An issue based power index
Autor: | Hans Peters, Qianqian Kong |
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Přispěvatelé: | QE Math. Economics & Game Theory, RS: GSBE other - not theme-related research, RS: FSE DACS Mathematics Centre Maastricht |
Rok vydání: | 2020 |
Předmět: |
Statistics and Probability
Computer Science::Computer Science and Game Theory Economics and Econometrics Class (set theory) Property (philosophy) Computer science Simple game Monotonic function Analysis of Collective Decision-Making: General Variation (game tree) Characterization (mathematics) Set (abstract data type) Mathematics (miscellaneous) c71 - Cooperative Games d70 - Analysis of Collective Decision-Making: General Simple (abstract algebra) 0502 economics and business 050207 economics Axiom 05 social sciences Power index ComputingMilieux_PERSONALCOMPUTING TheoryofComputation_GENERAL Cooperative Games OWEN Issue profile 050206 economic theory Statistics Probability and Uncertainty Mathematical economics Social Sciences (miscellaneous) |
Zdroj: | International Journal of Game Theory, 50(1), 23-38. Springer |
ISSN: | 1432-1270 0020-7276 |
DOI: | 10.1007/s00182-020-00737-x |
Popis: | An issue game is a combination of a monotonic simple game and an issue profile. An issue profile is a profile of linear orders on the player set, one for each issue within the set of issues: such a linear order is interpreted as the order in which the players will support the issue under consideration. A power index assigns to each player in an issue game a nonnegative number, where these numbers sum up to one. We consider a class of power indices, characterized by weight vectors on the set of issues. A power index in this class assigns to each player the weighted sum of the issues for which that player is pivotal. A player is pivotal for an issue if that player is a pivotal player in the coalition consisting of all players preceding that player in the linear order associated with that issue. We present several axiomatic characterizations of this class of power indices. The first characterization is based on two axioms: one says how power depends on the issues under consideration (Issue Dependence), and the other one concerns the consequences, for power, of splitting players into several new players (no advantageous splitting). The second characterization uses a stronger version of Issue Dependence, and an axiom about symmetric players (Invariance with respect to Symmetric Players). The third characterization is based on a variation on the transfer property for values of simple games (Equal Power Change), besides Invariance with respect to Symmetric Players and another version of Issue Dependence. Finally, we discuss how an issue profile may arise from preferences of players about issues. |
Databáze: | OpenAIRE |
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