Where does matching collide?

A pairing of members from two sides of a market so that no unmatched pair would both rather have each other than their assigned partners: such a pairing is called stable, and it can always be found by a step-by-step procedure in which one side proposes and the other tentatively holds its best offer so far. Gale and Shapley's 1962 paper College Admissions and the Stability of Marriage proved that a stable pairing always exists and gave the deferred-acceptance procedure that produces one. The referent here is a rule for assigning people or goods across a two-sided market, judged by whether any pair has an incentive to break away, and it is not a statistical step for balancing groups, a rate of behaviour, or a tendency to pair with a similar-looking partner.[1]

Unit

One assignment of the two sides to each other, called stable when no pair prefers each other to their match

Recovery means

Not applicable

Measured by

Checked by searching for blocking pairs, and computed by the deferred-acceptance procedure from each side's ranked preferences

A method for estimating a cause-and-effect relationship from observational data by pairing each treated unit with one or more untreated units that look alike on measured background characteristics, so the comparison approximates a controlled experiment. Rosenbaum and Rubin's 1983 paper The central role of the propensity score in observational studies for causal effects showed that units can be paired on a single summary number, the estimated probability of receiving the treatment, to balance many characteristics at once. Here matching is a data-analysis step for removing confounding before outcomes are compared, and it is not a market rule for stable assignment, a rate of responding, or an attraction between similar people.[2]

Unit

One treated case paired with one or more comparison cases that share similar measured traits

Recovery means

Not applicable

Measured by

Operationalised by nearest-neighbour or calliper pairing on the propensity score, then checking that the paired groups are balanced

A quantitative regularity in choice: when an animal or person can respond on two or more options that pay off at different rates, the share of responses put into each option tends to equal the share of reward it delivers. Herrnstein's 1961 study Relative and absolute strength of response as a function of frequency of reinforcement reported this proportional relation, later called the matching law, from pigeons responding on concurrent schedules of reinforcement. The referent is an observed pattern of how behaviour is spread across choices, described as a rate, and it is not a rule for pairing a market, a statistical balancing step, or a resemblance between romantic partners.[3]

Unit

The proportion of responses on an option, set against the proportion of reward that option yields

Recovery means

Not applicable

Measured by

Measured on concurrent reinforcement schedules by recording the response rate and the reward rate for each option

A prediction from social psychology that people tend to form couples with partners at roughly their own level of physical attractiveness, rather than always pursuing the most attractive partner available. Berscheid, Dion, Walster, and Walster's 1971 study Physical attractiveness and dating choice: A test of the matching hypothesis tested this idea. Here matching names a similarity between two people's traits that predicts who ends up paired with whom, and it is not a market rule for stable assignment, a statistical technique for balancing groups, or a proportional law of how responses are allocated.[4]

Unit

A couple, described by how close the two partners are in rated attractiveness

Recovery means

Not applicable

Measured by

Assessed by rating each partner's attractiveness independently and testing whether paired partners' ratings are more alike than chance would give