Abstract Voting theory can provide useful insights for multiagent preference aggregation. However, the standard setting assumes voters with preferences that are total orders, as well as a ballot language that coincides with the preference language. In typical AI scenarios, these assumptions do not hold: certain alternatives may be incomparable for some agents, and others may have their preferences encoded in a format that is different from how the preference aggregation mechanism wants them. We study the consequences of dropping these assumptions. In particular, we investigate the consequences for the important notion of strategy-proofness. While strategy-proofness cannot be guaranteed in the classical setting, we are able to show that there are situations in our more general framework where this is possible. We also consider computational aspects of the problem