Decision markets with good incentives

Decision markets both predict and decide the future. They allow experts to predict the effects of each of a set of possible actions, and after reviewing these predictions a decision maker selects an action to perform. When the future is independent of the market, strictly proper scoring rules myopically incentivize experts to predict consistent with their beliefs, but this is not generally true when a decision is to be made. When deciding, only predictions for the chosen action can be evaluated for their accuracy since the other predictions become counterfactuals. This limitation can make some actions more valuable than others for an expert, incentivizing the expert to mislead the decision maker. We construct and characterize decision markets that are --- like prediction markets using strictly proper scoring rules --- myopic incentive compatible. These markets require the decision maker always risk taking every available action, and reducing this risk increases the decision maker's worst-case loss. We also show a correspondence between strictly proper decision markets and strictly proper sets of prediction markets, creating a formal connection between the incentives of prediction and decision markets.