Persuasion, Delegation, and Private Information in Algorithm-Assisted Decisions
Ruqing Xu
TL;DR
The paper develops a Bayesian persuasion–delegation framework where a principal designs a public signal about a binary state and decides whether to delegate to a privately informed, potentially misaligned agent. It shows delegation is strictly valuable only when the agent could induce the principal to choose the same action the principal would choose given the agent's information, and that the most informative algorithm is not always optimal. The analysis reveals that optimal information design often emphasizes one-sided information and may pin one posterior at a threshold $\rho$, depending on the prior, with naive policies (like always delegating or maximizing accuracy) potentially worsening outcomes. These results provide a theoretical lens to explain underperformance in human–machine collaborations and offer guidance for designing decision aids that account for strategic information use and preference misalignment.
Abstract
A principal designs an algorithm that generates a publicly observable prediction of a binary state. She must decide whether to act directly based on the prediction or to delegate the decision to an agent with private information but potential misalignment. We study the optimal design of the prediction algorithm and the delegation rule in such environments. Three key findings emerge: (1) Delegation is optimal if and only if the principal would make the same binary decision as the agent had she observed the agent's information. (2) Providing the most informative algorithm may be suboptimal even if the principal can act on the algorithm's prediction. Instead, the optimal algorithm may provide more information about one state and restrict information about the other. (3) Well-intentioned policies aiming to provide more information, such as keeping a "human-in-the-loop" or requiring maximal prediction accuracy, could strictly worsen decision quality compared to systems with no human or no algorithmic assistance. These findings predict the underperformance of human-machine collaborations if no measures are taken to mitigate common preference misalignment between algorithms and human decision-makers.