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.
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- 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.
- Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
- repec:cup:cbooks:9780521424585 is not listed on IDEAS
- Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
- repec:cup:cbooks:9780521360555 is not listed on IDEAS
- 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).
- Martine Quinzii & Carmen Bevia & JosÅ A. Silva, 2003. "Buying Several Indivisible Goods," Working Papers 9720, University of California, Davis, Department of Economics.
- Carmen Bevia & Martine Quinzii & JosŽ A. Silva, . "Buying Several Indivisible Goods," Department of Economics 97-20, California Davis - Department of Economics.
- Kim, Taesung & Richter, Marcel K., 1986. "Nontransitive-nontotal consumer theory," Journal of Economic Theory, Elsevier, vol. 38(2), pages 324-363, April.
- Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
- Ralph W. Bailey, 1998. "The number of weak orderings of a finite set," Social Choice and Welfare, Springer, vol. 15(4), pages 559-562.
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