Let X be 1 if a Republican wins the next US presidential election, 0 otherwise. This will resolve the same as the following market on Polymarket: https://polymarket.com/event/which-party-will-win-the-2024-united-states-presidential-election
Let Y be the probability Polymarket assigns to that outcome at midnight ET before election day. This will be measured by the state of the Automated Market Maker.
This market will resolve PROB to (1 + Y - X) / 2. If Polymarket is an unbiased estimator, then the expected value of this is 50%. If Polymarket is biased in favor of Republicans, then the expected value of this would be larger.
@AaronKreider Or never mind. I wish I could delete my prior comment. That said, I don't think your method measures the most important bias - which will persist through to election day. That of Polymarket odds vs the real odds. Now it's also possible that Polymarket's odds are biased towards the Democrats. This could easily happen if one or more large bettors distort the odds in favor of the Democrats.
Unfortunately, there is no way to know the true odds for a party to win an election - as prediction market odds are systematically biased (often based on what happened last time).
@AaronKreider We’ll never really be sure whether Polymarket was right in their forecast on any particular market, but I think this market at least sets the incentive to estimate their bias.