Strategic incentives when implementing Dorfman testing with assortative matching

The Dorfman pooled testing scheme is a process in which individual specimens (e.g., blood, urine, swabs, etc.) are pooled and tested together; if the merged sample tests positive for infection, each specimen from the pool is tested individually. Through this procedure, laboratories can reduce the expected number of tests required to screen a population. The literature has often advocated in favor of using ordered partitions to screen the population, i.e., of pooling subjects with similar probability of infection together, as doing so simultaneously minimizes the expected number of tests, the expected number of false negatives, and the expected number of false positive classifications, provided that certain technical conditions hold. One potential limitation of using ordered partitions, however, is that they may incentivize some subjects to misreport their types to the tester. Indeed, if subjects wish to avoid being detected as infected, ordered partitions would incentivize them to falsely claim that they have a low probability of infection (assuming that pooled testing is subject to dilution effects). These incentives would disappear if subjects were matched randomly, regardless of their probability of infection. In this article, we derive conditions under which ordered partitions outperform matching subjects randomly, despite these incentives.