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

The logarithmic market scoring rule has emerged as a standard automated market maker. The approach is particularly useful for combinatorial markets, but this article argues that for a variety of prediction market applications, the quadratic market scoring rule may be more sensible. With that rule, liquidity is uniform across the probability or prediction spectrum. Moreover, the rule can easily be adapted for contexts in which greater liquidity is desired for some portion of the probability or prediction spectrum. For each binary or linear outcome being predicted, two separate markets are used, so that a forecaster can always buy shares in either the low market or the high market to change the group prediction. The approach can be used as the basis for both conditional and deliberative prediction markets