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Information that is of relevance for decision-making is often distributed,and held by self-interested agents. Decision markets are well-suited mechanismsto elicit such information and aggregate it into conditional forecasts that canbe used for decision-making. However, for incentive-compatible elicitation,decision markets rely on stochastic decision rules which entails that sometimesactions have to be taken that have been predicted to be sub-optimal. In thiswork, we propose three closely related mechanisms that elicit and aggregateinformation similar to a decision market, but are incentive compatible despiteusing a deterministic decision rule. Following ideas from peer predictionmechanisms, proxies rather than observed future outcomes are used to scorepredictions. The first mechanism requires the principal to have her own signal,which is then used as a proxy to elicit information from a group ofself-interested agents. The principal then deterministically maps theaggregated forecasts and the proxy to the best possible decision. The secondand third mechanisms expand the first to cover a scenario where the principaldoes not have access to her own signal. The principal offers a partial profitto align the interest of one agent and retrieve its signal as a proxy; oralternatively uses a proper peer prediction mechanism to elicit signals fromtwo agents. Aggregation and decision-making then follow the first mechanism. Weevaluate our first mechanism using a multi-agent bandit learning system. Theresult suggests that the mechanism can train agents to achieve a performancesimilar to a Bayesian inference model with access to all information held bythe agents.

Proxy Forecasting to Avoid Stochastic Decision Rules in Decision Markets