Independent collective identity functions as voting rules

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.