David Shmoys

Nikhil Garg, Wes Gurnee, David Rothschild et al.

Every representative democracy must specify a mechanism under which voters choose their representatives. The most common mechanism in the United States -- Winner takes all single-member districts -- both enables substantial partisan gerrymandering and constrains `fair' redistricting, preventing proportional representation in legislatures. We study the design of \textit{multi-member districts (MMDs)}, in which each district elects multiple representatives, potentially through a non-Winner takes all voting rule. We carry out large-scale empirical analyses for the U.S. House of Representatives under MMDs with different social choice functions, under algorithmically generated maps optimized for either partisan benefit or proportionality. Doing so requires efficiently incorporating predicted partisan outcomes -- under various multi-winner social choice functions -- into an algorithm that optimizes over an ensemble of maps. We find that with three-member districts using Single Transferable Vote, fairness-minded independent commissions would be able to achieve proportional outcomes in every state up to rounding, \textit{and} advantage-seeking partisans would have their power to gerrymander significantly curtailed. Simultaneously, such districts would preserve geographic cohesion. Through simulation, we find that the insights are robust to cross-party voting. In the process, we advance a rich research agenda at the intersection of social choice and computational gerrymandering.

Woo-Hyung Cho, Shane Henderson, David Shmoys

There is significant interest in deploying machine learning algorithms for diagnostic radiology, as modern learning techniques have made it possible to detect abnormalities in medical images within minutes. While machine-assisted diagnoses cannot yet reliably replace human reviews of images by a radiologist, they could inform prioritization rules for determining the order by which to review patient cases so that patients with time-sensitive conditions could benefit from early intervention. We study this scenario by formulating it as a learning-augmented online scheduling problem. We are given information about each arriving patient's urgency level in advance, but these predictions are inevitably error-prone. In this formulation, we face the challenges of decision making under imperfect information, and of responding dynamically to prediction error as we observe better data in real-time. We propose a simple online policy and show that this policy is in fact the best possible in certain stylized settings. We also demonstrate that our policy achieves the two desiderata of online algorithms with predictions: consistency (performance improvement with prediction accuracy) and robustness (protection against the worst case). We complement our theoretical findings with empirical evaluations of the policy under settings that more accurately reflect clinical scenarios in the real world.

Claire Chang, Arin Khare, David Shmoys

The seminal work of Roth, Sönmez, & Ünver shows that the Edmonds-Gallai structure theorem for non-bipartite matching can be leveraged to yield a randomized algorithm to match patient-donor pairs in kidney exchange with extraordinarily strong properties. This breakthrough led to randomized polynomial-time algorithms to find a maximum-cardinality matching maximizing individual fairness objectives--measured by the probability that nodes are matched--such as Nash social welfare. But the exchanges allowed in practice go beyond cardinality matching, generalizing to weighted variants and allowing structures such as paths and 3-cycles. We show that strongly polynomial algorithms guaranteeing the same fairness properties can be obtained in weighted settings for matching and 2-paths. While even maximum cardinality coverage with cycles and paths of length at least three is NP-hard, we provide a general result showing that any optimization subroutine (for whichever structure is allowed) can be bootstrapped using a polynomial number of calls to yield a mechanism that has analogous fairness properties to those obtained for matching. We complement these theoretical results with computational results, both on well-studied synthetic data-sets and on samples drawn from real data, that demonstrate the striking advantages of adding fairness considerations to more general kidney-exchange mechanisms.