In this paper, we study belief elicitation about an uncertain future event, where the reports will affect a principal's decision. We study two problems that can arise in this setting: (1) Agents may have an interest in the outcome of the principal's decision. We show that with intrinsic competing incentives (an interest in a decision that is internal to an agent) truthfulness cannot be guaranteed and there is a fundamental tradeoff between how much the principal allows reports to influence the decision, how much budget the principal has, and the degree to which a mechanism can be manipulated. Furthermore, we show that the Quadratic Scoring Rule is worst-case optimal in minimizing the degree of manipulation. In contrast, we obtain positive results and truthful mechanisms in a setting where the competing incentives stem instead from a rational briber who wants to promote a particular decision. We show that the budget required to achieve this robustness scales with the sum of squares of the degree to which agent reports can influence the decision. (2) We study the setting where the future event is only observed conditionally on the decision taken. We give a category of mechanisms that are truthful when agent beliefs are independent but fails with dependent beliefs, and show how to resolve this through a decoupling method.

翻译：本文研究关于不确定未来事件的信念 elicitation，其中报告将影响委托人的决策。我们研究了在此情境下可能出现的两个问题：（1）代理人可能对委托人的决策结果有利益关切。我们证明，在内在竞争激励（与代理人自身相关的决策利益）下，真实披露无法保证，且委托人允许报告影响决策的程度、委托人拥有的预算以及机制可被操纵的程度之间存在根本性权衡。此外，我们证明二次计分规则在最小化操纵程度上是 Worst-case 最优的。相反，在竞争激励源于理性贿赂者（希望推动特定决策）的情况下，我们获得了积极结果并设计了真实机制。我们证明，实现这种稳健性所需的预算与代理人报告影响决策程度的平方和成比例。（2）我们研究未来事件仅在决策做出后条件可观测的情境。我们给出了一类机制，当代理人信念独立时能实现真实披露，但在信念依赖时失效，并展示了如何通过解耦方法解决这一问题。