Cases where the Penrose limit theorem does not hold
Loading...
Authors
Lindner, Ines
Owen, Guillermo
Subjects
Game theory
Voting games
Limit theorems
Power indices
Voting games
Limit theorems
Power indices
Advisors
Date of Issue
2007-02
Date
2007-02
Publisher
Elsevier
Language
Abstract
Penrose's limit theorem (PLT, really a conjecture) states that the relative power measure of two voters
tends asymptotically to their relative voting weight (number of votes). This property approximately holds in
most of real life and in randomly generated WVGs for various measures of voting power. Lindner and
Machover prove it for some special cases; amongst others they give a condition for this theorem to hold for
the Banzhaf–Coleman index for a quota of 50%. We show here, by counterexamples, that the conclusion
need not hold for other values of the quota. In doing this, we present an analytic proof of a counterexample
recently given by Chang et al. using simulation techniques.
Type
Article
Description
The article of record as published may be located at http://doi.org/10.1016/j.mathsocsci.2007.01.005
Research performed while at the Naval Postgraduate School, Monterey, California, United States.
Research performed while at the Naval Postgraduate School, Monterey, California, United States.
Series/Report No
Department
Mathematics
Mathematics
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Funder
Format
7 p.
Citation
Ines Lindner, Guillermo Owen. "Cases where the Penrose limit theorem does not hold." ScienceDirect, Mathematical Social Sciences 53 (2007) 232–238
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.