Properties and Paradoxes of Common Voting Rules
Handbook of Social Choice and Voting (Jac C. Heckelman and Nicholas R. Miller (eds.)), Edward Elgar Press, pp. 263-283, 2015
Abstract. This chapter describes common practical voting rules used to choose among multiple alternatives, including those that assign scores to each alternative based on a voter's ranking, those that require majority support and utilize run-offs if necessary, those that are based on pairwise majority rule, and those that involve proportional lotteries. This chapter compares these rules with respect to their normative properties and provides examples that illustrate seemingly 'paradoxical' violations of such properties by particular voting rules.
Journal of Public Economic Theory 15: 108-123, 2013
Abstract. We develop a lottery procedure for selecting multiple winners that is strategy proof. The rule assigns points to each candidate based on any standard scoring rule method, and then uses one draw to select a single winning set of candidates in proportion to their collective score. In addition to being strategy proof, the lottery rule is also shown to have several other attractive normative properties. Violations of some other important normative properties are noted as well.
On Voting by Proportional Lottery
Korean Journal of Public Choice 2: 1-11, 2007
Abstract. Lottery rules are rarely used beyond breaking a tie vote. Yet, proportional lotteries have several attractive features which are discussed here. First, lotteries break the tyranny of the majority. Second, any proportional lottery which uses only a single round of voting to determine the lottery weights followed by a single weighted draw will ensure sincere preference revelation by the voters. Third, lotteries respect many of the general axiomatic principals invoked for social choice rules, in a probabilistic sense.
Economic Theory 26: 607-617, 2005
Abstract. 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 alternative's 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.
Social Choice and Welfare 21: 455-468, 2003
Abstract. An alternative voting system, referred to as probabilistic Borda rule, is developed and analyzed. The winning alternative under this system is chosen by lottery where the weights are determined from each alternative's Borda score relative to all Borda points possible. Advantages of the lottery include the elimination of strategic voting on the set of alternatives under consideration and breaking the tyranny of majority coalitions. Disadvantages include an increased incentive for strategic introduction of new alternatives to alter the lottery weights, and the possible selection of a Condorect loser. Normative axiomatic properties of the system are also considered. It is shown this system satisfies the axiomatic properties of the standard Borda procedure in a probabilistic fashion.