Lexicographic Composition of Simple Games

Barry O'Neill and Bezalel Peleg
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Barry O'Neill: University of California, Los Angeles

No 1559, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: A two-house legislature can often be modelled as a proper simple game whose outcome depends on whether a coalition wins, blocks or loses in two smaller proper simple games. It is shown that there are exactly five ways to combine the smaller games into a larger one. This paper focuses on one of the rules, lexicographic composition, where a coalition wins G_1 => G_2 when it either wins in G_1, or blocks in G_1 and wins in G_2. It is the most decisive of the five. A lexicographically decomposable game is one that can be represented in this way using components whose player sets partition the whole set. Games with veto players are not decomposable, and anonymous games are decomposable if and only if they are decisive and have two or more players. If a player's benefit is assessed by any semi-value, then for two isomorphic games a player is better off from having a role in the first game than having the same role in the second. Lexicographic decomposability is sometimes compatible with equality of roles. A relaxation of it is suggested for its practical benefits.

Keywords: simple games; voting; game composition; game decomposition; semi-value; decisiveness; fairness (search for similar items in EconPapers)
JEL-codes: C71 D71 (search for similar items in EconPapers)
Pages: 24 pages
Date: 2006-02
New Economics Papers: this item is included in nep-cdm and nep-gth
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Published in Games and Economic Behavior (2008), 62: 628-642

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Related works:
Journal Article: Lexicographic composition of simple games (2008)
Working Paper: Lexicographic Composition of Simple Games (2006)
Working Paper: Lexicographic Composition of Simple Games (2006)
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