Blake Riley

Posts Tagged ‘robin hanson

Market Scoring Rules

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Decision-makers in need of information face the dual tasks of finding experts and then motivating them to give accurate forecasts. If there is an obvious expert to rely on, proper scoring rules are a well-understood means of eliciting honest probabilities. Alternatively, if there is a large enough pool of people willing to participate in a market, prices from a continuous double auctions of contingent securities do well at aggregating information, without any need to screen for expertise. However, most prediction tasks are stuck between these two methods, with only a few, hard-to-identify individuals who can meaningfully give input. Market scoring rules bridge this gap, working with an arbitrary amount of agents without becoming deadlocked or breaking the bank of the decision-maker.

Market scoring rules, and their equivalent formulation as cost-function-based market makers, debuted in “Logarithmic market scoring rules for modular combinatorial information aggregation” by Robin Hanson, first circulated as a working paper in 2002 and published somewhat perfunctorily in 2007. Mechanisms that solved similar problems, like David Pennock’s dynamic pari-mutuel markets, came out around the same time, but Hanson’s innovation has shaped up to be the seminal advance in prediction market design.

At first glance, a market scoring rule is an almost trivial extension of typical scoring rule: each participant receives the difference between the score of his report and the score of the previous participant. This doesn’t affect incentive-compatibility or willingness to participate, because in the worse case, a participant could match the report of the previous agent and have no net payment. As a result, the sum of all the payments to participants telescope, leaving the sponsor of the market liable only for the difference in the scores of the last participant and some initial report.

Although developed in the context of a sequentially applied scoring rule, this system turns out to be equivalent to an automated market maker that sells shares of contingent securities. This feels more like a prediction market, but with some striking advantages. First, the prices of securities always form a coherent probability distribution by construction, simplifying interpretation. Second, the market has infinite liquidity because all transactions are conducted through the market-maker. Third, prices for all securities are updated whenever a sale or purchase is made. Together, these advantages mean markets for conjunctive or conditional events can be feasibly priced. Even if no one else ever trades on a joint security that Obama wins the 2012 presidential election and it snows in Washington DC on inauguration day, this security can be bought and the information expressed in the purchase percolates out to all other combinations of events.

The modern prediction market literature largely revolves around market-makers inspired by Hanson. A decade later, the logarithmic market-maker now has a air of classic elegance to it, in contrast to the seemingly primeval prior literature and the complex refinements that have followed.

Written by blakeriley

2012.01.23 at 23:29

Posted in economics

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