A Comparison Between the Methods of Apportionment Using Power Indices. The Case of the US Presidential Election
AbstractIn this paper we compare five well-known methods of apportionment, advanced respectively by Adams, Dean, Hill, Webster and Jefferson. The criterion used for this comparison is the minimization of the distance between a power vector and a population vector. Power is measured with the well-known Banzhaf power index; the populations are those of the constituent states of the U.S.A. We first explain the conditions under which this comparison has plausibility. We then compare apportionment methods in terms of their capacity to move power in states closer to their populations. The election of the U.S. President by an electoral college is studied by examining 22 censuses since 1790. Our analysis is largely based on that used in the book by Balinski and Young . The empirical findings are linked to theoretical results.
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Bibliographic InfoArticle provided by ENSAE in its journal Annals of Economics and Statistics.
Volume (Year): (2011)
Issue (Month): 101-102 ()
Other versions of this item:
- 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 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.
- C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
- D7 - Microeconomics - - Analysis of Collective Decision-Making
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