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Condorcet vs. Borda in Light of a Dual Majoritarian Approach

  • Eyal Baharad

    (University of Haifa)

  • Shmuel Nitzan

    ()

    (Bar-Ilan University)

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 ½ 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 approacht.

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File URL: http://www.biu.ac.il/soc/ec/wp/2010-07.pdf
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Paper provided by Bar-Ilan University, Department of Economics in its series Working Papers with number 2010-07.

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Date of creation: Apr 2010
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Handle: RePEc:biu:wpaper:2010-07
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  1. Nurmi, Hannu & Uusi-Heikkila, Yrjo, 1986. "Computer simulations of approval and plurality voting: The frequency of weak pareto violations and condorcet loser choices in impartial cultures," European Journal of Political Economy, Elsevier, vol. 2(1), pages 47-59.
  2. Eyal Baharad & Shmuel Nitzan, 2003. "The Borda rule, Condorcet consistency and Condorcet stability," Economic Theory, Springer, vol. 22(3), pages 685-688, October.
  3. Brams, Steven J. & Fishburn, Peter C., 2002. "Voting procedures," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 4, pages 173-236 Elsevier.
  4. Fabrice Valognes & Vincent Merlin & Monica Tataru, 2002. "On the likelihood of Condorcet's profiles," Social Choice and Welfare, Springer, vol. 19(1), pages 193-206.
  5. Gehrlein, William V. & Lepelley, Dominique, 1998. "The Condorcet efficiency of approval voting and the probability of electing the Condorcet loser," Journal of Mathematical Economics, Elsevier, vol. 29(3), pages 271-283, April.
  6. Eyal Baharad & Shmuel Nitzan, 2007. "The Costs of Implementing the Majority Principle: The Golden Voting Rule," Economic Theory, Springer, vol. 31(1), pages 69-84, April.
  7. Dominique Lepelley & Vincent Merlin, 2001. "Scoring run-off paradoxes for variable electorates," Economic Theory, Springer, vol. 17(1), pages 53-80.
  8. Gehrlein, William V. & Fishburn, Peter C., 1976. "The probability of the paradox of voting: A computable solution," Journal of Economic Theory, Elsevier, vol. 13(1), pages 14-25, August.
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