That sounds like a good idea. And as you said it leads to interaction between players as well. A player could also trade tokens with the game, such as 2 tokens for 1 token of a specific color (to be able to choose something the player think is favourable for the situation).

The token part sounds really good.

I would however use the tokens to increase the chance for an outcome.

Your players could earn/trade(great suggestion suliman) tokens ingame and spent them to increase the chance to get their result.

It still leaves a lot to chance but if a token would eliminate the chance, it will feel unfair to the other players who want a different outcome.

You can treat every option as having received one vote already to add a bit of chance for other outcomes to occur or only count voted options if you want the players to have the only control of what outcome occurs.

Increasing the chances instead of having a fixed outcome would also help if players are indecisive and let's say several pairs of players pick different outcomes (e.g. 2-2-3 which would lead to each outcome having a 29% chance but one has 43% chance instead of the outcome with 3 votes getting picked).

My suggestion would be to implement the tokens as currency and have an ingame use as well.

This way a player will have to evaluate if he uses his tokens for the current game or have a slightly better chance in the next game.