On Some Limitations of the Median Voting Rule

Median Voting Rule (MVR) has been proposed as a voting rule,based on the argument that MVR will be less manipulable thanBorda Rule. We find that plurality rule has only a slightlygreater probability of manipulability than MVR, and thatCopeland Rule has a smaller probability of manipulability thanMVR. In addition Borda Rule, plurality rule and Copeland Ruleall have both a greater probability of producing a decisiveresult and a greater strict Condorcet efficiency than MVR.Based on all characteristics, MVR does not seem to be viablereplacement for either plurality rule or for Copeland Rule.

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

[2]  Dominique Lepelley,et al.  Strategic Manipulation in Committees Using the Plurality Rule: Alternative Concepts and Frequency Calculations , 1997 .

[3]  William V. Gehrlein Condorcet efficiency and constant scoring rules , 1982, Math. Soc. Sci..

[4]  William V. Gehrlein Obtaining representations for probabilities of voting outcomes with effectively unlimited precision integer arithmetic , 2002, Soc. Choice Welf..

[5]  Salvador Barberà,et al.  Maximal domains of preferences preserving strategy-proofness for generalized median voter schemes , 1999 .

[6]  W. Gehrlein,et al.  A Note on the Probability of Having a Strong Condorcet Winner , 1999 .

[7]  Dominique Lepelley,et al.  The proportion of coalitionally unstable situations under the plurality rule , 1987 .

[8]  Dominique Lepelley Condorcet efficiency of positional voting rules with single-peaked preferences , 1994 .

[9]  William V. Gehrlein,et al.  The Condorcet efficiency of Borda Rule with anonymous voters , 2001, Math. Soc. Sci..

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

[11]  W. Gehrlein Consistency in Measures of Social Homogeneity: A Connection with Proximity to Single Peaked Preferences , 2004 .

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

[13]  Thierry Marchant The probability of ties with scoring methods: Some results , 2001, Soc. Choice Welf..

[14]  S. Berg,et al.  Voting cycles, plurality rule and strategic manipulation , 1990 .

[15]  Dolors Berga,et al.  Single-peakedness and strategy-proofness of generalized median voter schemes , 2002, Soc. Choice Welf..

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

[17]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

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