Procedurally fair and stable matching

Abstract

We motivate procedural fairness for matching mechanisms and study two procedurally fair and stable mechanisms: employment by lotto (Aldershof et al., 1999) and the random order mechanism (Roth and Vande Vate, 1990, Ma, 1996). For both mechanisms we give various examples of probability distributions on the set of stable matchings and discuss properties that differentiate employment by lotto and the random order mechanism. Finally, we consider an adjustment of the random order mechanism, the equitable random order mechanism, that combines aspects of procedural and "endstate" fairness.

Median Stable Matching for College Admissions

“…Klaus and Klijn (2006) demonstrated for the same example that none of the procedurally fair and stable matching mechanisms they analyzed ever chooses the endstate compromise matching. For notational convenience, in this and the next example we only list acceptable colleges (students) in students' (colleges') preferences.…”

“…In the absence of a clear criterion for what constitutes a fair outcome, Klaus and Klijn (2006) therefore applied Rawls's (1971) principle of 'pure procedural justice' and identified two procedurally fair and stable matching mechanisms. Given Masarani and Gokturk's (1989) negative and Klaus and Klijn's (2006) positive results, it would seem that we could only expect procedural fairness, but not endstate fairness, in combination with stability. However, median stable matchings satisfy various aspects of endstate fairness different from those of Masarani and Gokturk (1989).…”

A computational approach to modeling commodity markets

“…Specifically we analyze the issues pertaining to matching buyers and suppliers in a decentralized or bilateral market. In a simulation setting, it is common to either randomly match the buyers and suppliers or do index based matching to simulate pairing (Atkins et al 2004a;Klaus and Klijn 2006;Roth et al 1990). In the absence of any apriori knowledge, this appears to be the most fair and rational way to create the matches.…”

On the Stable Matchings That Can Be Reached When the Agents Go Marching in One By One

“…Klaus and Klijn [13] argued that while both ROM and EBL do not guarantee end-state fairness (i.e., they may not output the stable matchings of the instance with equal probability), they are procedurally fair because "the sequence of moves for the agents is drawn uniformly at random. "…”