Abstract
In this paper we consider a fuzzy variantof the Borda count taking into accountagents' intensities of preference. Thisfuzzy Borda count is obtained by means ofscore gradation and normalization processesfrom its original pattern. The advantagesof the Borda count hold, and are evenimproved, providing an appropriate schemein collective decision making. In addition,both classic and fuzzy Borda counts arerelated to approval voting, establishing aunified framework from distinct points ofview.
Article PDF
Similar content being viewed by others
References
Arrow, K.J. (1963). Social choice and individual values. 2nd edition. New York: Wiley.
Baigent, N. and Xu, Y. (1991). Independent necessary and sufficient conditions for approval voting. Mathematical Social Sciences 21: 21-29.
Bana e Costa A. and Vansnick J.C. (1997). The MACBETH approach: Basic ideas, software, and an application. In N. Meskens and M. Roubens (Eds.), Advances in decision analysis, 131-157. Dordrecht: Kluwer Academic Publishers.
Basset Jr., G.W. and Perski, J. (1999). Robust voting. Public Choice 99: 299-310.
Bezdek, J.C. and Harris, J.D. (1978). Fuzzy partitions and relations: An axiomatic basis for clustering. Fuzzy Sets and Systems 1: 111-127.
Bezdek, J.C., Spillman, B. and Spillman, R. (1978). A fuzzy relation space for group decision theory. Fuzzy Sets and Systems 1: 255-268.
Biswas, T. (1994). Efficiency and consistency in group decisions. Public Choice 80: 23-34.
Black, D. (1958). The theory of committees and elections. London: Cambridge University Press.
Black, D. (1976). Partial justification of the Borda count. Public Choice 28: 1-15.
Brams, S.J. (1990). Constrained approval voting: A voting system to elect a governing board. New York: New York Economic Research Reports.
Brams, S.J. and Fishburn, P.C. (1978). Approval voting. American Political Science Review 72: 831-847.
Brams, S.J. and Fishburn, P.C. (1983). Approval voting. Boston: Birkhäuser.
Candeal, J.C. and Induráin, E. (1995). Aggregation of preferences from algebraic models on groups. Social Choice and Welfare 12: 165-173.
Candeal, J.C., Induráin, E. and Uriarte, J.R. (1992). Some issues related to the topological aggregation of preferences. Social Choice and Welfare 9: 213-227.
Chichilnisky, G. and Heal, G. (1983). Necessary and sufficient conditions for a resolution of the social choice paradox. Journal of Economic Theory 31: 68-87.
Cook, W.D. and Seiford, L.M. (1982). On the Borda-Kendall consensus method for priority ranking problems. Management Science 28: 621-637.
Copeland, A.H. (1951). A ‘reasonable’ social welfare function. Mimeo. Notes from a seminar on applications of mathematics to the social sciences, University of Michigan.
Dasgupta, M. and Deb, R. (1996). Transitivity and fuzzy preferences. Social Choice and Welfare 13: 305-318.
Debord, B. (1992). An axiomatic characterization of Borda's k-choice function. Social Choice and Welfare 9: 337-343.
Dummett, M. (1998). The Borda count and agenda manipulation. Social Choice and Welfare 15: 289-296.
Fishburn, P.C. (1978). Axioms for approval voting: direct proof. Journal of Economic Theory 19: 180-185. Corrigendum (1988) 45: 212.
García-Lapresta, J.L. and Llamazares, B. (2000). Aggregation of fuzzy preferences: Some rules of the mean. Social Choice and Welfare 17: 673-690.
Hansson, B. and Sahlquist, H. (1976). A proof technique for social choice with variable electorate. Journal of Economic Theory 13: 193-300.
Kemeny, J. (1959). Mathematics without numbers. Daedalus 88: 571-591.
Le Breton, M. and Uriarte, J.R. (1990). On the robustness of the impossibility result in the topological approach to Social Choice. Social Choice and Welfare 7: 131-140.
Lines, M. (1986). Approval voting and strategic analysis: A venetian example. Theory and Decision 20: 155-172.
Ludwin, W.G. (1978). Strategic voting and the Borda method. Public Choice 33: 85-90.
Marchant, T. (1996a). Agrégation de relations valuées par la méthode de Borda en vue d'un rangement. Considérations axiomatiques. Ph.D. Thesis, Université Libre de Bruxelles.
Marchant, T. (1996b). Valued relations aggregation with the Borda method. Journal of Multi-Criteria Decision Analysis 5: 127-132.
Marchant, T. (2000). Does the Borda Rule provide more than a ranking? Social Choice and Welfare 17: 381-391.
McLean, I. (1995). Independence of irrelevant alternatives before Arrow. Mathematical Social Sciences 30: 107-126.
McLean, I. and Urken, A.B. (eds.) (1995). Classics of Social Choice. Ann Arbor: The University of Michigan Press.
Morales, J.I. (1797). Memoria Matemática sobre el Cálculo de la Opinion en las Elecciones. Madrid: Imprenta Real. English version in McLean and Urken (1995: 197-235).
Morales, J.I. (1805). Apéndice á la Memoria Matemática sobre el Cálculo de la Opinion en las Elecciones. Madrid: Imprenta de Sancha.
Mueller, D.C. (1979). Public choice. London: Cambridge University Press.
Nitzan, S. and Rubinstein, A. (1981). A further characterization of Borda ranking method. Public Choice 36: 153-158.
Nurmi, H. (1981). Approaches to collective decision making with fuzzy preference relations. Fuzzy Sets and Systems 6: 249-259.
Quesada, A. (2000). Manipulability, anonimity and merging functions. Social Choice and Welfare 17: 481-506.
Saari, D.G. (1995). Basic geometry of voting. Berlin: Springer-Verlag.
Saari, D.G. and Merlin, V.R. (1996). The Copeland method I: Relationships and the dictionary. Economic Theory 8: 51-76.
Sen, A.K. (1977). Social choice theory: A re-examination. Econometrica 45: 53-89.
Sen. A.K. (1984). Strategy-proofness of a class of Borda rules. Public Choice 43: 251-285.
Sertel, M.R. (1988). Characterizing approval voting. Journal of Economic Theory 45: 207-211.
Straffin Jr., P.D. (1980). Topics in the theory of voting. Boston: Birkhäuser.
Sugden, R. (1981). The political economy of public choice: An introduction to welfare economics. Oxford: Martin Robertson.
Tangian, A.S. (2000). Unlikelihood of Condorcet's paradox in a large society. Social Choice and Welfare 17: 337-365.
Tanguiane, A.S. (1991). Aggregation and representation of preferences. Introduction to mathematical theory of democracy. Berlin: Springer-Verlag.
Tanino, T. (1984). Fuzzy preference orderings in group decision making. Fuzzy Sets and Systems 12: 117-131.
Weber, R.J. (1977). Comparison of voting systems. Cowles Foundation Discussion Paper No. 498. Cowles Foundation, Yale University.
Weber, R.J. (1995). Approval voting. Journal of Economic Perspectives 9: 39-49.
Ylmaz, M.R. (1999). Can we improve upon approval voting? European Journal of Political Economy 15: 89-100.
Young, H.P. (1974). An axiomatization of Borda's rule. Journal of Economic Theory 9: 43-52.
Young, H.P. (1988). Condorcet's theory of voting. American Political Science Review 82: 1231-1244.
Young, H.P. (1995). Optimal voting rules. Journal of Economic Perspectives 9: 51-64.
Zadeh, L.A. (1971). Similarity relations and fuzzy orderings. Information Sciences 22: 203-213.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
García-Lapresta, J.L., Martínez-Panero, M. Borda Count Versus Approval Voting: A Fuzzy Approach. Public Choice 112, 167–184 (2002). https://doi.org/10.1023/A:1015609200117
Issue Date:
DOI: https://doi.org/10.1023/A:1015609200117