Randomness and Fairness in Two-Sided Matching with Limited Interviews

Authors Hedyeh Beyhaghi, Éva Tardos

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Hedyeh Beyhaghi
  • Toyota Technological Institute at Chicago, IL, USA
Éva Tardos
  • Department of Computer Science, Cornell University, Ithaca, NY, USA


The authors are thankful to Mark Braverman and Robert Kleinberg for fruitful discussions.

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Hedyeh Beyhaghi and Éva Tardos. Randomness and Fairness in Two-Sided Matching with Limited Interviews. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 74:1-74:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We study the outcome in a matching market where both sides have limited ability to consider options. For example, in the national residency matching program, doctors are limited to apply to a small set of hospitals, and hospitals are limited by the time required to interview candidates. Our main findings are the following: (1) In markets where jobs can only consider a limited number of candidates for interview, it increases the size of the resulting matching if the system has a limit on the number of applications a candidate can send. (2) The fair system of all applicants being allowed to apply to the exact same number of positions maximizes the expected size of the matching. More particularly, starting from an integer k as the number of applications, the matching size decreases as a few applicants are allowed to apply to one additional position (and then increases again as they are all allowed to apply to k+1). Although it seems natural to expect that the size of the matching would be a monotone increasing and concave function in the number of applications, our results show that neither is true. These results hold even in a market where a-priori all jobs and all candidates are equally likely to be good, and the judgments of different employers and candidates are independent. Our main technical contribution is computing the expected size of the matching found via the deferred acceptance algorithm as a function of the number of interviews and applications in a market where preferences are uniform and independent. Through simulations we confirm that these findings extend to markets where rankings become correlated after the interviews.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic mechanism design
  • Matching with Short Lists
  • Stable Matching
  • Balls in Bins Problem


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