Limiting Distributions for Continuous State Markov Voting Models
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.
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.Attached Files
Submitted - sswp394.pdf
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Additional details
- Eprint ID
- 82100
- Resolver ID
- CaltechAUTHORS:20171004-165602546
- Created
-
2017-10-06Created from EPrint's datestamp field
- Updated
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2019-10-03Created from EPrint's last_modified field
- Caltech groups
- Social Science Working Papers
- Series Name
- Social Science Working Paper
- Series Volume or Issue Number
- 394