Strategic Voting Under Uncertainty About the Voting Method

Much of the theoretical work on strategic voting makes strong assumptions about what voters know about the voting situation. A strategizing voter is typically assumed to know how other voters will vote and to know the rules of the voting method. A growing body of literature explores strategic voting when there is uncertainty about how others will vote. In this paper, we study strategic voting when there is uncertainty about the voting method. We introduce three notions of manipulability for a set of voting methods: sure, safe, and expected manipulability. With the help of a computer program, we identify voting scenarios in which uncertainty about the voting method may reduce or even eliminate a voter's incentive to misrepresent her preferences. Thus, it may be in the interest of an election designer who wishes to reduce strategic voting to leave voters uncertain about which of several reasonable voting methods will be used to determine the winners of an election.

[1]  Jérôme Lang,et al.  Strategic voting and the logic of knowledge , 2012, TARK.

[2]  Emerson M. S. Niou.  A note on Nanson's rule , 1987 .

[3]  Keith Dowding,et al.  In Praise of Manipulation , 2007, British Journal of Political Science.

[4]  Alan D. Taylor,et al.  Social choice and the mathematics of manipulation , 2005 .

[5]  Peter Railton,et al.  Probability, explanation, and information , 1981, Synthese.

[6]  Jean-Pierre Benoît,et al.  Strategic Manipulation in Voting Games When Lotteries and Ties Are Permitted , 2002, J. Econ. Theory.

[7]  A. Gibbard.  Manipulation of Voting Schemes: A General Result , 1973 .

[8]  R. Jeffrey.  Statistical Explanation vs. Statistical Inference , 1969 .

[9]  Edith Elkind,et al.  The Complexity of Safe Manipulation under Scoring Rules , 2011, IJCAI.

[10]  Elchanan Mossel,et al.  A quantitative Gibbard-Satterthwaite theorem without neutrality , 2015, Comb..

[11]  M. Satterthwaite.  Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions , 1975 .

[12]  A. Feldman,et al.  Strongly nonmanipulable multi-valued collective choice rules , 1980 .

[13]  John Duggan,et al.  Strategic manipulability without resoluteness or shared beliefs: Gibbard-Satterthwaite generalized , 2000, Soc. Choice Welf..

[14]  Vincent Conitzer,et al.  Barriers to Manipulation in Voting , 2016, Handbook of Computational Social Choice.

[15]  Shmuel Nitzan,et al.  The vulnerability of point-voting schemes to preference variation and strategic manipulation , 1985 .

[16]  Piotr Faliszewski,et al.  AI's War on Manipulation: Are We Winning? , 2010, AI Mag..

[17]  Georges-Théodule Guilbaud.  Les théories de l'intérêt général et le problème logique de l'agrégation , 2012 .

[18]  Felix Brandt,et al.  Rolling the Dice : Recent Results in Probabilistic Social Choice , 2017 .

[19]  Vincent Conitzer,et al.  Dominating Manipulations in Voting with Partial Information , 2011, AAAI.

[20]  Arkadii Slinko,et al.  On Asymptotic Strategy-Proofness of Classical Social Choice Rules , 2002 .

[21]  Rohit Parikh,et al.  The Logic of Communication Graphs , 2004, DALT.

[22]  P. Gärdenfors.  Manipulation of social choice functions , 1976 .

[23]  4. Minimal manipulability and local strategy-proofness , 1988 .

[24]  A. Gibbard.  Manipulation of Schemes That Mix Voting with Chance , 1977 .

[25]  M. Satterthwaite.  The Existence of a Strategy Proof Voting Procedure , 1973 .

[26]  Jerry S. Kelly,et al.  STRATEGY-PROOFNESS AND SOCIAL CHOICE FUNCTIONS WITHOUT SINGLEVALUEDNESS , 1977 .

[27]  Ulrich Endriss,et al.  Voter response to iterated poll information , 2012, AAMAS.

[28]  Hervé Moulin,et al.  A New Solution to the Random Assignment Problem , 2001, J. Econ. Theory.

[29]  Ariel Rubinstein,et al.  Sampling equilibrium, with an application to strategic voting , 2003, Games Econ. Behav..

[30]  Rohit Parikh,et al.  Knowledge-Theoretic Properties of Strategic Voting , 2004, JELIA.

[31]  Felix Brandt,et al.  On the tradeoff between efficiency and strategyproofness , 2018, Games Econ. Behav..

[32]  S. Merrill,et al.  Strategic Voting in Multicandidate Elections under Uncertainty and under Risk , 1981 .

[33]  Arkadii M. Slinko,et al.  Is it ever safe to vote strategically? , 2014, Soc. Choice Welf..

[34]  Marcus Pivato,et al.  Truth-Revealing Voting Rules for Large Populations , 2016, Games Econ. Behav..