I wrote yesterday about an apparent arbitrage in US presidential election prediction markets: Donald Trump contracts on Polymarket trade at about a 53% chance of him winning the election, while they trade on other prediction markets at more like a 49% chance.[2] If you can buy Trump at 49 elsewhere and sell him at 53 on Polymarket, you can make a quick 4-point profit. I did not take this too seriously, and you shouldn’t either. I assumed that it probably wasn’t a feasible arbitrage: “I am sure there are some fees that I am not accounting for,” I wrote, “and I don’t know how good liquidity is on any of these places.” Also Polymarket is in theory off-limits to US investors. Those sorts of things — trading costs, liquidity, capital constraints, etc. — are the normal explanations for differences in prices in different locations, “limits to arbitrage” that prevent people from selling the expensive contract on Polymarket and buying the cheap one on Kalshi or wherever. But the other natural reaction you might have to seeing the same contract trade at different prices in different locations would be: Well,** are they the same contract?** What if “Donald Trump will win the election” is worth more — that is, has a higher probability — on Polymarket than it does elsewhere? That seems implausible: There is only one presidential election, and Trump will either win it or he won’t. But that might not be exactly right. There is some history of epistemic uncertainty when Donald Trump loses elections. Different prediction markets might resolve that uncertainty in different ways.