Markov chain: Difference between revisions
Add more references about applying Markov chains to voting methods
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Each Markov chain is associated with a stationary (or steady state) distribution, which is a distribution of events so that if an event is chosen at random according to the distribution, then the future event will also come from that distribution.
The [[Keener eigenvector]] and [[Sinkhorn]] voting methods are based on Markov chains, and by calculating the steady state for a particular family of Markov matrices, it's possible to construct a number of [[Smith-efficient]] voting methods.<ref>{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2002-December/008923.html|title=The Copeland/Borda wv hybrid (fwd)|website=Election-methods mailing list archives|date=2002-12-03|last=Simmons|first=F.}}</ref><ref>{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-May/078240.html|title=Markov chain approaches|website=Election-methods mailing list archives|date=2004-05-15|last=Heitzig|first=J.}}</ref> Due to their construction, these methods give each candidate a score, not just an order of finish.
Some nondeterministic methods can be derandomized by using Markov chains, for instance a semiproportional multi-winner generalization of [[random ballot]].<ref>{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2019-October/002323.html|title=Semiproportional methods 2: derandomizing the obvious|website=Election-methods mailing list archives|date=2019-10-04|last=Munsterhjelm|first=K.}}</ref>
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