How hard is it to get around this problem? Not hard at all -- it just means considering the system that was used to vote for the first four U.S. presidents. That's Approval Voting.
Under approval voting, you can vote for as few or as many choices as you like in each election. Then, every vote for every candidate is added up, and the candidate with the most votes (approvals) wins. Easy.
More here, at the Center for Election Science.