Before revision:  In this work  we formally and empirically study individual fairness and its mathematical formalization as robustness for counterfactual explanations as a prominent instance of contrasting explanations. In addition , we propose to use plausible counterfactuals instead of closest counterfactuals for improving the individual fairness of counterfactual explanations.
After revision:  In this work we formally and empirically study the robustness of counterfactual explanations in general, as well as under different models and different kinds of perturbations. Furthermore , we propose to use plausible counterfactuals instead of closest counterfactuals for improving the individual fairness of counterfactual explanations.