When are plurality rule voting games dominance-solvable?

This paper studies the dominance-solvability (by iterated deletion of weakly dominated strategies) of plurality rule voting games. For K > 3 alternatives and n > 3 voters, we find sufficient conditions for the game to be dominance-solvable (DS) and not to be DS. These conditions can be stated in terms of only one statistic of the game, the largest proportion of voters who agree on which alternative is worst in a sequence of subsets of the original set of alternatives. When n is large, "almost all" games can be classified as either DS or not DS. If the game is DS, a Condorcet Winner always exists when n > 4, and the outcome is always the Condorcet Winner when the electorate is sufficiently replicated.

[1]  Robin Farquharson,et al.  Theory of voting , 1969 .

[2]  Jeroen M. Swinkels,et al.  Order Independence for Iterated Weak Dominance , 1997, Games Econ. Behav..

[3]  Thomas A. Rietz,et al.  An experimental study of voting rules and polls in three-candidate elections , 1996 .

[4]  Cox.  Making Votes Count , 1997 .

[5]  Strategic stability and non cooperative voting games: the plurality rule , 1998 .

[6]  Adam Brandenburger,et al.  The Role of Common Knowledge Assumptions in Game Theory , 1989 .

[8]  Steven J. Brams,et al.  Chapter 30 Voting procedures , 1994 .

[9]  Marco Mariotti,et al.  Maximum Games, Dominance Solvability, and Coordination , 2000, Games Econ. Behav..

[10]  Ruth C. Silva,et al.  Making votes count , 1963 .

[11]  Tilman Börgers,et al.  On the Dominance Solvability of Large Cournot Games , 1995 .

[12]  L. A. Goodman,et al.  Social Choice and Individual Values , 1951 .

[13]  Tilman Börgers.  Iterated elimination of dominated strategies in a bertrand-edgeworth model , 1992 .

[14]  P. Fishburn,et al.  Voting Procedures , 2022 .

[15]  H. Moulin.  The strategy of social choice , 1983 .

[16]  Roger B. Myerson,et al.  Comparison of Scoring Rules in Poisson Voting Games , 2002, J. Econ. Theory.

[17]  William V. Gehrlein,et al.  The Condorcet efficiency of approval voting and the probability of electing the Condorcet loser , 1998 .

[18]  Uday Rajan,et al.  Trembles in the Bayesian Foundations of Solution Concepts of Games , 1998 .

[19]  Barry Nalebuff,et al.  An Introduction to Vote-Counting Schemes , 1995 .

[20]  Ben Lockwood,et al.  Multiple Equilibria in the Citizen-Candidate Model of Representative Democracy , 2002 .

[21]  R. Weber,et al.  A Theory of Voting Equilibria , 1993, American Political Science Review.

[22]  Dominique Lepelley,et al.  On the probability of electing the Condorcet , 1993 .

[23]  Stephen Coate,et al.  An Economic Model of Representative Democracy , 1997 .

[24]  J. Mertens,et al.  ON THE STRATEGIC STABILITY OF EQUILIBRIA , 1986 .

[25]  Francesco De Sinopoli.  Sophisticated voting and equilibrium refinements under plurality rule , 2000, Soc. Choice Welf..

[26]  Ox,et al.  A NEW THEORY OF STRATEGIC VOTING , 2002 .