Allocation Mechanisms without Reduction

We study a simple variant of the house allocation problem (one-sided matching). We demonstrate that agents with recursive preferences may systematically prefer one allocation mechanism to the other, even among mechanisms that are considered to be the same in standard models, in the sense that they induce the same probability distribution over successful matchings. Using this, we propose a new priority groups mechanism and provide conditions under which it is preferred to two popular mechanisms, random top cycle and random serial dictatorship. (JEL C78, D44, D82)

Order Symmetry: A New Fairness Criterion for Assignment Mechanisms

We introduce a new fairness criterion, order symmetry, for assignment mechanisms that match n objects to n agents with ordinal preferences over the objects. An assignment mechanism is order symmetric with respect to some probability measure over preference profiles if every agent is equally likely to receive their favorite object, every agent is equally likely to receive their second favorite, and so on. When associated with a sufficiently symmetric probability measure, order symmetry is a relaxation of anonymity that, crucially, can be satisfied by discrete assignment mechanisms. Furthermore, it can be achieved without sacrificing other desirable axiomatic properties satisfied by existing mechanisms. In particular, we show that it can be achieved in conjunction with strategyproofness and ex post efficiency via the top trading cycles mechanism (but not serial dictatorship). We additionally design a novel mechanism that is both order symmetric and ordinally efficient. The practical utility of order symmetry is substantiated by simulations on Impartial Culture and Mallows-distributed preferences for four common assignment mechanisms.

Pure-Chance Jobs versus a Labor Market: The Impact on Careers of a Random Serial Dictatorship for First Job Seekers

Do workers' first jobs affect their careers? Do such first-job effects (FJEs) vary across worker types? If so, can policy improve upon a “free” labor market by altering initial worker-employer matches? We study these questions using Norway's pre-2013 system of assigning doctors to their first job–residencies–through a random serial dictatorship. This generated individual-level variation in workers' choice sets over employers, which we use as instrumental variables to estimate FJEs. We then decompose workers' preferences over first employers into FJEs-on-earnings and employer “amenity value” components, showing how matches and worker welfare changed in the post-2013 decentralized labor market.

School Choice in Guangzhou: Why High-Scoring Students Are Protected?

Each year, millions of middle school graduates in China take a standardized test and compete for high school positions. Unlike other cities, Guangzhou still uses the immediate acceptance mechanism but implements a policy that students in the high-scoring group receive their allocations before those in the low-scoring group. In this paper, we study a class of the Guangzhou mechanisms, including the immediate acceptance (IA) and the serial dictatorship (SD) mechanism. We show that, if a collection of groups is refined by splitting its groups into a larger number of smaller subgroups, then the Guangzhou mechanism will perform more stably and less manipulable than before. This result provides a tool for policy makers to improve the allocation outcome of the IA mechanism under homogeneous priorities and justifies the use of a high-scoring student protection policy in Guangzhou’s high school admission.

Serial dictatorship mechanisms with reservation prices: heterogeneous objects

We adapt a set of mechanisms introduced by Klaus and Nichifor (Econ Theory 70:665–684, 2020), serial dictatorship mechanisms with (individual) reservation prices, to the allocation of heterogeneous indivisible objects, e.g., specialist clinic appointments. We show how the characterization of serial dictatorship mechanisms with reservation prices for homogeneous indivisible objects (Klaus and Nichifor 2020, Theorem 1) can be adapted to the allocation of heterogeneous indivisible objects by adding neutrality: mechanism $$\varphi $$ φ satisfies minimal tradability, individual rationality, strategy-proofness, consistency, independence of unallocated objects, neutrality, and non wasteful tie-breaking if and only if there exists a reservation price vector r and a priority ordering $$\succ $$ ≻ such that $$\varphi $$ φ is a serial dictatorship mechanism with reservation prices based on r and $$\succ $$ ≻ .

Efficiency, Justified Envy, and Incentives in Priority-Based Matching

Top trading cycles (TTC) is Pareto efficient and strategy-proof in priority-based matching, but so are other mechanisms including serial dictatorship. We show that TTC minimizes justified envy among all Pareto-efficient and strategy-proof mechanisms in one-to-one matching. In many-to-one matching, TTC admits less justified envy than serial dictatorship in an average sense. Empirical evidence from New Orleans OneApp and Boston Public Schools shows that TTC has significantly less justified envy than serial dictatorship. (JEL C78, D61)

Keeping Your Friends Close: Land Allocation with Friends

We examine the problem of assigning plots of land to prospective buyers who prefer living next to their friends. In this setting, each agent's utility depends on the plot she receives and the identities of the agents who receive the adjacent plots. We are interested in mechanisms without money that guarantee truthful reporting of both land values and friendships, as well as Pareto optimality and computational efficiency. We explore several modifications of the Random Serial Dictatorship (RSD) mechanism, and identify one that performs well according to these criteria, We also study the expected social welfare of the assignments produced by our mechanisms when agents' values for the land plots are binary; it turns out that we can achieve good approximations to the optimal social welfare, but only if the agents value the friendships highly.

College Assignment Problems Under Constrained Choice, Private Preferences, and Risk Aversion

Many countries use a centralized admission system for admitting students to universities. Typically, each student reports a ranking of his preferred colleges to a planner, and the planner allocates students to colleges according to the rules of a predefined mechanism. A recurrent feature in these admission systems is that students are constrained in the number of colleges that they can rank. In addition, students normally have private preferences over colleges and are risk-averse. Hence, they face a strategic decision under uncertainty to determine their optimal reports to the planner. We characterize students’ equilibrium behavior when the planner uses a Serial Dictatorship (SD) mechanism by solving an endogenous decision problem. We show that if students are sufficiently risk-averse, their optimal strategy is to truthfully report the “portfolio of colleges” with the highest probabilities of being available. We then analyze the welfare implications of constraining student choice by stressing the differences between the so-called consideration and conditional-allocation effects.

Random Serial Dictatorship: The One and Only

Fix a Pareto-optimal, strategy-proof, and nonbossy deterministic matching mechanism and define a random matching mechanism by assigning agents to the roles in the mechanism via a uniform lottery. Given a profile of preferences, the lottery over outcomes that arises under the random matching mechanism is identical to the lottery that arises under random serial dictatorship, where the order of dictators is uniformly distributed. This result extends the celebrated equivalence between the core from random endowments and random serial dictatorship to the grand set of all Pareto-optimal, strategy-proof, and nonbossy matching mechanisms.