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A comparison between the methods of apportionment using power indices: the case of the U.S. presidential elections

Fabrice Barthélémy () and Mathieu Martin

No 2011-13, THEMA Working Papers from THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise

Abstract: In 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.

Keywords: Banzhaf index; methods of apportionment; distances; balance population-power. (search for similar items in EconPapers)
JEL-codes: C7 D7 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-cdm, nep-gth and nep-pol
Date: 2011
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http://thema.u-cergy.fr/IMG/documents/2011-13.pdf (application/pdf)

Related works:
Journal Article: A Comparison Between the Methods of Apportionment Using Power Indices: the Case of the US Presidential Elections (2011) Downloads
Working Paper: A comparison between the methods of apportionment using power indices: the case of the U.S. presidential election (2007) Downloads
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