Social homogeneity and Condorcet's paradox

Peter Fishburn and William Gehrlein

Public Choice, 1980, vol. 35, issue 4, 403-419

Abstract: This paper has examined the relationship between social homogeneity measured by σ(p)=p 1 2 + ... + p 6 2 and the likelihood of Condorcet's paradox. Attention was restricted to three-candidate elections. It was shown first that the most general restriction on p vectors that produces a definite inverse relationship between σ(p) and the limit-in-voters probability P ∞ (p) of Condorcet's paradox is the dual culture restriction. We then deleted this restriction to allow any p vector and considered the relationship between σ(p) and the paradox probability when Abrams' positioning effect was removed by averaging the P n (p) values all over rearrangements of the components of p. The resultant averaged probability of Condorcet's paradox with n voters was denoted as Q n (p). Theorem 1 showed that there are p vectors for all odd n ≥ 3 which deny a definite inverse relationship between Q n (p) and σ(p). However, Theorem 2 verified for n=3 that the intervals of possible Q n (p) values for fixed values of σ(p) decrease as σ(p) increases. It was shown also that the latter relationship does not hold for large n although there is a partial tendency for Q n (p) to decrease as σ(p) increases for large n. Copyright Martinus Nijhoff Publishers bv 1980

Date: 1980
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://hdl.handle.net/10.1007/BF00128119 (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:35:y:1980:i:4:p:403-419

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

DOI: 10.1007/BF00128119

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 ().