Iterative Voting with Partial Preferences

Voting platforms can offer participants the option to sequentially modify their preferences, whenever they have a reason to do so. But such iterative voting may never converge, meaning that a state where all agents are happy with their submitted preferences may never be reached. This problem has received increasing attention within the area of computational social choice. Yet, the relevant literature to date hinges on the rather stringent assumption that the agents are able to rank all alternatives they are presented with, i.e., that they hold preferences that are linear orders. We relax this assumption and investigate iterative voting under partial preferences. To that end, we define and study two families of rules that extend the well-known k-approval rules in the standard voting framework. Although we show that for none of these rules convergence is guaranteed in general, we also are able to identify natural conditions under which such guarantees can be given. Finally, we conduct simulation experiments to test the practical implications of our results.