  The most popular methods for measuring importance of the variables in a black
box prediction algorithm make use of synthetic inputs that combine predictor
variables from multiple subjects. These inputs can be unlikely, physically
impossible, or even logically impossible. As a result, the predictions for such
cases can be based on data very unlike any the black box was trained on. We
think that users cannot trust an explanation of the decision of a prediction
algorithm when the explanation uses such values. Instead we advocate a method
called Cohort Shapley that is grounded in economic game theory and unlike most
other game theoretic methods, it uses only actually observed data to quantify
variable importance. Cohort Shapley works by narrowing the cohort of subjects
judged to be similar to a target subject on one or more features. We illustrate
it on an algorithmic fairness problem where it is essential to attribute
importance to protected variables that the model was not trained on.
