A New Solution to the Random Assignment Problem

On Popular Random Assignments

“…However, it can be easily shown that the assignment returned by any of these rules may not be popular. Perhaps closest to our work are the papers by Kavitha et al [13], who introduced popular random assignments, and Bogomolnaia and Moulin [4], who outlined a systematic way of studying the properties of random assignments and random assignment rules. In particular, Bogomolnaia and Moulin [4] popularized the use of first-order stochastic dominance to formalize various notions of envy-freeness, efficiency, and strategyproofness that we also consider in this paper.…”

“…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.…”

“…An important assumption in this setting is that monetary transfers between the agents are not permitted. 4 The assignment problem has numerous applications in a variety of settings such the assignment of dormitories to students, jobs to applicants, rooms to housemates, processor time slots to jobs, parking spaces to employees, offices to workers, kidneys to patients, school seats to student applicants, etc. Clearly, deterministic assignments may fail to satisfy even extremely mild fairness criteria such as equal treatment of equals.…”

“…Random assignment rules have received enormous attention in recent years. Most notable among these rules are random serial dictatorship (RSD) (see e.g., [4,16]) and the probabilistic serial rule (PS) [4]. Each of these rules has its own merits.…”

The Computational Complexity of Random Serial Dictatorship

“…1 RSD retains the important properties of ex post efficiency and strategyproofness and is well-established in the context of random assignment [see e.g., 12,1,5,8].…”