On the Road to Making Science of “Art”: Risk Bias in Market Scoring Rules

We study market scoring rule (MSR) prediction markets in the presence of risk-averse or risk-seeking agents that have unknown yet bounded risk preferences. It is well known that if agents can be prescreened, then MSRs can be corrected to elicit agents’ beliefs. However, agents cannot always be screened, and instead, an online MSR mechanism is needed. We show that agents’ submitted reports always deviate from their beliefs, unless their beliefs are identical to the current market estimate. This means, in most cases it is impossible for a MSR prediction market to elicit an individual agent’s exact belief. To analyze this issue, we introduce a measure to calculate the deviation between an agent’s reported belief and personal belief. We further derive the necessary and sufficient conditions for a MSR to yield a lower deviation relative to another MSR. We find that the deviation of a MSR prediction market is related to the liquidity provided in the MSR’s corresponding cost-function prediction market. We use the relation between deviation and liquidity to present a systematic approach to help determine the amount of liquidity required for cost-function prediction markets, an activity that up to this point has been described as “art” in the literature.