Posted by: Paul Hewitt | March 9, 2009

Market Scoring Rules in Prediction Markets

Robin Hanson has developed a class of market scoring rule market makers that are, perhaps, the most prominently used in public prediction markets.  In particular, it is his Logarithmic Market Scoring Rule (LMSR) that is most widely used.  Having played around with many public prediction markets that utilize the LMSR, it appears to be an excellent mechanism for ensuring adequate trading takes place in thin markets, where there are only two outcomes.   Where there are only two outcomes (e.g. which of two sports teams will win the big game?), the odds/prices will tend to be within a relatively narrow range around 50%, giving rise to reasonable returns for a reasonable risk.  However, in markets where there are more than two outcomes, I believe the LMSR distorts trading behavior, by creating substantial incentives for traders to become risk seekers.

For example, on Hubdub, there are markets to predict the DJIA close, with the possible outcomes expressed in ranges.  The more ranges offered, the lower are the prices (odds) in the ranges, because the bets are spread out among more options.  The lower the odds, the higher to potential payoff.  Often, it is advantageous to place bets in several of the likely ranges.  You may lose on one or two bets, but you will end up with a tidy profit on the one that does “win”.  Given that these markets run daily, it is a relatively easy way to increase your “wealth”, quickly.  Part of the reason that this strategy works is that you can always sell to limit your losses as it gets close to the market closing.  The LMSR guarantees that you will be able to sell out of unwanted positions.  I believe the LMSR creates an incentive for traders to become risk seeking, and I don’t think this is a good thing for prediction markets.

Ideally, in the corporate world, prediction markets should be able to more accurately determine the level of uncertainty about future events, conditions and actions.  Corporations tend to be risk averse, or at best, risk-neutral.  In the current economic environment, the last thing you want is a corporation that is risk-seeking.  So, why would you want to base corporate decisions on a prediction market that rewards risky behavior?

I find it interesting that David Pennock’s Dynamic Parimutuel Market Maker (DPM) mechanism has not been put to wider use in prediction markets.  Under this system (similar to horse race betting), market liquidity is automatically created by allowing all traders to purchase any share (horse) at any time.  Under a straight parimutuel system, it pays to wait until just before the market closes, because there is no way to sell a “bad” bet before the start of the race.  Under Pennock’s DMP, he provides a mechanism to allow traders to sell their previous investments, under a Continuous Double Auction (CDA).  If there is sufficient liquidity (i.e. large number of traders), bad investments may be sold to other traders before the market closes.  However, there is no guarantee that a trader would be able to do so, except at a heavily discounted price (which would take into account the current risks).  This is a good thing!  If purchasers were unsure that they would be able to reverse their bad investments, they would exercise more caution before purchasing.  They would tend to act in a risk averse or risk neutral manner.  This is the type of trader behavior that we would like to see in an internal prediction market.

So, I ask, why hasn’t David Pennock’s DPM market maker achieved more widespread use?



  1. […] How does the price algorithm affect trading behaviour?  View my initial comments […]

  2. Hi Paul,

    I am Vishu. I got introduced to Pred. Markets recently from Data Mining and Machine Learning background. I am trying to work on ambiguity within binary and multiple option based PM’s. As of now I am working out with some research on methods.

    I would like to stay in touch with you.

    Contact me on

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