Maximizing Welfare with Incentive-Aware Evaluation Mechanisms
This addresses the problem of welfare maximization in strategic environments for decision-makers in domains such as education and insurance, representing an incremental advance in mechanism design.
The paper tackles the problem of designing evaluation mechanisms for strategic individuals who can modify their features at a cost, aiming to maximize overall welfare in applications like college admission and insurance. It provides theoretical results, including an optimal mechanism for linear settings and a polynomial-time algorithm with a (1/4)-approximation guarantee under smooth distributions.
Motivated by applications such as college admission and insurance rate determination, we propose an evaluation problem where the inputs are controlled by strategic individuals who can modify their features at a cost. A learner can only partially observe the features, and aims to classify individuals with respect to a quality score. The goal is to design an evaluation mechanism that maximizes the overall quality score, i.e., welfare, in the population, taking any strategic updating into account. We further study the algorithmic aspect of finding the welfare maximizing evaluation mechanism under two specific settings in our model. When scores are linear and mechanisms use linear scoring rules on the observable features, we show that the optimal evaluation mechanism is an appropriate projection of the quality score. When mechanisms must use linear thresholds, we design a polynomial time algorithm with a (1/4)-approximation guarantee when the underlying feature distribution is sufficiently smooth and admits an oracle for finding dense regions. We extend our results to settings where the prior distribution is unknown and must be learned from samples.