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Limiting distributions for continuous state Markov voting models

Ferejohn, J. A. and McKelvey, R. D. and Packel, E. W. (1984) Limiting distributions for continuous state Markov voting models. Social Choice and Welfare, 1 (1). pp. 45-67. ISSN 0176-1714. https://resolver.caltech.edu/CaltechAUTHORS:20171006-130531403

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Abstract

This paper proves the existence of a stationary distribution for a class of Markov voting models. We assume that alternatives to replace the current status quo arise probabilistically, with the probability distribution at time t+1 having support set equal to the set of alternatives that defeat, according to some voting rule, the current status quo at time t. When preferences are based on Euclidean distance, it is shown that for a wide class of voting rules, a limiting distribution exists. For the special case of majority rule, not only does a limiting distribution always exist, but we obtain bounds for the concentration of the limiting distribution around a centrally located set. The implications are that under Markov voting models, small deviations from the conditions for a core point will still leave the limiting distribution quite concentrated around a generalized median point. Even though the majority relation is totally cyclic in such situations, our results show that such chaos is not probabilistically significant.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/BF00297059DOIArticle
http://resolver.caltech.edu/CaltechAUTHORS:20171004-165602546Related ItemSocial Science Working Paper 394
Additional Information:© Springer-Verlag 1984. Received: 19 July 1983 ; Accepted: 24 November 1983. We acknowledge the support of NSF Grants #SOC79-21588, SES-8106215 and SES-8106212.
Funders:
Funding AgencyGrant Number
NSFSOC-79-21588
NSFSES-8106215
NSFSES-8106212
Issue or Number:1
Record Number:CaltechAUTHORS:20171006-130531403
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20171006-130531403
Official Citation:Ferejohn, J.A., McKelvey, R.D. & Packel, E.W. Soc Choice Welfare (1984) 1: 45. https://doi.org/10.1007/BF00297059
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:82166
Collection:CaltechAUTHORS
Deposited By: Katherine Johnson
Deposited On:06 Oct 2017 20:11
Last Modified:03 Oct 2019 18:51

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