On the performance of the Shapley Shubik and Banzhaf power indices for the allocations of mandates
AbstractA classical problem in the power index literature is to design a voting mechanism such as the distribution of power of the different players is equal (or closer) to a pre established target. This tradition is especially popular when considering two tiers voting mechanisms: each player votes in his own jurisdiction to designate a delegate for the upper tier; and the question is to assign a certain number of mandates for each delegate according the population of the jurisdiction he or she represents. Unfortunately, there exist several measures of power, which in turn imply different distributions of the mandates for the same pre established target. The purposes of this paper are twofold: first, we calculate the probability that the two most important power indices, the Banzhaf index and the Shapley-Shubik index, lead to the same voting rule when the target is the same. Secondly, we determine which index on average comes closer to the pre established target.
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Bibliographic InfoPaper provided by THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise in its series THEMA Working Papers with number 2007-25.
Date of creation: 2007
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Banzhaf; Shapley-Shubik; power indices;
Find related papers by JEL classification:
- C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
- D7 - Microeconomics - - Analysis of Collective Decision-Making
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-11-10 (All new papers)
- NEP-CDM-2007-11-10 (Collective Decision-Making)
- NEP-GTH-2007-11-10 (Game Theory)
- NEP-POL-2007-11-10 (Positive Political Economics)
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- Fabrice Barthelemy & Mathieu Martin, 2011.
"A comparison between the methods of apportionment using power indices: the case of the U.S. presidential elections,"
THEMA Working Papers
2011-13, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
- Fabrice BARTHELEMY & Mathieu MARTIN, 2011. "A Comparison Between the Methods of Apportionment Using Power Indices. The Case of the US Presidential Election," Annales d'Economie et de Statistique, ENSAE, issue 101-102, pages 87-106.
- Fabrice Barthélémy & Mathieu MARTIN, 2007. "A comparison between the methods of apportionment using power indices: the case of the U.S. presidential election," THEMA Working Papers 2007-26, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
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