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ЖУРНАЛЫ // Contributions to Game Theory and Management // Архив

Contributions to Game Theory and Management, 2010, том 3, страницы 82–90 (Mi cgtm77)

Detection of Paradoxes of Power Indices for Simple Games

Josep Freixasab, Xavier Molineroac

a Technical University of Catalonia (Campus Manresa); E-08242 Manresa, Spain
b Department of Applied Mathematics 3
c Department of Computer Science

Аннотация: Within the context of weighted simple games, we consider some well–known postulates — relative normalized measures — for relative power indices. We essentially refer to the postulates: of monotonicity, donation and bloc; and to the power indices by: Banzhaf, Johnston, Deegan–Packel and Holler. We do not consider the Shapley–Shubik index because satisfies all these three postulates.
If a power index fails to satisfy one of the above postulates then the phenomena is regarded to be paradoxical. This work considers the paradoxes that arise from considering a particular postulate and a particular power index. The question that naturally appears for each simple voting game and pair, postulate & power index, is: how frequently does the paradox arise?
We develop some theoretical methods and experimental results to partially answer the above question.

Ключевые слова: Power indices, paradoxes, counting.

MSC: 91A12, 91A40, 91A80, 91B12

Язык публикации: английский



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