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Rules of k names are frequently used methods to appoint individuals to o¢ ce.They are two-stage procedures where a …rst set of agents, the proposers, select k individuals from an initial set of candidates, and then another agent, the chooser, appoints one among those k in the list. In practice, the list of k names is often arrived at by letting each of the proposers screen the proposed candidates by voting for v of them and then choose those k with the highest support. We then speak of v-rules of k names. Our main purpose in this paper is to study how di¤erent choices of the parameters v and k a¤ect the balance of power between the proposers and the choosers. From a positive point of view, we analyze a strategic game where the proposers interact to determine what list of candidates to submit. From a normative point of view, we study 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.