Board games involving players' consensus for who wins?
For starters, you cannot objectively have the scoring based on precision, cleanliness, etc. Players will vote however they want, which - depending on the system you use to collect votes - can allow for votes in bad faith, votes in error, and random votes. To compound the situation, more players voting on a single set of submissions will result in fewer and fewer unanimous votes. 

For voting, you should look at Apples to Apples/Cards Against Humanity for one person judging all the other submissions. Bad Medicine has each player submit and judge each round. Dead Last is a different sort of voting system, but it could be very cool to implement this system in a more subjective context (e.g. All players secretly and simultaneously vote on the single best of several entries. After simultaneously revealing the votes, all players who did not vote with the majority lose).

You could also look at the video game "Quiplash", as part of the Jackbox party packs.