Measuring the informativeness of prediction markets

Friedrich Hayek claimed that prices act as a mechanism to transmit information. Claude Shannon claimed the transmission of information reduced uncertainty and could be quantified probabilistically in 'bits'. The overlap here instantly poses the question: to what extent can we measure the informativeness of prices?

It is quite hard to test this in financial markets as there is no objective 'true value' to compare the price against. Without this, we cannot say what prices are informative about. Prediction markets offer an interesting alternative. These markets are futures contracts where a price of $p$ cents implies a $p%$ probability of the event happening. Now we have a target which tells us what prices are informative about: outcomes of events.

In Shannon's terms, our goal would be to estimate $I(\text{Outcome}; \text{Price})$ to measure how informative prices are regarding prediction market outcomes. We test this along with other hypotheses in results.pdf.

Using Polymarket's data aggregated on Dune, we find that $I(\text{Outcome}; \text{Price})$ is in fact positive both 4 hours and 12 hours before resolution. We also have some evidence ($p=0.145$) that the informativeness of the price signal rises over time. In the context of prediction markets, this gives us empirical information theoretic evidence that prices carry measurable information about future outcomes and reduce uncertainty in a quantifiable way.