Imperfect Voting

There are a couple things that are interesting to consider. First, there is Pareto efficiency. That is to say, can we be assured that the final selection is done such that there are no changes that could be made in terms of players in teams or project selected for implementing such that it improves at least one person's situation while not diminishing anyone else's?

Then there is Arrow's impossibility theorem. It states that we cannot have a fair ranking system and at the same time have everyone's preferences considered equally, with Pareto efficiency, and such that adding a new proposal to the group won't change the over all results besides giving the new proposal a chance to win.

These suggest a couple different voting systems. First, people can vote in some manner and have the bottom scorers removed from the pool, and then have the voting continue again. It could be made in one pass if everyone's preferences were ranked, and when options were removed, all the options below them would be augmented and the votes re-totaled, continuing until we hit the top five.

Second, we could have people vote and result in a top 10 or so projects. After that, the people who gave the proposals would be the only ones with a vote, and they pick the top 5 projects. I think that system would lead to some interesting results and some good debate.

For the basic voting schema, I still think people should give all proposals a ranking between 1 and 5, and then add all the scores together. Also, these rankings should be prefigured and no one should know the overall results until all the votes had been decided. The top 10 or so results from there can have the people who made the proposals decide which they want to do.

If the top proposal people decide to team up and choose, say, only 3 proposals, the rest of the class should be able to re-vote, and form groups to tackle whichever proposal wins.