Power indices in large voting bodies

Dennis Leech ()

Public Choice, 2013, vol. 155, issue 1, 79 pages

Abstract: There is no consensus on the properties of voting power indices when there is a large number of voters in a weighted-voting body. On the one hand, in some real-world cases that have been studied the power indices have been found to be nearly proportional to the weights (e.g., the EUCM, US Electoral College); this is true for both the Penrose-Banzhaf and the Shapley-Shubik indices. It has been suggested that this is a manifestation of a conjecture by Penrose (known subsequently as the Penrose limit theorem, that has been shown to hold under certain conditions). On the other hand, we have the older literature from cooperative game theory, due to Shapley and his collaborators, showing that, where there is a finite number of voters whose weights remain constant in relative terms, and where the quota remains constant in relative terms, while the total number of voters increases without limit, the powers of the voters with finite weight tend to limiting values that are, in general, not proportional to the weights. These results, too, are supported by empirical studies of large voting bodies (e.g., the IMF/WB boards, corporate shareholder meetings). This paper proposes a restatement of the Penrose limit theorem and shows that, in general, both the ‘classical’ power indices converge in the limit to proportionality with weights as the Laakso-Taagepera index of political fragmentation increases. This new version reconciles the different theoretical and empirical results that have been found for large voting bodies. Copyright Springer Science+Business Media, LLC 2013

Keywords: Voting power; Power index; Penrose; Banzhaff; Shapley-Shubik; Laakso-Taagepera (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://hdl.handle.net/10.1007/s11127-011-9840-9 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:kap:pubcho:v:155:y:2013:i:1:p:61-79

Ordering information: This journal article can be ordered from
http://www.springer. ... ce/journal/11127/PS2

DOI: 10.1007/s11127-011-9840-9

Access Statistics for this article

Public Choice is currently edited by WIlliam F. Shughart II

More articles in Public Choice from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().