Limiting distributions for continuous state Markov voting models Export

@article{citeulike:3815205, 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.}, author = {Ferejohn, J. A. and Mckelvey, R. D. and Packel, E. W.}, citeulike-article-id = {3815205}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/BF00297059}, citeulike-linkout-1 = {http://www.springerlink.com/content/h472672856qm4360}, day = {1}, doi = {10.1007/BF00297059}, journal = {Social Choice and Welfare}, keywords = {political\_economy, social\_choice, voting}, month = {May}, number = {1}, pages = {45--67}, posted-at = {2008-12-21 08:55:12}, priority = {3}, title = {Limiting distributions for continuous state Markov voting models}, url = {http://dx.doi.org/10.1007/BF00297059}, volume = {1}, year = {1984} }

TY - JOUR ID - citeulike:3815205 L3 - citeulike-article-id:3815205 N2 - 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. IS - 1 JF - Social Choice and Welfare EP - 67 TI - Limiting distributions for continuous state Markov voting models VL - 1 SP - 45 KW - political_economy KW - social_choice KW - voting AU - Ferejohn, JA AU - Mckelvey, RD AU - Packel, EW PY - 1984/05/01/ UR - http://dx.doi.org/10.1007/BF00297059 ER -