Statistical evaluation of voting rules

We generate synthetic elections using two sources of survey data, two spatial models, and two standard models from the voting literature, IAC and IC. For each election that we generate, we test whether each of 54 voting rules is (1) non-manipulable, and (2) efficient in the sense of maximizing summed utilities. We find that Hare and Condorcet–Hare are the most strategy-resistant non-dictatorial rules. Most rules have very similar efficiency scores, apart from a few poor performers such as random dictator, plurality and anti-plurality. Our results are highly robust across data-generating processes. In addition to presenting our numerical results, we explore analytically the effects of adding a Condorcet provision to a base rule and show that, for all but a few base rules, this modification cannot introduce a possibility of manipulation where none existed before. Our analysis provides support for the Condorcet–Hare rule, which has not been prominent in the literature.

[1]  Miguel A. Ballester,et al.  On the Justice of Decision Rules , 2011 .

[2]  Dominique Lepelley,et al.  Voting Rules, Manipulability and Social Homogeneity , 2003 .

[3]  Dominique Lepelley,et al.  The vulnerability of four social choice functions to coalitional manipulation of preferences , 1994 .

[4]  Robert F. Bordley,et al.  A Pragmatic Method for Evaluating Election Schemes through Simulation , 1983, American Political Science Review.

[5]  G. Thompson,et al.  The Theory of Committees and Elections. , 1959 .

[6]  F. W. Roush,et al.  Statistical manipulability of social choice functions , 1996 .

[7]  D. Saari.  Geometry of voting , 1994 .

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

[9]  T. Tideman,et al.  Collective Decisions and Voting: The Potential for Public Choice , 2006 .

[10]  Steggall.  On Methods of Election , 1895, Proceedings of the Edinburgh Mathematical Society.

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

[12]  James Green-Armytage.  Four Condorcet-Hare Hybrid Methods for Single-Winner Elections , 2011 .

[13]  Jeffrey T. Richelson,et al.  A comparative-analysis of social choice functions, I, II, III: A summary , 1979 .

[14]  S. Merrill.  A Comparison of Efficiency of Multicandidate Electoral Systems , 1984 .

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

[16]  James Green-Armytage,et al.  Strategic voting and nomination , 2014, Soc. Choice Welf..

[17]  C. Coombs.  A theory of data. , 1965, Psychology Review.

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

[19]  P.-C.-F. Daunou,et al.  Mémoire sur les élections au scrutin , 1803 .

[20]  J. Richelson.  A comparative analysis of social choice functions, IV , 1978 .

[21]  Michael X Cohen,et al.  Toward Applicable Social Choice Theory: A Comparison of Social Choice Functions under Spatial Model Assumptions , 1978, American Political Science Review.

[22]  Samuel Merrill,et al.  The Relative Efficiency of Approval and Condorcet Voting Procedures , 1991 .

[23]  Hong Zhang,et al.  A knowledge warehouse system for enterprise resource planning systems , 2006 .

[24]  S. Berg.  Paradox of voting under an urn model: The effect of homogeneity , 1985 .

[25]  Fuad Aleskerov,et al.  Degree of manipulability of social choice procedures , 1999 .

[26]  Michel Regenwetter,et al.  The impartial culture maximizes the probability of majority cycles , 2003, Soc. Choice Welf..

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

[28]  Dan S. Felsenthal,et al.  Review of Paradoxes Afflicting Procedures for Electing a Single Candidate , 2012 .

[29]  Douglas Muzzio,et al.  Approval voting , 1983 .

[30]  P. Fishburn,et al.  Condorcet's paradox and anonymous preference profiles , 1976 .

[31]  Scott L. Feld,et al.  Who's Afraid of the Big Bad Cycle? Evidence from 36 Elections , 1992 .

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

[33]  Dominique Lepelley,et al.  Borda rule, Copeland method and strategic manipulation , 2002 .

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