A comparison between the methods of apportionment using power indices: the case of the U.S. presidential elections
AbstractIn this paper, we compare five well-known methods of apportionment, the ones by 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 and the populations are the ones of the different States of the U.S. We first explain under which conditions this comparison makes sense. We then compare the apportionment methods in terms of their ability to bring closer the power of the States to their relative population. 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 2011-13.
Date of creation: 2011
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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 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-08-09 (All new papers)
- NEP-CDM-2011-08-09 (Collective Decision-Making)
- NEP-GTH-2011-08-09 (Game Theory)
- NEP-POL-2011-08-09 (Positive Political Economics)
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