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 asymtotically 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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Paper provided by California Institute of Technology, Division of the Humanities and Social Sciences in its series Working Papers with number
1199.
Length: 17 pages Date of creation: Apr 2004 Date of revision: Publication status: Published: Published in Games and Economic Behavior 58 (2007) 231-245. Handle: RePEc:clt:sswopa:1199
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