  Counterfactual fairness requires that a person would have been classified in
the same way by an AI or other algorithmic system if they had a different
protected class, such as a different race or gender. This is an intuitive
standard, as reflected in the U.S. legal system, but its use is limited because
counterfactuals cannot be directly observed in real-world data. On the other
hand, group fairness metrics (e.g., demographic parity or equalized odds) are
less intuitive but more readily observed. In this paper, we use $\textit{causal
context}$ to bridge the gaps between counterfactual fairness, robust
prediction, and group fairness. First, we motivate counterfactual fairness by
showing that there is not necessarily a fundamental trade-off between fairness
and accuracy because, under plausible conditions, the counterfactually fair
predictor is in fact accuracy-optimal in an unbiased target distribution.
Second, we develop a correspondence between the causal graph of the
data-generating process and which, if any, group fairness metrics are
equivalent to counterfactual fairness. Third, we show that in three common
fairness contexts$\unicode{x2013}$measurement error, selection on label, and
selection on predictors$\unicode{x2013}$counterfactual fairness is equivalent
to demographic parity, equalized odds, and calibration, respectively.
Counterfactual fairness can sometimes be tested by measuring relatively simple
group fairness metrics.
