[sga]

I like the concept of "the most popular move for the day, voted by the group, will be taken as the group's move".

It would be interesting to use this concept in a game where the set of possible moves could be ranked in order of best move for that turn such that the users could see a distribution of number of votes versus this set. In this way you could see the quality of the groups choice and compare it to the best choice and your choice (if they were different). This would also lend itself to user scores. Not sure which game would lend itself to this.

Also you might consider number of votes as an alternative or additional progress trigger. For HN vs Reddit set it at 100 votes per side. If you don't hit the limit it switches on a per day basis, but if you do hit the limit it switches immediately. Not only would this potentially speed the game but it also could create a sense of urgency to get your vote in to have it count.