Utilitarian Distortion with Predictions
Aris Filos-Ratsikas, Georgios Kalantzis, Alexandros A. Voudouris
TL;DR
This work studies the distortion of deterministic, learning-augmented mechanisms for two core social choice problems—single-winner voting and one-sided matching—under ordinal preferences augmented with predictions about cardinal values. It develops tight consistency–robustness tradeoffs, showing that in voting, sublinear consistency with bounded robustness is unattainable when predictions are weak, but a tunable line (consistency $O(\lambda m)$, robustness $O(m^3/\lambda)$) is achievable using per-agent first-choice predictions; in one-sided matching, full valuation predictions yield optimal consistency, while $k$-truncated predictions offer a linear improvement in consistency with robust $O(n^2)$ guarantees, both supported by matching lower bounds. The results delineate how partial and full cardinal predictions influence worst-case performance and provide error-aware distortion analyses, advancing the understanding of mechanism design under imperfect predictive information. Overall, the paper clarifies when and how predictions improve utilitarian outcomes and establishes tight limits guiding the use of predictions in social choice.
Abstract
We study the utilitarian distortion of social choice mechanisms under the recently proposed learning-augmented framework where some (possibly unreliable) predicted information about the preferences of the agents is given as input. In particular, we consider two fundamental social choice problems: single-winner voting and one-sided matching. In these settings, the ordinal preferences of the agents over the alternatives (either candidates or items) is known, and some prediction about their underlying cardinal values is also provided. The goal is to leverage the prediction to achieve improved distortion guarantees when it is accurate, while simultaneously still achieving reasonable worst-case bounds when it is not. This leads to the notions of consistency and robustness, and the quest to achieve the best possible tradeoffs between the two. We show tight tradeoffs between the consistency and robustness of ordinal mechanisms for single-winner voting and one-sided matching, for different levels of information provided by as prediction.