Binary effectivity rules |
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Authors: | Hans Keiding Bezalel Peleg |
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Affiliation: | (1) Institute of Economics, University of Copenhagen, Studiestraede 6, 1455 Copenhagen K, Denmark;(2) Institute of Mathematics, Center for the Study of Rationality, The Hebrew University of Jerusalem, Givat-Ram, 91904 Jerusalem, Israel |
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Abstract: | A social choice rule (SCR) is a collection of social choice correspondences, one for each agenda. An effectivity rule is a collection of effectivity functions, one for each agenda. We prove that every monotonic and superadditive effectivity rule is the effectivity rule of some SCR. A SCR is binary if it is rationalized by an acyclic binary relation. The foregoing result motivates our definition of a binary effectivity rule as the effectivity rule of some binary SCR. A binary SCR is regular if it satisfies unanimity, monotonicity, and independence of infeasible alternatives. A binary effectivity rule is regular if it is the effectivity rule of some regular binary SCR. We characterize completely the family of regular binary effectivity rules. Quite surprisingly, intrinsically defined von Neumann–Morgenstern solutions play an important role in this characterization. |
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Keywords: | Social choice correspondences Effectivity functions Nakamura’ s number Von Neumann– Morgenstern solutions |
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