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Limiting Distributions for Continuous State Markov Voting Models

Ferejohn, John A. and McKelvey, Richard D. and Packel, Edward W. (1981) Limiting Distributions for Continuous State Markov Voting Models. Social Science Working Paper, 394. California Institute of Technology , Pasadena, CA. (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20171004-165602546

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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:Report or Paper (Working Paper)
Additional Information:Published as Ferejohn, John A., Richard D. McKelvey, and Edward W. Packel. "Limiting distributions for continuous state Markov voting models." Social Choice and Welfare 1.1 (1984): 45-67.
Group:Social Science Working Papers
Series Name:Social Science Working Paper
Issue or Number:394
Record Number:CaltechAUTHORS:20171004-165602546
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20171004-165602546
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:82100
Collection:CaltechAUTHORS
Deposited By: Jacquelyn Bussone
Deposited On:06 Oct 2017 20:12
Last Modified:03 Oct 2019 18:50

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