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Priya wanted the hiring tool to be fair in two ways at the same time . She wanted each group of applicants to be selected at the same rate . She also wanted the tool to make the same kinds of mistakes in each group : the same share of suitable people rejected , and the same share of unsuitable people accepted . Both demands sounded like plain justice . She asked the engineer to satisfy both . The engineer could not , and the reason was not a missing line of code . The records the model had learned from did not show the same share of suitable applicants in every group . When those base rates differ , the two demands pull apart . Equal selection rates are one definition of fairness , often called demographic parity . Matching those mistake rates across groups , the same true positive rate and the same false positive rate , is another , often called equalized odds . If the base rates differ , a model cannot meet both definitions at once , except in a trivial case : a model that does not really separate suitable applicants from unsuitable ones . Priya had asked for two guarantees that cannot be kept together . That conflict does not make the tool innocent , and it does not turn every gap into a law of mathematics . A model trained on old hiring records can repeat who was hired before . If those records left some people out , the model can treat that absence as a pattern . A choice of which details to feed the model can do the same work when one included detail tracks a trait the team left out . None of this requires a designer who meant to discriminate . It does require someone to look . Looking is harder when the model will not show , in plain steps , how a score was built . A deep network can turn an application into a number without a short reason a person can check . Tools that try to explain a score can help . They can also mislead , if the story they tell is simpler than the calculation , or if they point at a detail that did not drive the result . Priya could ask for a reason . She could not treat the reason on the screen as the cause . She left the meeting with the choice the mathematics had forced into the open . The team could hold selection rates equal , or it could hold those mistake rates equal , or it could argue for some other rule and say so . It could not keep the first two rules at once while the base rates differed . Calling the tool fair , without saying which rule the word meant , was how the conflict had stayed hidden .
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