Geodesic
Detection of Paradoxes of Power Indices for Simple Games
Contributions to game theory and management, Tome 3 (2010), pp. 82-90

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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.
Keywords: Power indices, paradoxes, counting. 
@article{CGTM_2010_3_a7,
     author = {Josep Freixas and Xavier Molinero},
     title = {Detection of {Paradoxes} of {Power} {Indices} for {Simple} {Games}},
     journal = {Contributions to game theory and management},
     pages = {82--90},
     publisher = {mathdoc},
     volume = {3},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2010_3_a7/}
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Josep Freixas; Xavier Molinero. Detection of Paradoxes of Power Indices for Simple Games. Contributions to game theory and management, Tome 3 (2010), pp. 82-90. http://geodesic.mathdoc.fr/item/CGTM_2010_3_a7/