A Probabilistic Model for Positional Voting  Spectrum Games 
(2001) Abstract
 This thesis considers a class of cooperative nperson games (voting games) in which the voters are spread across an ideological scale. The two most commonly used measures of individual voting power in voting games are the ShapleyShubik index and the BanzhafColeman index. In both indices, the actors are assumed anomymous and treatad symmetrically. That is, the indices do not take into account that there might be communicative problems among the actors. This fact suggests that the indices should be suitably modified to better reflect the true individual strength of the actors in such voting situations. Several attempts to solve this problem have been made and we focus on the approach suggested by Edelman. The idea is to use the... (More)
 This thesis considers a class of cooperative nperson games (voting games) in which the voters are spread across an ideological scale. The two most commonly used measures of individual voting power in voting games are the ShapleyShubik index and the BanzhafColeman index. In both indices, the actors are assumed anomymous and treatad symmetrically. That is, the indices do not take into account that there might be communicative problems among the actors. This fact suggests that the indices should be suitably modified to better reflect the true individual strength of the actors in such voting situations. Several attempts to solve this problem have been made and we focus on the approach suggested by Edelman. The idea is to use the ShapleyShubik index only on the connected coalitions, i.e. those coalitions where there cannot be any nonmembers who are ideologically in an intermediate position between any two coalition members. This approach, however, gives some counterintuitive results, and one part of the thesis provides a reason for this phenomenon. The Edelman approach is then extended by combining connected coalitions with a probabilistic model for these coalitions.
Paper 1 uses Edelman's extension of the ShapleyShubik index to determine the voting power distribution in a number of common voting situations. Paper 2 extends the ideological scale to admit each position to contain more than one voter and suggests several ways to generalize the concept connected coalitions. Using a simple binary probabilistic process, Paper 3 introduces the MarkovPólya index as a parametrized family of power indices which has Edelman's model as a special case. Paper 4 investigates the MarkovPólya index further, and, finally, in Paper 5 the MarkovPólya index is compared with other power indices suggested for ideological voting. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/41332
 author
 Perlinger, Thommy ^{LU}
 opponent

 Professor Mercik, Jacek, Tech. Univ. Wroclaw
 organization
 publishing date
 2001
 type
 Thesis
 publication status
 published
 subject
 keywords
 operations research, Statistics, MarkovPólya index, initiator, Voting power index, Spectrum game, connected coalitions, programming, actuarial mathematics, Statistik, operationsanalys, programmering, aktuariematematik
 pages
 104 pages
 publisher
 Department of Statistics, Lund university
 defense location
 MH:B
 defense date
 20010316 10:15
 external identifiers

 other:LUSADG/SAST1009/1104
 language
 English
 LU publication?
 yes
 id
 99f0abcbb743498ca3bb1690800305e4 (old id 41332)
 date added to LUP
 20070801 08:31:14
 date last changed
 20160919 08:45:02
@phdthesis{99f0abcbb743498ca3bb1690800305e4, abstract = {This thesis considers a class of cooperative nperson games (voting games) in which the voters are spread across an ideological scale. The two most commonly used measures of individual voting power in voting games are the ShapleyShubik index and the BanzhafColeman index. In both indices, the actors are assumed anomymous and treatad symmetrically. That is, the indices do not take into account that there might be communicative problems among the actors. This fact suggests that the indices should be suitably modified to better reflect the true individual strength of the actors in such voting situations. Several attempts to solve this problem have been made and we focus on the approach suggested by Edelman. The idea is to use the ShapleyShubik index only on the connected coalitions, i.e. those coalitions where there cannot be any nonmembers who are ideologically in an intermediate position between any two coalition members. This approach, however, gives some counterintuitive results, and one part of the thesis provides a reason for this phenomenon. The Edelman approach is then extended by combining connected coalitions with a probabilistic model for these coalitions.<br/><br> <br/><br> Paper 1 uses Edelman's extension of the ShapleyShubik index to determine the voting power distribution in a number of common voting situations. Paper 2 extends the ideological scale to admit each position to contain more than one voter and suggests several ways to generalize the concept connected coalitions. Using a simple binary probabilistic process, Paper 3 introduces the MarkovPólya index as a parametrized family of power indices which has Edelman's model as a special case. Paper 4 investigates the MarkovPólya index further, and, finally, in Paper 5 the MarkovPólya index is compared with other power indices suggested for ideological voting.}, author = {Perlinger, Thommy}, keyword = {operations research,Statistics,MarkovPólya index,initiator,Voting power index,Spectrum game,connected coalitions,programming,actuarial mathematics,Statistik,operationsanalys,programmering,aktuariematematik}, language = {eng}, pages = {104}, publisher = {Department of Statistics, Lund university}, school = {Lund University}, title = {A Probabilistic Model for Positional Voting  Spectrum Games }, year = {2001}, }