Lexicographic composition of simple games |
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Authors: | Barry O'Neill Bezalel Peleg |
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Affiliation: | aDepartment of Political Science, 4289 Bunche Hall, University of California, Los Angeles, 90095-147203, USA;b210, Feldman Building, Center for the Study of Rationality, The Hebrew University of Jerusalem, Giv'at Ram, Jerusalem, Israel 91904 |
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Abstract: | Certain voting bodies can be modeled as a simple game where a coalition's winning depends on whether it wins, blocks or loses in two smaller simple games. There are essentially five such ways to combine two proper games into a proper game. The most decisive is the lexicographic rule, where a coalition must either win in G1, or block in G1 and win in G2. When two isomorphic games are combined lexicographically, a given role for a player confers equal or more power when held in the first game than the second, if power is assessed by any semi-value. A game is lexicographically separable when the players of the two components partition the whole set. Games with veto players are not separable, and games of two or more players with identical roles are separable only if decisive. Some separable games are egalitarian in that they give players identical roles. |
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Keywords: | Simple games Legislatures Compound games Power index Lexicographic composition |
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