Introduction to the Special Issue on EC?15
As part of a collaboration with a major California school district, we study the problem of fairly allocating unused classrooms in public schools to charter schools. Our approach revolves around the randomized leximin mechanism. We extend previous work to the classroom allocation setting, showing that the leximin mechanism is proportional, envy-free, efficient, and group strategyproof. We also prove that the leximin mechanism provides a (worst-case) 4-approximation to the maximum number of classrooms that can possibly be allocated. Our experiments, which are based on real data, show that a nontrivial implementation of the leximin mechanism scales gracefully in terms of running time (even though the problem is intractable in theory), and performs extremely well with respect to a number of efficiency objectives. We take great pains to establish the practicability of our approach, and discuss issues related to its deployment.
We consider a setting where n buyers, with combinatorial preferences over m items, and a seller, running a priority-based allocation mechanism, repeatedly interact. Our goal, from observing limited information about the results of these interactions, is to reconstruct both the preferences of the buyers and the mechanism of the seller. More specifically, we consider an online setting where at each stage, a subset of the buyers arrive and are allocated items, according to some unknown priority that the seller has among the buyers. Our learning algorithm observes only which buyers arrive and the allocation produced (or some function of the allocation, such as just which buyers received positive utility and which did not), and its goal is to predict the outcome for future subsets of buyers. For this task, the learning algorithm needs to reconstruct both the priority among the buyers and the preferences of each buyer. We derive mistake bound algorithms for additive, unit-demand and single minded buyers. We also consider the case where buyers' utilities for a fixed bundle can change between stages due to different (observed) prices. Our algorithms are efficient both in computation time and in the maximum number of mistakes (both polynomial in the number of buyers and items).
Team performance is a ubiquitous area of inquiry in the social sciences, and it motivates the problem of team
selection choosing the members of a team for maximum performance. Influential work of Hong and Page
has argued that testing individuals in isolation and then assembling the highest-scoring ones into a team is
not an effective method for team selection. For a broad class of performance measures, based on the expected
maximum of random variables representing individual candidates, we show that tests directly measuring
individual performance are indeed ineffective, but that a more subtle family of tests used in isolation can
provide a constant-factor approximation for team performance. These new tests measure the "potential" of
individuals, in a precise sense, rather than performance; to our knowledge they represent the first time
that individual tests have been shown to produce near-optimal teams for a non-trivial team performance
measure. We also show families of subdmodular and supermodular team performance functions for which
no test applied to individuals can produce near-optimal teams, and discuss implications for submodular
maximization via hill-climbing.
Border's theorem gives an intuitive linear characterization of the feasible interim allocation rules of a Bayesian single-item environment, and it has several applications in economic and algorithmic mechanism design. All known generalizations of Border's theorem either restrict attention to relatively simple settings, or resort to approximation. This paper identifies a complexity-theoretic barrier that indicates, assuming standard complexity class separations, that Border's theorem cannot be extended significantly beyond the state-of-the-art. We also identify a surprisingly tight connection between Myerson's optimal auction theory, when applied to public project settings, and some fundamental results in the analysis of Boolean functions.