The voting should be between the participants themselves. Each of them should vote on a 1 to 10 scale to others who participated. Once everyone has voted, the one with the most votes wins.
According to the game theory in this case noone will vote
If the voting is mandatory on a scale 1 to 10 then everybody will poll 1
We can eliminated that everyone votes 1. In addition to voting they also must put a reason why they rated a logo low or high.
They won't get to see the results until the voting ends.