Tråden om Anders Lindberg, Aftonbladet

The plot illustrates four points:

• Within each risk category, the proportion of defendants who reoffend is approximately the same regardless of race; this is Northpointe’s definition of fairness.
• The overall recidivism rate for black defendants is higher than for white defendants (52 percent vs. 39 percent).
• Black defendants are more likely to be classified as medium or high risk (58 percent vs. 33 percent). While Northpointe’s algorithm does not use race directly, many attributes that predict reoffending nonetheless vary by race. For example, black defendants are more likely to have prior arrests, and since prior arrests predict reoffending, the algorithm flags more black defendants as high risk even though it does not use race in the classification.
• Black defendants who don’t reoffend are predicted to be riskier than white defendants who don’t reoffend; this is ProPublica’s criticism of the algorithm.

The key — but often overlooked — point is that the last two disparities in the list above are mathematically guaranteed given the first two observations.

If the recidivism rate for white and black defendants is the same within each risk category, and if black defendants have a higher overall recidivism rate, then a greater share of black defendants will be classified as high risk. And if a greater share of black defendants are classified as high risk, then, as the plot illustrates, a greater share of black defendants who do not reoffend will also be classified as high risk.