A conditional match rate anomaly and ranking pressure in residency matching programs

In the medical residency matching markets of the U.S. and Japan, we observe that an applicant's probability of matching with their first-listed program is disproportionately higher than that of matching with their second-listed program, given that they were rejected by the first. In contrast, the conditional probabilities of matching with lower-ranked programs are markedly lower and remain relatively stable. Furthermore, several experts have noted that participating programs sometimes exert pressure on applicants to manipulate the order of their rank-order lists. In this study, we show that this pressure can account for the observed probability pattern, considering the verifiability of being ranked first on the list. Using empirical data, we identify the prevalence of ranking pressure and quantify its impact on rank-order list changes and welfare under a simplified acceptance and pressure process. Additionally, we explore the implementation of a random permutation of the submitted rank-order list as a measure to counteract list reordering due to pressure. Our analysis shows that the benefits of this intervention outweigh the associated efficiency losses.