Even if you assume perfectly spherical rational traders with equal fixed budgets, prediction market prices aren't guaranteed to converge to the average belief:

Even if you assume perfectly spherical rational traders with equal fixed budgets, prediction market prices aren't guaranteed to converge to the average belief: https://quantian.substack.com/p/market-prices-are-not-probabilities https://quantian.substack.com/p/market-prices-are-not-probab... You cannot really do postprocessing to the market price to get the average belief back out, because the bounds aren't very tight: a market price of 50% could correspond to an average belief anywhere between 29% and 71%.