Combinatorial Information Market Design (2003)

• Market scoring rules can be used more efficiently than single agent scoring rules to provide markets with more depth and less susceptible to manipulation.
• The problem of ‘standard information markets’: Standard information markets also suffer from an irrational participation problem. Once rational agents have hedged their risks regarding the events covered by an information market, they should not want to trade with each other. Even if they have substantial private information not reflected in previous market prices, agents who care only about what they can buy with the assets they might gain must realize that the gains of some can only can from the losses of others (Milgrom and Stokey, 1982; Aumann, 1976). Now real markets do show surprisingly high levels of speculative activity, perhaps due to widespread irrationality, or to people using bets to signal their expertise to observers (as in “bar bets”). But it may not be possible to induce much more such activity, in order to support new information markets without taking away from other markets.
• Scoring rules have a longer history, starting in the 1950s. Theory being that experts give a score of a possible outcome distribution with weightings. They can be rewarded with strict incentive compatible systems to incentivize honest reporting. On these simple scoring rules more sophisticated models have been built including quadratic and logarithmic scoring rules. Scoring rules are used in different disciplines such as weather forecasting, economics etc. There are several problems with expert forecasts, including biases, risk aversion and the challenge in predicting multi variable problems. There is one big problem however: “One big problem with scoring rules remains largely unsolved, however. When different people are asked to estimate the same random variable, they can and often do give different estimates. Yet what we really want is a single estimate that aggregates information from different people. Unfortunately, the literature on “pooling opinions,” i.e., constructing a single pooled probability distribution from a set of individual distributions, is mostly discouraging (Genest and Zidek, 1986).”
• Market scoring rules are more effective the more participants they have. When the activity shrinks towards fewer participants it is more efficient to shift from information aggregation towards simple scoring rules.
• By using a sequential scoring rule we effectively give experts the ability to create a market, an AMM of sorts, regarding the prediction. Thus experts can ‘buy’ the expert prediction from each other when convinced there is upside. The benefit is that the cost to the market maker is quantifiable and is the difference in accuracy between the initial prediction by the market maker upon forming the market and how correct the last prediction is.