Balancing the power to appoint officers

Rules of k names are two-stage procedures where a first set of agents, the proposers, select k individuals from a set 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 v candidates and then choosing those k with the highest support. We then speak of v-rules of k names. We study how different choices of the parameters v and k affect the balance of power between the proposers and the choosers. We analyze a strategic game where the proposers interact to determine what list of candidates to submit. We investigate the impact of the choice of parameters v and k upon the distribution of power among the proposers and the chooser, and we discuss how to eventually balance it.