> We find that people who submit multiple applications to positions screened by the same algorithmic hiring vendor are more likely to be rejected from every position to which they apply than would be true if the companies made decisions statistically independently from one another. Ten percent of applicants who submit four applications are rejected from all the places to which they apply.

> Our research also found that this pattern does not appear to be the case in other circumstances. We analyzed data from the largest prior study of hiring decisions, which sent 83,000 applications to 108 Fortune 500 firms during the same time period as our study and did not focus on whether AI was used to make decisions. We found that the rate at which applicants were rejected from every firm they applied to in this data was no higher than what you’d expect if each company decided independently of the others.

It sounds like this study was using real-world applicants, and the other study they're comparing against was using synthetic applicants.

Consider the chance of being accepted as being composed of signal+bias+noise. Noise is random. Signal is a per-applicant value, and what's meant to be measured. Bias is a per-group value, and an artifact of the measuring process.

If acceptance/rejection is independent between positions applied for (as in the synthetic applicant study), that suggests that it's random or composed entirely of noise; ie there is no signal; ie the applicants are all equally qualified.

If acceptance/rejection is correlated, that means there is some nonzero amount of (signal+bias). But real-world applicants are not all identical, so there should be some amount of signal. So you can't just assume zero signal in order to infer that there must be bias.