In their paper Reducing Leximin Fairness to Utilitarian Optimization, Eden Hartman, Yonatan Aumann, Avinatan Hassidim and Erel Segal-Halevi present a scheme for addressing social choice problems. In this interview, Eden tells us more about such problems, the team's methodology, and why this is such a fascinating and challenging area for study. The paper looks at social choice problems -- situations where a group of people (called agents) must make a decision that affects everyone. For example, imagine we need to decide how to divide an inheritance among several heirs. Each agent has their own preferences over the possible outcomes, and the goal is to choose the outcome that is "best" for society as a whole.

Machine learning is increasingly used to select which individuals receive limited-resource interventions in domains such as human services, education, development, and more. However, it is often not apparent what the right quantity is for models to predict. In particular, policymakers rarely have access to data from a randomized controlled trial (RCT) that would enable accurate estimates of treatment effects -- which individuals would benefit more from the intervention. Observational data is more likely to be available, creating a substantial risk of bias in treatment effect estimates. Practitioners instead commonly use a technique termed "risk-based targeting" where the model is just used to predict each individual's status quo outcome (an easier, non-causal task). Those with higher predicted risk are offered treatment. There is currently almost no empirical evidence to inform which choices lead to the most effect machine learning-informed targeting strategies in social domains. In this work, we use data from 5 real-world RCTs in a variety of domains to empirically assess such choices. We find that risk-based targeting is almost always inferior to targeting based on even biased estimates of treatment effects. Moreover, these results hold even when the policymaker has strong normative preferences for assisting higher-risk individuals. Our results imply that, despite the widespread use of risk prediction models in applied settings, practitioners may be better off incorporating even weak evidence about heterogeneous causal effects to inform targeting.

Participatory budgeting (PB) is a voting paradigm for distributing a divisible resource, usually called a budget, among a set of projects by aggregating the preferences of individuals over these projects. It is implemented quite extensively for purposes such as government allocating funds to public projects and funding agencies selecting research proposals to support. This PhD dissertation studies the welfare-related and fairness-related objectives for different PB models. Our contribution lies in proposing and exploring novel PB rules that maximize welfare and promote fairness, as well as, in introducing and investigating a range of novel utility notions, axiomatic properties, and fairness notions, effectively filling the gaps in the existing literature for each PB model. The thesis is divided into two main parts, the first focusing on dichotomous and the second focusing on ordinal preferences. Each part considers two cases: (i) the cost of each project is restricted to a single value and partial funding is not permitted and (ii) the cost of each project is flexible and may assume multiple values.

Two prominent objectives in social choice are utilitarian - maximizing the sum of agents' utilities, and leximin - maximizing the smallest agent's utility, then the second-smallest, etc. Utilitarianism is typically computationally easier to attain but is generally viewed as less fair. This paper presents a general reduction scheme that, given a utilitarian solver, produces a distribution over outcomes that is leximin in expectation. Importantly, the scheme is robust in the sense that, given an approximate utilitarian solver, it produces an outcome that is approximately-leximin (in expectation) - with the same approximation factor. We apply our scheme to several social choice problems: stochastic allocations of indivisible goods, giveaway lotteries, and fair lotteries for participatory budgeting.

In the context of fair division, the concept of price of fairness has been introduced to quantify the loss of welfare when we have to satisfy some fairness condition. In other words, it is the price we have to pay to guarantee fairness. Various settings of fair division have been considered previously; we extend to the setting of indivisible goods by using egalitarian welfare as the welfare measure, instead of the commonly used utilitarian welfare. We provide lower and upper bounds for various fairness and efficiency conditions such as envy-freeness up to one good (EF1) and maximum Nash welfare (MNW).

We consider the obnoxious facility location problem (in which agents prefer the facility location to be far from them) and propose a hierarchy of distance-based proportional fairness concepts for the problem. These fairness axioms ensure that groups of agents at the same location are guaranteed to be a distance from the facility proportional to their group size. We consider deterministic and randomized mechanisms, and compute tight bounds on the price of proportional fairness. In the deterministic setting, not only are our proportional fairness axioms incompatible with strategyproofness, the Nash equilibria may not guarantee welfare within a constant factor of the optimal welfare. On the other hand, in the randomized setting, we identify proportionally fair and strategyproof mechanisms that give an expected welfare within a constant factor of the optimal welfare.

Mechanisms for aggregating the preferences of agents in elections need to balance many different considerations, including efficiency, information elicited from agents, and manipulability. We consider the utilitarian social welfare of mechanisms for preference aggregation, measured by the distortion. We show that for a particular input format called threshold approval voting, where each agent is presented with an independently chosen threshold, there is a mechanism with nearly optimal distortion when the number of voters is large. Threshold mechanisms are potentially manipulable, but place a low informational burden on voters. We then consider truthful mechanisms. For the widely-studied class of ordinal mechanisms which elicit the rankings of candidates from each agent, we show that truthfulness essentially imposes no additional loss of welfare. We give truthful mechanisms with distortion O(√m log m) for k-winner elections, and distortion O(√m log m) when candidates have arbitrary costs, in elections with m candidates. These nearly match known lower bounds for ordinal mechanisms that ignore the strategic behavior. We further tighten these lower bounds and show that for truthful mechanisms our first upper bound is tight. Lastly, when agents decide between two candidates, we give tight bounds on the distortion for truthful mechanisms.

In cooperation with a social startup, FoodBank Local, we have been helping Food Bank Australia develop technologies We study an online model of fair division designed to operate more effectively. So far, this has involved building to capture features of a real world charity problem.

We consider the computational complexity of computing welfare maximizing partitions for fractional hedonic games — a natural class of coalition formation games that can be succinctly represented by a graph. For such games, welfare maximizing partitions constitute desirable ways to cluster the vertices of the graph. We present both intractability results and approximation algorithms for computing welfare maximizing partitions.