Learning performance of prediction markets with kelly bettors

inc.com In evaluating prediction markets (and other crowd-prediction mechanisms), investigators have repeatedly observed a so-called wisdom of crowds effect, which can be roughly sum-marized as follows: the average of participants performs much better than the average participant. The market price— an average or at least aggregate of traders ’ beliefs—offers a better estimate than most any individual trader’s opinion. In this paper, we ask a stronger question: how does the market price compare to the best trader’s belief, not just the average trader. We measure the market’s worst-case log regret, a notion common in machine learning theory. To ar-rive at a meaningful answer, we need to assume something about how traders behave. We suppose that every trade