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
Okay then, they have to rank every other entry out of however many entries there are and can only use each number once. If there are 20 entries, 20 rankings, lowest to highest.