<p>We study voting situations in which multiple positions or seats are to be distributed among parties or groups of parties, using voting methods that generalize the Single Non-Transferable Vote (SNTV). Assuming that these groups can both nominate their preferred candidates and decide how to vote for them, we identify the equilibrium distributions that emerge from Nash equilibria in these nomination-voting games. The results obtained and the approach used are relevant in the design of procedures, if a direct relationship between the number of positions held by each group and the size of that group is desired. Although the studied family of voting situations is very broad, special attention is paid to one subfamily called MI, which directly generalizes the SNTV mechanism. For many mechanisms within the broader family, and for all mechanisms in the MI subfamily, the results show that the equilibrium distributions align with allocation methods that generalize the d’Hondt rule. In the case of MI mechanisms, these distributions fall between the outcomes produced by the d’Hondt method and those resulting from block voting.</p>