Since relying on Kelly is equivalent to maximizing log utility of wealth, I’d initially guess there is some equivalence between a group of risk-neutral agents trading via the LMSR and a group of Kelly agents with equal wealth trading directly. I haven’t seen anything around in the literature though.
I’ve started work on a rudimentary play money binary prediction market using LMSR in django (still very much incomplete, PM me for a link if you’d like), and my present interface is one of buying and selling shares, which isn’t very user friendly.
With a “changing the price” interface that Hanson details in his paper, accurate participants can easily lose all their wealth on predictions that they’re moderately confident in, depending on their starting wealth. If I have it so agents can always bet, then the wealth accumulation in accurate predictors won’t happen and the market won’t actually learn which agents are more accurate.
With an automated Kelly interface, it seems that participants should be able to input only their probability estimates, and either change the price to what they believe it to be if the cost is less than Kelly, or it would find a price which matches the Kelly criterion, so that agents with poorer predictive ability can keep playing and learn to do better, and agents with better predictive ability accumulate more wealth and contribute more to the predictions.
However, I’m uncertain as to whether a) the markets would be as accurate as if I used a conventional “changing the price” interface (due to the fact that it seems we’re doing log utility twice), and b) whether I can find find the Kelly criterion for this, with a probability estimate being the only user input and the rest calculated from data about the market, the user’s balance, etc.
What do you mean by applying Kelly to the LMSR?
Since relying on Kelly is equivalent to maximizing log utility of wealth, I’d initially guess there is some equivalence between a group of risk-neutral agents trading via the LMSR and a group of Kelly agents with equal wealth trading directly. I haven’t seen anything around in the literature though.
“Learning Performance of Prediction Markets with Kelly Bettors” looks at the performance of double auction markets with Kelly agents, but doesn’t make any reference to Hanson even though I know Pennock is aware of the LMSR.
“The Parimutuel Kelly Probability Scoring Rule” might point to some connection.
Sorry, should’ve been more clear.
I’ve started work on a rudimentary play money binary prediction market using LMSR in django (still very much incomplete, PM me for a link if you’d like), and my present interface is one of buying and selling shares, which isn’t very user friendly.
With a “changing the price” interface that Hanson details in his paper, accurate participants can easily lose all their wealth on predictions that they’re moderately confident in, depending on their starting wealth. If I have it so agents can always bet, then the wealth accumulation in accurate predictors won’t happen and the market won’t actually learn which agents are more accurate.
With an automated Kelly interface, it seems that participants should be able to input only their probability estimates, and either change the price to what they believe it to be if the cost is less than Kelly, or it would find a price which matches the Kelly criterion, so that agents with poorer predictive ability can keep playing and learn to do better, and agents with better predictive ability accumulate more wealth and contribute more to the predictions.
However, I’m uncertain as to whether a) the markets would be as accurate as if I used a conventional “changing the price” interface (due to the fact that it seems we’re doing log utility twice), and b) whether I can find find the Kelly criterion for this, with a probability estimate being the only user input and the rest calculated from data about the market, the user’s balance, etc.