What do prediction markets predict?

Abstract

We show that prediction markets cannot be relied on to always elicit any interesting statistic of aggregate beliefs. Formal derivations of the bets placed in prediction markets can be viewed as demands for state-contingent commodities. We provide derivations for two popular cases, log utility and Constant Relative Risk Aversion (CRRA) utility, connecting these derivations to familiar scoring rules. We then use these results to demonstrate how the properties of prediction markets depend critically on the assumed homogeneity of participants.

Acknowledgement

Harrison thanks the US National Science Foundation for research support under grants NSF/HSD 052675 and NSF/SES 0616746.

Notes

¹There is no claim that these markets elicit individual beliefs or that they are free of individual irrationalities: see Forsythe et al. (1999) for a survey of field and laboratory evidence on this issue. The claim about aggregate beliefs rests on informal statements about the propensity of ‘marginal traders’ to get market prices right (in some sense).

²A separate issue is the ability of prediction markets to reliably elicit beliefs in ‘informationally complex’ environments: see Healy et al. (2008). As the state space of events grows, markets defined over each possible event-combination would be expected to become thin, resulting in unreliable information aggregation. Another issue is whether prediction markets and hypothetical polls are forecasting the same thing: the former pay out depending on the actual outcome when it is realized, and the latter are often posed counterfactually as eliciting beliefs if the outcome were to be realized ‘today.’ We have no interest in counterfactuals here.

³In private correspondence Gjerstad shows that symmetric bi-modal beliefs will also lead to near-perfect aggregate belief elicitation in his model.

⁴Ottaviani and Sørensen (2007) consider the way in which trade in prediction markets might lead agents with heterogeneous prior beliefs to revise those beliefs in a rational expectations equilibrium.

⁵The simulation is implemented using version 11 of Stata, and the command file is available on request.

⁶It is possible to use prediction markets in a setting in which there is ‘forced feed betting’, where individuals have tokens to bet with and that are useless unless used to place a bet. Such settings arise in laboratory experiments and some corporate, in-house applications of prediction markets.

⁷Specifically, they have 100 units of wealth more than the baseline, and their discount rates are cut in half.

⁸Specifically, that the CRRA coefficient is lower by 0.25, as long as this would not make them risk-loving.