New prospects in social choice theory: median and average as tools for measuring, electing and ranking

Ngoie, Ruffin-Benoît M. and Savadogo, Zoïnabo and Ulungu, Berthold E.-L. (2014): New prospects in social choice theory: median and average as tools for measuring, electing and ranking. Published in: Advanced Studies in Contemporary Mathematics , Vol. 25, No. 1 (January 2015): pp. 19-38.

Abstract

The goal of this paper is to show that neither mean-based voting systems nor median-based ones can fulfill requirements of an ideal democracy. We then work out an original voting function obtained by hydrizing Borda Majority Count (mean-based) and Majority Judgment (median-based). The so-called “Mean-Median Compromise Method” slices between mean and average values. It proposes, moreover, a new tiebreaking method computing intermedian grades mean.

• Item Type: MPRA Paper
• Language: English
• Keywords: Borda Majority Count, Majority Judgment, Mean-Median Compromise Method
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C70 - General; D - Microeconomics > D6 - Welfare Economics > D63 - Equity, Justice, Inequality, and Other Normative Criteria and Measurement; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice ; Clubs ; Committees ; Associations; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D72 - Political Processes: Rent-Seeking, Lobbying, Elections, Legislatures, and Voting Behavior; I - Health, Education, and Welfare > I3 - Welfare, Well-Being, and Poverty > I31 - General Welfare, Well-Being

References

Alcantud, J.C.R. and Laruelle, A. (2014), Dis&approval voting: a characterization. Social Choice and Welfare, 43(1): 1-10.

Arrow, K. J. (1950), A difficulty in the concept of social welfare. Journal of Political Economy, 58(4): 328-346.

Arrow, K. J. (1951), Social choice and individual values, Yale University Press.

Arrow, K. J. (1963), Social choice and individual values, 2ème ed., Yale University Press.

Balinski, M. and Laraki, R. (2007), A theory of measuring, electing and ranking. Proceedings of the National Academy of Sciences of the United States of America, 104: 8720-8725.

Balinski, M. and Laraki, R. (2010), Majority Judgment: measuring, ranking and electing. MIT Press.

Balinski, M. and Laraki, R. (2011), In Situ and Laboratory Experiments on Electoral Law Reform, chapter 2: Election by Majority Judgment: Experimental Evidence. Studies in Public Choice. Springer.

Balinski, M. and Laraki, R. (2012a), Jugement majoritaire vs vote majoritaire. Cahier 2012-37, CNRS.

Balinski, M. and Laraki, R. (2012b), Rendre les élections aux électeurs: le jugement majoritaire. Technical report, Terra Nova.

Baujard, A. Gavrel, F., Igersheim, H., Laslier, J.-F. and Lebon, I. (2013), Who's favored by evaluative voting ? an experiment conducted during the 2012 french presidential election. Cahier 2013-05, CNRS.

Baujard, A. and Igersheim, H. (2007), Expérimentation du vote par note et du vote par approbation lors de l'élection présidentielle française du 22 avril 2007. Technical report, Centre d'analyse stratégique.

Baujard, A. and Igersheim, H. (2009), Expérimentation du vote par note et du vote par approbation le 22 avril 2007. Premiers résultats. Revue économique, 60(1): 189-201.

Bialik, C. (2009), And the oscar goes to... not its voting system. The Wall Street Journal, February 6.

Brams, S. (2011), Grading candidates. American Scientist.

Falco, E. and Garcia-Lapresta, J.-L. (2011), A distance-based extension of the majority judgement voting system. In Acta Universitatis Belii, Mathematics 18: 17-27.

Falco, E., Garcia-Lapresta, J.-L. and Rosello, L. (2013), Allowing voters to be imprecise: a proposal using multiple linguistic terms. Information Sciences.

Falco, E., Garcia-Lapresta, J.-L. and Rosello, L. (2014), Aggregating imprecise linguistic expressions. In P. Guo and W. Pedrycz, editors, Human-Centric Decision Making Models for Social Sciences.

Farvaque, E., Jayet, H. and Ragot, L. (2009), Quel mode de scrutin pour quel “vainqueur”? une expérience sur le vote préférentiel transférable. Revue d'économie politique, 119(2): 221-246.

Gibbard, A. (19973) Manipulation of voting schemes: a general result. Econometrica, 41: 587-601.

Laslier, J.-F. (2010), A note on choosing the alternative with the best median evaluation. Cahier 2010-17, CNRS.

Laslier, J.-F. (2011), In Situ and Laboratory Experiments on Electoral Law Reform, chapter 5: Lessons from In Situ Experiments during French Elections. Studies in Public Choice. Springer.

Laslier, J.-F. (2012), On choosing the alternative with the best median evaluation. Public Choice, 153(3): 269-277.

Laslier, J.-F. and Van der Straeten, K. (2004), Une expérience de vote par assentiment. Revue française de science politique, 54(1): 99-130.

Satterthwaite, M. A. (1975), Strategy-proofness and arrow's conditions: existence and correspondence theorems for voting procedures and social welfare functions. Journal of Economic Theory, 10: 187-217.

Sen, A. K. (1970a), Collective choice and social welfare. Holden-Day, London.

Sen, A. K. (1970b), The impossibility of a paretian liberal. Journal of Political Economy, 78:152-157.

Taylor, A. (2005), Social Choice and the Mathematics of manipulation. Cambridge University Press, New York.