Panos Ipeirotis in a comment here:
[W]e should try to separate two things: Market efficiency and market accuracy. Efficiency is the rate in which the market incorporates new information and prevents any arbitrage opportunities. Accuracy is the probability in which the market predicts the correct outcome of an event. The main claim to fame for the [prediction] markets is that they self-report their accuracy, and that “the prices are probabilities”.
We can measure the effectiveness of the market by following the outline discussed above. One axis is the price of the contract at time t before the expiration of the contract and the other axis is the rate in which this event happens. (…60% of the cases the event that trades at 0.6 happens, 30% of the cases the event that trades at 0.3 happens, and so on…). A perfectly accurate market should have a straight line as an outcome when time t gets close to 0. Any deviation of the experimental results indicates an accuracy bias. There are many papers that indicate the favorite-longshot biases in the market (underprice the favorite, overprice the longshots) so there is no need to really repeat this here. An interesting thing is to see how big it can be and still have reasonable accuracy. Furthermore, if we have systematic and robust biases, then we can use a calibration function that will adjust the market prices, compensating for the biases, to reflect real-life probabilities.
Measuring efficiency is a trickier concept. The general definition of efficiency is that “the market immediately incorporates all available information”. Being able to predict price movements indicates inefficiency. Having prices for an event summing up to anything other than 1, indicates inefficiency. However, it is difficult to have a definite proof that the market is efficient. We can only say that “we were not able to spot inefficiencies”. It is very difficult to prove that “the market is efficient”.
The two metrics are, of course, highly connected close to the expiration of the contract. If the market is not efficient, then it will not be accurate, as it will not have had incorporated all the available information, if any material information becomes available just before the expiration of the contract.