Designing Random Allocation Mechanisms: Theory and Applications

Abstract

Randomization is commonplace in everyday resource allocation. We generalize the theory of randomized assignment to accommodate multi-unit allocations and various real-world constraints, such as group-specific quotas ("controlled choice") in school choice and house allocation, and scheduling and curriculum constraints in course allocation. We develop new mechanisms that are ex-ante efficient and fair in these environments, and that incorporate certain non-additive substitutable preferences. We also develop a "utility guarantee" technique that limits ex-post unfairness in random allocations, supplementing the ex-ante fairness promoted by randomization. This can be applied to multi-unit assignment problems and certain two-sided matching problems.

Improving Community Cohesion in School Choice via Correlated-Lottery Implementation

“…More precisely, one would express the original assignment probabilities as a convex combination of such constrained deterministic assignments. This idea has been previously explored in Budish et al (2013). However, by the above argument, one would expect gains in diversity to be small.…”

“…Our approach of defining a mechanism by implementing the marginal assignment probabilities is similar to Budish et al (2013). They study a more general framework and address the issues of group-specific quotas, ex-ante efficiency, ex-post fairness, and implementability of lotteries under general constraints.…”

On Popular Random Assignments

“…One of the most fundamental and ubiquitous problems in microeconomics and operations research is how to assign objects to agents based on their individual preferences (see, e.g., [21,4,5]). In its simplest form, the problem is known as the assignment problem, the house allocation problem, or two-sided matching with one-sided preferences.…”

“…Taking cue from this observation, McCutchen [17] proposed two quantities-the unpopularity margin and the unpopularity factor -to measure the unpopularity of an assignment and defined the notion of a least unpopular assignment, which is guaranteed to exist. 5 However, computing least unpopular assignments turned out to be NP-hard. Alternatively, Kavitha et al [13] suggested the notion of popular random assignments.…”

“…-There are no strategyproof popular random assignment rules if n ≥ 3. 5 The unpopularity margin of a matching is the maximum majority difference by which it is dominated by any other matching. The unpopularity factor of a matching is the maximum factor by which it is dominated by any other matching.…”