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Rules of k names is a two-stage procedure where a first set of agents, the proposers, select k individuals from an initial list of candidates, and then another agent, the chooser, appoints one among those k in the list. The list of k names is often arrived at by letting each of the proposers vote for a fixed number q of candidates, and then choosing the k most voted ones. We can then speak of q-rules of k names. We study strong Nash equilibrium of the game induced by the q-rules of k names and we characterize the utilitarian and egalitarian optimal parameters of these rules (k,q) as functions of players´ degrees of risk aversion. The paper generalizes and extends results in our first exploration of the topic (Barberà and Coelho, 2010).

Voting rules; Constitutional design; Strong Nash equilibrium; Rule of k Names