Information markets are markets created to aggregate information. Such markets usually estimate a probability distribution over the values of certain variables, via bets on those values. Combinatorial information markets would aggregate information on the entire joint probability distribution over many variables, by allowing bets on all variable value combinations.

In practice, scoring rules elicit good probability estimates from individuals, while betting markets elicit good consensus estimates from groups. Market scoring rules combine these features, eliciting estimates from individuals or groups, with groups costing no more than individuals.

Participants in prediction markets such as the Iowa Electronic Markets trade all-or-nothing contracts that pay a dollar if and only if specified future events occur. Researchers engaged in empirical study of prediction markets have argued broadly that equilibrium prices of the contracts traded are “market probabilities ” that the specified events will occur. This paper shows that if traders are risk-neutral price takers with heterogenous beliefs, the price of a contract in a prediction market reveals nothing about the dispersion of traders ’ beliefs and partially identifies the central tendency of beliefs. Most persons have beliefs higher than price when price is above 0.5, and most have beliefs lower than price when price is below 0.5. The mean belief of traders lies in an interval whose midpoint is the equilibrium price. These findings persist even if traders use price data to revise their beliefs in plausible ways.

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While a simple information market lets one trade on the probability of each value of a single variable, a full combinatorial information market lets one trade on any combination of values of a set of variables, including any conditional or joint probability. In laboratory experiments, we compare the accuracy of simple markets, two kinds of combinatorial markets, a call market and a market maker, isolated individuals who report to a scoring rule, and two ways to combine those individual reports into a group prediction. We consider two environments with asymmetric information on sparsely correlated binary variables, one with three subjects and three variables, and the other with six subjects and eight variables (and so 256 states). ∗ For their comments, we thank David Porter, Ryan Oprea, and participants of seminars at George Mason

Election markets have been praised for their ability to forecast election outcomes, and to forecast better than trial-heat polls. This paper challenges that optimistic assessment of election markets, based on an analysis of Iowa Electronic Market (IEM) data from presidential elections between 1988 and 2004. We argue that it is inappropriate to naively compare market forecasts of an election outcome with exact poll results on the day prices are recorded, that is, market prices reflect forecasts of what will happen on Election Day whereas trial-heat polls register preferences on the day of the poll. We then show that when poll leads are properly discounted, poll-based forecasts outperform vote-share market prices. Moreover, we show that win-projections based on the polls dominate prices from winner-take-all markets. Traders in these markets generally see more uncertainty ahead in the campaign than the polling numbers warrant—in effect, they overestimate the role of election campaigns. Reasons for the performance of the IEM election markets are considered in concluding sections.

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In this paper we study the problem of centrally organizing a market where the participants submit bids for contingent claims over the outcome of a future event and the market organizer must determine which bids to accept. The bidder will select a set of future states and a price at which he is willing to buy the contingent claims. By accepting a bid, the market organizer agrees to pay the bidder a fixed amount if one of the bidder’s selected states is realized. We will specifically study markets which are run as call auctions where the organizer holds the auction open until a certain time and then determines the bids to accept and reject. This type of market has broad usage in financial markets, betting markets and general prediction markets. Lange and Economides [8] have developed a parimutuel mechanism for solving such a market with many positive characteristics. However, one drawback of their formulation is that their mathematical model is not convex and no efficient algorithm is known to solve it. In this paper, we introduce a new mathematical formulation called the Convex Parimutuel Call Auction Mechanism (CPCAM). This formulation produces many of the same advantageous properties of the Lange and Economides model but can more easily be solved due to its convexity. In particular, our model yields the first fully polynomial–time approximation scheme (FPTAS) for the problem. Moreover, we show that our model actually produces identical state prices as the Lange and Economides model. As a corollary, we show that by first obtaining the state prices from our model, the Lange and Economides model becomes a linear program and hence can be solved in polynomial time.

Abstract: Decision markets are social media for decision making where the options to choose from are traded for (with real or play money) by the decision makers. The market equilibrium resulting from the competition between the options offered by sellers and sought for by buyers is interpreted as a collective consent and the relative market prices are interpreted as a ranking of the options. However, on decision markets like on financial markets market equilibrium prices may also arise out of mimicry resulting from either indecision or pure greed. The more the trading behavior is driven by indecision or greed, the less the equilibrium prices reflect genuine preferences. This article proposes a novel approach to decision making. It further describes to rely on artificial perturbations of a market’s equilibrium for uncovering indecision or greed on decision markets. Based on the hypothesis that profit seeking is affected by psychological norms that can be activated by context cues and social interaction, an experimental evaluation is proposed that shifts a market’s framing between a competitive individualistic and a collaborative communal setting. Social norms in the collaborative communal setting are expected to lessen greed and thus give ways to true preferences: The equilibria of markets with a collaborative communal setting are therefore expected to be less vulnerable to artificial pertubations than those with a competitive individualistic setting. This article describes in a principled manner first the market perturbations, second the experimental evaluation framework. 1

Democracies often fail to aggregate information, while speculative markets excel at this task. We consider a new form of governance, wherein voters would say what we want, but speculators would say how to get it. Elected representatives would oversee the after-the-fact measurement of national welfare, while market speculators would say which policies they expect to raise national welfare. Those who recommend policies that regressions suggest will raise GDP should be willing to endorse similar market advice. Using a qualitative engineering-style approach, we present three scenarios, consider thirty-three design issues, and finally a more specific design responding to those concerns.