Decision and prediction markets are designed to determine the likelihood of future events; prediction markets predict what will happen, and decision markets predict the results of a choice, or what would happen. Both allow multiple participants to review and make predictions, and participants are typically scored for improving the accuracy of the market’s prediction. Previous work has demonstrated prediction markets can reward accuracy improvements, as can a single participant informing a decision. We construct and characterize decision markets where all participants are scored for improving the market’s accuracy. These markets require the decision maker always risk taking an action at random, and reducing this risk increases its potential loss. We also relate these decision markets to sets of prediction markets, demonstrating a correspondence between their perfect Bayesian equilibria.