The Hidden Beauty of the Quadratic Market Scoring Rule: A Uniform Liquidity Market Maker, with Variations

For some applications, prediction markets that rely entirely on voluntary transactions between individual participants may provide insufficient liquidity to aggregate information effectively, especially where the number of participants is small. A solution to this problem is to rely on an automated market maker, which allows participants to buy from or sell to the house. Robin Hanson has described a class of automated market makers called market scoring rules. This Article examines a member of this class that has received little attention, the quadratic market scoring rule. Its prime virtue is that it provides uniform liquidity across the probability or prediction spectrum. Market participants will thus have the same incentive to do research that is expected to produce an expected change in the market prediction, regardless of the current prediction. Formulas are provided for implementing the quadratic market scoring rule, as well as variations, for example to implement conditional markets.