 of its probability. If the mean is larger than 50%, it resolves YES. Otherwise, it resolves NO. 

The particular mean I am using is the f-mean with f(p) = sgn(p-.5)*(p-.5)^2. In other words, I take the difference of the probability p from 50%, square it, add a positive sign if it's >50% and a negative sign if it's <50%, and take the average of that over the entire time the market is open (time-weighted, as always). Then I convert it back into a number between 0 and 1 (everything is symmetric between p and 1-p here, so 0.5 would be the mean if the average of sgn(p-.5)*(p-.5)^2 is 0). 

The standard arithmetic mean is exactly equivalent to this procedure if you replace (p-.5)^2 with |p-.5|. In other words, this market is like a standard arithmetic mean market, except with all the probabilities weighted by their distance from 1/2. This means it rewards you more for bringing the market to more 

 probabilities. For example, holding it at 70% helps Team YES four times as much as holding it at 60%, instead of just twice as much. Therefore, the typical strategy of, "Don't waste effort bringing the market that much higher/lower than 50%, instead keep it slightly above or below for a long time," might not work as well.