Recently, I made three markets inspired by "The Market", but instead of using the arithmetic mean to determine the average, they used other types of means:

Since the geometric mean skews lower than the arithmetic mean, while the other two skew higher, I didn't use a mean of 1/2 as the cutoff point between a YES and NO victory. Instead, I used a mean of all values between 0 and 1. Even though this was calculated as a "fair" threshold, it actually gives an advantage to one side. The mean of each market would only be close to the mean of all values between 0 and 1 if the market's pobability over time was uniformly distributed between 0 and 1, but in reality, it is much more likely to be close to 50% for most of the run than at extreme values, and it is very hard for one team to hold the market at an extreme value. This gives the team that wins if the final mean is 50% an advantage, since all they have to do is prevent the market from going to extreme values for too long, while the other team needs to push the market to extreme values to win.

Thus, Team YES has an advantage on the geometric mean market, and Team NO has an advantage on the other two. These advantages can also become self-fulfilling prophecies, since people will bet on whichever side has the advantage, making the results favor that side even more.

This market will resolve YES if the advantaged team wins in all three of these markets, i.e., if Team YES wins the geometric mean market and Team NO wins in the RMS and exponential mean markets. It will resolve NO if the disadvantaged team wins any of them.