A NEW MEASURE OF THE DIFFICULTY OF MANIPULATION OF VOTING RULES

We introduce a new measure of manipulability of anonymous voting rules, which reflects both the size and the prevalence of the manipulating coalitions. We give a simple common framework that describes this and previously known measures and connects them to recent literature. We discuss aspects of computation of the measures and present exact numerical results in the case of 3 candidates that allow for comparison of various common voting rules. We present several asymptotic conjectures inspired by this work.

[1]  Piotr Faliszewski,et al.  Copeland voting: ties matter , 2008, AAMAS.

[2]  Vincent Conitzer,et al.  Nonexistence of Voting Rules That Are Usually Hard to Manipulate , 2006, AAAI.

[3]  Aki Lehtinen,et al.  The welfare consequences of strategic behaviour under approval and plurality voting , 2008 .

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

[5]  David A. Smith.  Manipulability measures of common social choice functions , 1999 .

[6]  Guy Kindler,et al.  The Geometry of Manipulation: A Quantitative Proof of the Gibbard-Satterthwaite Theorem , 2010, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science.

[7]  John R. Chamberlin.  An investigation into the relative manipulability of four voting systems , 1985 .

[8]  Dominique Lepelley,et al.  On Ehrhart polynomials and probability calculations in voting theory , 2008, Soc. Choice Welf..

[9]  D. Saari.  Susceptibility to manipulation , 1990 .

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

[11]  Vincent Conitzer,et al.  When are elections with few candidates hard to manipulate? , 2007, J. ACM.

[12]  Geoffrey Pritchard,et al.  On the Average Minimum Size of a Manipulating Coalition , 2006, Soc. Choice Welf..

[13]  John J. Bartholdi,et al.  Single transferable vote resists strategic voting , 2015 .

[14]  Ariel D. Procaccia,et al.  Frequent Manipulability of Elections: The Case of Two Voters , 2008, WINE.

[15]  Arkadii M. Slinko.  How the size of a coalition affects its chances to influence an election , 2006, Soc. Choice Welf..

[16]  Dominique Lepelley,et al.  Some Further Results on the Manipulability of Social Choice Rules , 2006, Soc. Choice Welf..

[17]  Vincent Conitzer,et al.  Generalized scoring rules and the frequency of coalitional manipulability , 2008, EC '08.

[18]  Arkadii M. Slinko,et al.  How large should a coalition be to manipulate an election? , 2004, Math. Soc. Sci..

[19]  Geoffrey Pritchard,et al.  Asymptotics of the minimum manipulating coalition size for positional voting rules under impartial culture behaviour , 2009, Math. Soc. Sci..

[20]  A. A. J. Marley,et al.  Behavioral Social Choice - Probabilistic Models, Statistical Inference, and Applications , 2006 .

[21]  Geoffrey Pritchard,et al.  Exact results on manipulability of positional voting rules , 2007, Soc. Choice Welf..

[22]  Ariel D. Procaccia,et al.  Algorithms for the coalitional manipulation problem , 2008, SODA '08.

[23]  M. Trick,et al.  The computational difficulty of manipulating an election , 1989 .

[24]  Geoffrey Pritchard,et al.  Probability calculations under the IAC hypothesis , 2007, Math. Soc. Sci..

[25]  Noam Nisan,et al.  Elections Can be Manipulated Often , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.

[26]  Vincent Conitzer,et al.  A sufficient condition for voting rules to be frequently manipulable , 2008, EC '08.

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