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Approval voting and positional voting methods: Inference, relationship, examples


  • Michel Regenwetter
  • Ilia Tsetlin


Approval voting is the voting method recently adopted by the Society for Social Choice and Welfare. Positional voting methods include the famous plurality, antiplurality, and Borda methods. We extend the inference framework of Tsetlin and Regenwetter (2003) from majority rule to approval voting and all positional voting methods. We also establish a link between approval voting and positional voting methods whenever Falmagne et al.’s (1996) size-independent model of approval voting holds: In all such cases, approval voting mimics some positional voting method. We illustrate our inference framework by analyzing approval voting and ranking data, with and without the assumption of the size-independent model. For many of the existing data, including the Society for Social Choice and Welfare election analyzed by Brams and Fishburn (2001) and Saari (2001), low turnout implies that inferences drawn from such elections carry low (statistical) confidence. Whenever solid inferences are possible, we find that, under certain statistical assumptions, approval voting tends to agree with positional voting methods, and with Borda, in particular. Copyright Springer-Verlag 2004

Suggested Citation

  • Michel Regenwetter & Ilia Tsetlin, 2004. "Approval voting and positional voting methods: Inference, relationship, examples," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(3), pages 539-566, June.
  • Handle: RePEc:spr:sochwe:v:22:y:2004:i:3:p:539-566
    DOI: 10.1007/s00355-003-0232-z

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    Cited by:

    1. Darmann, Andreas & Grundner, Julia & Klamler, Christian, 2019. "Evaluative voting or classical voting rules: Does it make a difference? Empirical evidence for consensus among voting rules," European Journal of Political Economy, Elsevier, vol. 59(C), pages 345-353.
    2. Jean-François Laslier & Karine Straeten, 2008. "A live experiment on approval voting," Experimental Economics, Springer;Economic Science Association, vol. 11(1), pages 97-105, March.
    3. Andreas Darmann & Christian Klamler, 2023. "Does the rule matter? A comparison of preference elicitation methods and voting rules based on data from an Austrian regional parliamentary election in 2019," Public Choice, Springer, vol. 197(1), pages 63-87, October.
    4. Eric Kamwa, 2023. "On two voting systems that combine approval and preferences: fallback voting and preference approval voting," Public Choice, Springer, vol. 196(1), pages 169-205, July.
    5. Marc Vorsatz, 2008. "Scoring rules on dichotomous preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 151-162, June.
    6. Regenwetter, Michel, 2008. "Perspectives on preference aggregation," Papers 08-26, Sonderforschungsbreich 504.
    7. Michel Regenwetter & Elena Rykhlevskaia, 2007. "A general concept of scoring rules: general definitions, statistical inference, and empirical illustrations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(2), pages 211-228, September.
    8. Jordi Massó & Marc Vorsatz, 2008. "Weighted approval voting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(1), pages 129-146, July.
    9. Arnaud Dellis & Sean D’Evelyn & Katerina Sherstyuk, 2011. "Multiple votes, ballot truncation and the two-party system: an experiment," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(2), pages 171-200, July.

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