A comparison between the methods of apportionment using power indices: the case of the U.S. presidential election
AbstractIn this paper, we compare the five more famous methods of apportionment, the methods of Adams, Dean, Hill, Webster and Jefferson. The criteria used for this comparison is the minimization of a distance between a power vector and a population vector. The power is measured with the well-known Banzhaf power index. The populations are the ones of the different States of the U.S. We then compare the apportionment methods in terms of their ability to bring closer the power of the States to their relative population: this ensures that every citizen in the country gets the same power. The U.S. presidential election by Electors is studied through 22 censuses since 1790. Our analysis is largely based on the book written by Balinski and Young (2001). The empirical findings are linked with theoretical results.
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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 2007-26.
Date of creation: 2007
Date of revision:
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Banzhaf index; methods of apportionment; distances; balance population-power.;
Other versions of this item:
- 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 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.
- 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-2008-01-05 (All new papers)
- NEP-GTH-2008-01-05 (Game Theory)
- NEP-POL-2008-01-05 (Positive Political Economics)
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