Belief Elicitation from Agents with Competing Incentives

Abstract

We study the problem of eliciting beliefs about an uncertain future event, where the reported beliefs are used to inform a decision. Unlike the standard model of belief elicitation, in our model the belief-reporting agents (or recommenders) have a vested interest in the decision and may attempt to change the decision by reporting untruthfully. For instance, a climate scientist with ties to construction companies may overstate the risk of an extreme weather event to encourage investment into flood barriers. A mechanism takes reported beliefs, and consists of a decision rule and a payment rule. We quantify the lowest achievable manipulation under any mechanism in terms of the (i) sensitivity of the target decision function, (ii) the size of competing incentives, (iii) the mechanism's budget, and (iv) the number of recommenders. We design a mechanism that achieves these bounds up to log factors for a family of target decision functions. When the competing incentives are not intrinsic but correspond to a bribe from a rational third party, we characterize the size of the mechanism's budget required for there to be no bribe in equilibrium. We illustrate the effectiveness of the adaptive-payment mechanism in a simple loan setting.

Significantly revised with further simulations and examples