The method used to liquidate positions is called "FIFO" and it stands for "first in, first out". Shares are sold off in the order they were bought. This is the method used by regulated exchanges in the U.S. PredictIt has adopted the same procedure. At present there are no plans to change this in the future.
My preference would be to use average cost basis. The problem with FIFO is that if I get into a position, then the market move against me and I go in deeper, then it moves back towards the price where i first bought in and so I reduce the size of my position, this is coded as a loss even if I'm selling at price that is better than my average. The results is that when (technically if, but I'm pretty confident about the ultimate result) the contract gets resolved in my favor, I will get charged fees based on profits that are greater than what I actually made, because they add must cancel out these phantom losses that I incurred when adjusting my position in response to market moves. This isn't the end of the world, but I find it annoying.
Note also average cost basis would be much more transparent, since what it easiest to monitor is the average price for you holding, not the oldest shares you still own.
100% agree with gabewell.