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Dis&approval voting: a characterization

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Abstract

The voting rule considered in this paper belongs to a large class of voting systems, called “range voting” or “utilitarian voting”, where each voter rates each candidate with the help of a given evaluation scale and the winner is the candidate with the highest total score. In approval voting the evaluation scale only consists of two levels: 1 (approval) and 0 (non approval). However non approval may mean disapproval or just indifference or even absence of sufficient knowledge for evaluating the candidate. In this paper we propose a characterization of a rule (that we refer to as dis&approval voting) that allows for a third level in the evaluation scale. The three levels have the following interpretation: 1 means approval, 0 means indifference, abstention or ‘do not know’, and \(-1\) means disapproval.

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Notes

  1. That is, voters are not asked to compare candidate but grade them instead. For a relative question where voters are asked to give their best and worst candidates, see García-Lapresta et al. (2010).

  2. For a review of the axiomations of approval voting see Xu (2010). More generally Ju (2010) provides a survey on “simple preferences”, i.e., the case when individuals have either dichotomous or trichotomous preferences.

  3. There is however evidence that the votes vary with the precise specification that is conveyed to the voters. The first scale tends to produce fewer ‘penalising’ or ‘disapproval’ votes than the second one: see Baujard et al. (2012).

  4. This is in line with the role of this property in the characterization by Alós-Ferrer (2006), as explained in his Footnote 3.

  5. We are indebted to an anonymous referee for providing the proof of Theorem 1 that we present here, which is more direct than our original argument. Furthermore, we stress that working with ballot aggregation functions on voter response profiles implicitly builds anonymity into the framework.

  6. http://www.parliament.uk/site-information/glossary/pairing/.

  7. If all voters have a clear-cut (i.e., positive or negative) opinion on each candidate, the rule that asks voters to cross out the names of candidates they do not want and then selects the candidates with the least number of crosses is equivalent to approval voting: candidates who are not crossed off the list are the approved candidates. It is not rare that voters are indifferent or even lack the sufficient knowledge to express a positive or a negative opinion on some candidates. If this is the case, then the two rules differ because the non disapproved candidates consist of the approved candidates and those who leave the voter indifferent.

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Authors and Affiliations

  1. Universidad de Salamanca, Campus Miguel de Unamuno, 37007 , Salamanca, Spain

    José Carlos R. Alcantud

  2. Bridge, Fundamentos del Análisis Económico I, University of the Basque Country (UPV/EHU), Avenida Lehendakari Aguirre, 83, 48015 , Bilbao, Spain

    Annick Laruelle

  3. IKERBASQUE, Basque Foundation for Science, 48011 , Bilbao, Spain

    Annick Laruelle

Authors
  1. José Carlos R. Alcantud
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  2. Annick Laruelle
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Correspondence to Annick Laruelle.

Additional information

The authors greatly appreciate the insightful reports of two reviewers and the associate editor, J.-F. Laslier. They thank C. Alós-Ferrer, A. Baujard, S. Brams, D. Felsenthal, R. Sanver, H. de Swart, and the participants in the IX Meeting of the Spanish Network of Social Choice (Salamanca 2012) and the 13th international meeting of the Association for Public Economic Theory (Lisbon 2013) for their helpful comments. This research is supported by the Spanish Ministerio de Economía y Competitividad under projects ECO2012–31933 and ECO2012–31346 and the Departamento de Educación, Política Lingüística y Cultura from the Basque Government (Research Group IT568-13).

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Alcantud, J.C.R., Laruelle, A. Dis&approval voting: a characterization. Soc Choice Welf 43, 1–10 (2014). https://doi.org/10.1007/s00355-013-0766-7

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