Abstract
Many voting rules and, in particular, the plurality rule and Condorcet-consistent voting rules satisfy the simple-majority decisiveness property. The problem implied by such decisiveness, namely, the universal disregard of the preferences of the minority, can be ameliorated by applying unbiased scoring rules such as the classical Borda rule, but such amelioration has a price; it implies erosion in the implementation of the widely accepted “majority principle”. Furthermore, the problems of majority decisiveness and of the erosion in the majority principle are not necessarily severe when one takes into account the likelihood of their occurrence. This paper focuses on the evaluation of the severity of the two problems, comparing simple-majoritarian voting rules that allow the decisiveness of the smallest majority larger than 1/2 and the classical Borda method of counts. Our analysis culminates in the derivation of the conditions that determine, in terms of the number of alternatives k, the number of voters n, and the relative (subjective) weight assigned to the severity of the two problems, which of these rules is superior in light of the dual majoritarian approach.
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References
Baharad E., Nitzan S. (2002) Ameliorating majority decisiveness through expression of preference intensity. American Political Science Review 96(4): 745–754
Baharad E., Nitzan S. (2003) The Borda rule, Condorcet consistency and Condorcet stability. Economic Theory 22(3): 685–688
Baharad E., Nitzan S. (2007) The costs of implementing the majority principle: The golden voting rule. Economic Theory 31(1): 69–84
Brams, S. J., & Fishburn, P. C. (2002). Voting procedures. In K. Arrow, A. Sen, & K. Suzumura (Eds.), Handbook of social choice and welfare (Vol. I, Chap. 4, pp. 173–236) Amsterdam: Elsevier Science.
Fishburn P.C. (1973) The theory of social choice. Princeton University Press, Princeton
Gehrlein W.V. (1983) Condorcet’s paradox. Theory and Decision 15: 161–197
Gehrlein W.V., Fishburn P.C. (1976) The probability of paradox of voting: A computable solution. Journal of Economic Theory 13: 14–25
Gehrlein W.V., Lepelley D. (1998) The Condorcet efficiency of approval voting and the probability of electing the Condorcet loser. Journal of Mathematical Economics 29(3): 271–283
Lepelley D., Merlin V. (2001) Scoring run-off paradoxes for variable electorates. Economic Theory 17(1): 53–80
Merlin V., Tataru M., Valognes F. (2002) On the likelihood of Condorcet’s profiles. Social Choice and Welfare 19(1): 193–206
Merrill S. III. (1984) A comparison of efficiency of multi-candidate elections systems. American Journal of Political Science 28: 23–48
Mueller, D. C. (2003). Public choice III. Cambridge University Press.
Nurmi H. (1999) Voting paradoxes and how to deal with them. Springer-Verlag, Berlin, Heidelberg, New York
Nurmi H. (2002) Voting procedures under uncertainty. Springer-Verlag, Berlin, Heidelberg, New York
Nurmi H., Uusi-Heikkila Y. (1986) Computer simulations of approval and plurality voting. European Journal of Political Economy 2: 54–78
Saari D.G. (1990) The Borda dictionary. Social Choice and Welfare 7: 279–317
Saari D.G. (1995) Basic geometry of voting. Springer, Berlin
Saari, D. G. (2001). Chaotic elections! A mathematician looks at voting. American Mathematical Society, Providence.
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Baharad, E., Nitzan, S. Condorcet vs. Borda in light of a dual majoritarian approach. Theory Decis 71, 151–162 (2011). https://doi.org/10.1007/s11238-009-9157-z
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DOI: https://doi.org/10.1007/s11238-009-9157-z