Independent collective identity functions as voting rules

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In this paper we study collective identity functions that deal with formation of clubs. Usually the choice offered to individuals is to cast a vote in favor of qualification or not, and the final outcome is qualification or non-qualification. In this context we show that independent collective identity functions are naturally characterized by voting rules, and in particular, consent rules can be represented by one single collection of weighted majorities. In addition, we consider the extended model where voters are allowed to abstain and we distinguish between disqualification and a neutral outcome. We show that this environment allows agents to act in different capacities that cannot be distinguished in the original formulation of the problem.

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  1. 1.

    Here we do not consider the cases that lead to constant rules, i.e., rules where all individuals are qualified, resp., non-qualified.

  2. 2.

    As commented upon in Samet and Schmeidler (2003), this condition guarantees monotonicity.


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The authors are grateful to the two anonymous referees and the Coordinating Editor for their helpful comments and suggestions. A. Laruelle acknowledges the support of the Spanish Ministerio de Economía y Competitividad under project ECO2015-67519, and of the Departamento de Educación, Pol ítica Lingüística y Cultura from the Basque Government (Research Group IT1367-19).

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Correspondence to Annick Laruelle.

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Alcantud, J.C.R., Laruelle, A. Independent collective identity functions as voting rules. Theory Decis (2020).

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  • Collective identity function
  • Voting rules
  • Abstention