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Winning probabilities in a pairwise lottery system with three alternatives
Authors:Frederick H. Chen  Jac C. Heckelman
Affiliation:(1) Department of Economics, Wake Forest University, P.O. Box 7505, NC 27109-7505 Winston-Salem, USA
Abstract:Summary. The pairwise lottery system is a multiple round voting procedure which chooses by lot a winner from a pair of alternatives to advance to the next round where in each round the odds of selection are based on each alternativersquos majority rule votes. We develop a framework for determining the asymptotic relative likelihood of the lottery selecting in the final round the Borda winner, Condorcet winner, and Condorcet loser for the three alternative case. We also show the procedure is equivalent to a Borda lottery when only a single round of voting is conducted. Finally, we present an alternative voting rule which yields the same winning probabilities as the pairwise lottery in the limiting case as the number of rounds of the pairwise lottery becomes large.Received: 5 June 2003, Revised: 17 June 2004, JEL Classification Numbers: D71. Correspondence to: Jac C. HeckelmanWe thank Keith Dougherty and Andrew Yates for their comments.
Keywords:Probabilistic voting  Lottery systems  Markov chain  Majority Rule  Borda Rule  Condorcet Rule.
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