preference relations over individual agents- --which has positive implications for the Gale-Shapley algorithm of matching theory.
References listed on IDEAS
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- Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
- Bevia, Carmen & Quinzii, Martine & Silva, Jose A., 1999.
"Buying several indivisible goods,"
Mathematical Social Sciences,
Elsevier, vol. 37(1), pages 1-23, January.
- Carmen Beviá Baeza & José Angel Silva Reus, 1997. "Buying several indivisible goods," Working Papers. Serie AD 1997-27, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- Carmen Bevia & Martine Quinzii & JosŽ A. Silva, "undated". "Buying Several Indivisible Goods," Department of Economics 97-20, California Davis - Department of Economics.
- Martine Quinzii & Carmen Bevia & JosÅ A. Silva, 2003. "Buying Several Indivisible Goods," Working Papers 9720, University of California, Davis, Department of Economics.
- Moulin,Hervi, 1989.
"Axioms of Cooperative Decision Making,"
Cambridge University Press, number 9780521360555, December.
- Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
- Kim, Taesung & Richter, Marcel K., 1986. "Nontransitive-nontotal consumer theory," Journal of Economic Theory, Elsevier, vol. 38(2), pages 324-363, April.
- Ralph W. Bailey, 1998. "The number of weak orderings of a finite set," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(4), pages 559-562.
- Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
- Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992.
Cambridge University Press, number 9780521437882, December.
- Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541 Elsevier.
- Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
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