Although it is generally good strategy to allocate points equally among all choices under cumulative voting, there seem to be exceptions. For example, in an election to fill several seats with a number of different factions, you have two similar factions of equal size, who are just barely "entitled" to three seats between them. Ideally, they should be able to run one candidate each, plus one "shared" candidate that the two groups agree on. With paper ballots, and each voter allowed 3 points to allocate, a voter could give 2 points to his/her "own" candidate, and one point to the "shared" candidate. With the Peoria system, where a vote is always allocated equally among a voter's choices, you can resort to massive coordination, or simply instruct the voters to use a die from a Parcheesi game. If the voter rolls a 1 or 2, he should vote only for the party's favorite. If the voter rolls 3 or higher, vote for both the party favorite and the shared candidate.