Binary Effectivity Rules

Hans Keiding () and Bezalel Peleg ()

Discussion Paper Series from Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem

Abstract: A social choice rule 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 social choice rule. A social choice rule 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 social choice rule. A binary social choice rule 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 social choice rule. 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.

Keywords: social choice correspondences; effectivity functions; Nakamura’s number; von Neumann-Morgenstern solutions (search for similar items in EconPapers)
JEL-codes: D71 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-dcm
Date: 2004-10
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Published in Review of Economic Design, 2006, vol. 10, pp. 167-181.

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