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Scoring rule sensitivity to weight selection

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  • William Gehrlein
  • Peter Fishburn

Abstract

This essay examines the sensitivity of collective rankings and winners to the weights used in score vectors that are applied to sets of individual rankings to yield collectieve rankings in a typical additive manner. The paper considers probabilities of getting the same winner and the same collective ranking when different score vectors are used for three-element sets. It then discusses the propensities of score vectors to preserve the orginal winner or collective ranking when one or more elements is removed from this ranking and a lower dimensional score vector is applied to the reduced situation. The latter case is examined for three- and four-element sets. The model used for the assessments is based on equally-likely choices of rankings by individuals and applies to situations that involve large numbers of individuals. Roughly speaking, best agreements and minimum sensitivities center around linear (Borda) score vectors. The greatest discrepancies arise from the so-called plurality and reverse plurality score vectors. Copyright Martinus Nijhoff Publishers 1983

Suggested Citation

  • William Gehrlein & Peter Fishburn, 1983. "Scoring rule sensitivity to weight selection," Public Choice, Springer, vol. 40(3), pages 249-261, January.
    • Handle: RePEc:kap:pubcho:v:40:y:1983:i:3:p:249-261
    DOI: 10.1007/BF00114522
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    References listed on IDEAS

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    1. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    2. Gehrlein, William V., 1981. "Single-stage election procedures for large electorates," Journal of Mathematical Economics, Elsevier, vol. 8(3), pages 263-275, October.
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    Cited by:

    1. Mostapha Diss & Vincent Merlin, 2010. "On the stability of a triplet of scoring rules," Theory and Decision, Springer, vol. 69(2), pages 289-316, August.
    2. Mostapha Diss & Patrizia Pérez-Asurmendi, 2016. "Consistent collective decisions under majorities based on difference of votes," Theory and Decision, Springer, vol. 80(3), pages 473-494, March.
    3. William Gehrlein, 1999. "On the Probability that all Weighted Scoring Rules Elect the Condorcet Winner," Quality & Quantity: International Journal of Methodology, Springer, vol. 33(1), pages 77-84, February.
    4. Merlin, V. & Tataru, M. & Valognes, F., 2000. "On the probability that all decision rules select the same winner," Journal of Mathematical Economics, Elsevier, vol. 33(2), pages 183-207, March.
    5. Gehrlein, William V. & Lepelley, Dominique, 2000. "The probability that all weighted scoring rules elect the same winner," Economics Letters, Elsevier, vol. 66(2), pages 191-197, February.
    6. Mostapha Diss & Patrizia Pérez-Asurmendi, 2016. "Probabilities of Consistent Election Outcomes with Majorities Based on Difference in Support," Group Decision and Negotiation, Springer, vol. 25(5), pages 967-994, September.
    7. Mostapha Diss & Patrizia Pérez-Asurmendi, 2015. "Consistent collective decisions under majorities based on difference of votes," Working Papers halshs-01241996, HAL.

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