They correctly note the existence of a tradeoff, but I don't find their statement of it very clear. Ideally, a model would be fair in the senses that:
1. In aggregate over any nationality, people face the same probability of a false positive.
2. Two people who are identical except for their nationality face the same probability of a false positive.
In general, it's impossible to achieve both properties. If the output and at least one other input correlate with nationality, then a model that ignores nationality fails (1). We can add back nationality and reweight to fix that, but then it fails (2).
This tradeoff is most frequently discussed in the context of statistical models, since those make that explicit. It applies to any process for deciding though, including human decisions.
1. In aggregate over any nationality, people face the same probability of a false positive.
2. Two people who are identical except for their nationality face the same probability of a false positive.
In general, it's impossible to achieve both properties. If the output and at least one other input correlate with nationality, then a model that ignores nationality fails (1). We can add back nationality and reweight to fix that, but then it fails (2).
This tradeoff is most frequently discussed in the context of statistical models, since those make that explicit. It applies to any process for deciding though, including human decisions.