It might depend on how close this poll is. If there's a third poll and only two options on it, I think it'd work better if everyone had to pick only one faction. With three factions it'd kinda suck if you picked faction C because you liked it the best, but noone else picked them and faction A, your least favorite, won by just one or two votes.
If the third poll has three choices I might leave it multiple choice. If anyone voted for all three it would be a non-vote anyway, and that way people could choose their favorite and second favorite.
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