Correlation of Rankings in Matching Markets
Résumé
We study the role of correlation in matching, where multiple decision-makers are simultaneously facing selection problems from the same pool of candidates. We propose a model where decision-makers have varying information on candidates from different socio-demographic groups
when evaluating and ranking them, thus leading to varying correlation of a candidate’s priority scores. Such differential correlation arises, for example, when cost of information acquisition, decision-maker preferences, or prevalence of selection criteria vary across socio-demographic
groups. We show that lower correlation for one of the groups worsens the outcome for all groups, thus leading to efficiency loss. Moreover, the proportion of students from a given group remaining unmatched is increasing in its own correlation level. This implies that it is advantageous to
belong to the low-correlation group. Finally, we extend results from the tie-breaking literature to multiple priority classes and intermediate levels of correlation. Overall, our results point to a previously overlooked systemic source of group inequalities in school, university, and job
admissions.
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