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The reinforcement axiom under sequential positional rules

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  • Sébastien Courtin
  • Boniface Mbih
  • Issofa Moyouwou
  • Thomas Senné

Abstract

The reinforcement axiom roughly states that when an alternative is selected by two different constituencies, it must also be selected by their union. Hare and Coombs rules are special cases of sequential positional voting rules, which are known to violate this axiom. In this article, we first show that reinforcement can be violated by all such rules. We then evaluate, by the use of Monte Carlo simulations and the Fishburn-Gehrlein technique, the proportion of profiles at which this phenomenon occurs.
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  • Sébastien Courtin & Boniface Mbih & Issofa Moyouwou & Thomas Senné, 2010. "The reinforcement axiom under sequential positional rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(3), pages 473-500, September.
    • Handle: RePEc:spr:sochwe:v:35:y:2010:i:3:p:473-500
    DOI: 10.1007/s00355-010-0449-6
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    1. Dominique Lepelley, 1996. "Constant scoring rules, Condorcet criteria and single-peaked preferences (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(3), pages 491-500.
    2. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    3. Dominique Lepelley & Vincent Merlin, 2001. "Scoring run-off paradoxes for variable electorates," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 17(1), pages 53-80.
    4. Boniface Mbih & Issofa Moyouwou & Xingyu Zhao, 2010. "On the positive association of parliamentary social choice functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(1), pages 107-127, June.
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    1. Sébastien Courtin & Boniface Mbih & Issofa Moyouwou, 2014. "Are Condorcet procedures so bad according to the reinforcement axiom?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 927-940, April.
    2. Eric Kamwa & Vincent Merlin & Faty Mbaye Top, 2023. "Scoring Run-off Rules, Single-peaked Preferences and Paradoxes of Variable Electorate," Working Papers hal-03143741, HAL.

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