Incentives in Group Decision-Making With Uncertainty and Subjective Beliefs

We address the problem of decision-making in group settings where there is uncertainty and disagreement about the utility that actions will yield. While previous mechanism design work deals with uncertainty by assuming agents are Bayesian with common prior beliefs, we instead take agent subjectivity more seriously, considering individual beliefs as primitives and eschewing any assumptions about their origins. Each individual brings his own private subjective beliefs about each action with respect to social welfare, which a decision-maker aims to maximize. Agents and the decision-maker revise beliefs based on those held by others; motivated by the psychological belief aggregation literature, we adopt a weighted averaging model, where the weight one agent assigns to another's beliefs can be thought of as the agent's "trust" in the other. Each agent—and also the decision-maker—has his own trust level for each other agent. For instance if there are two agents and two actions, with one agent expecting the social welfare of the first action to be 10 and the second to be 8, and the other agent expecting the social welfare of the first action to be 5 and the second to be 8, if the center trusts each agent equally he will prefer the second action. But since heterogeneity of agent (and decision-maker) trust levels can lead to conflicting revised-beliefs about which action is optimal, there is a problem of incentives. In the above example, even assuming a scheme that aligns all agents' incentives towards maximizing social welfare, if the first agent puts all weight on his own opinion and zero weight on the other's he can expect to benefit by overstating his beliefs about the superiority of the first action. The discrepancy between the agent's trust levels and those used by the decision-maker leads to manipulation. We provide a payment mechanism that yields truthful reporting and thus implementation of the decision-maker's desired choice in an ex post equilibrium for arbitrary beliefs and arbitrary trust levels. In other words, we solve the disensus problem that arises when agents (and perhaps the decision-maker) disagree about how to weigh each others' information in aggregating beliefs. The main contribution is to show that efficient choice is possible with strategic agents even when "efficient" is defined subjectively by the decision-maker (according to his particular trust levels) and the foundational assumption of Bayesian reasoning is abandoned. A stubborn weakness of the proposal is that it requires agent trust levels to be a priori known by the decision-maker, while in many practical settings they are likely to be essentially private.