  Recently, a groundswell of research has identified the use of counterfactual
explanations as a potentially significant solution to the Explainable AI (XAI)
problem. It is argued that (a) technically, these counterfactual cases can be
generated by permuting problem-features until a class change is found, (b)
psychologically, they are much more causally informative than factual
explanations, (c) legally, they are GDPR-compliant. However, there are issues
around the finding of good counterfactuals using current techniques (e.g.
sparsity and plausibility). We show that many commonly-used datasets appear to
have few good counterfactuals for explanation purposes. So, we propose a new
case based approach for generating counterfactuals using novel ideas about the
counterfactual potential and explanatory coverage of a case-base. The new
technique reuses patterns of good counterfactuals, present in a case-base, to
generate analogous counterfactuals that can explain new problems and their
solutions. Several experiments show how this technique can improve the
counterfactual potential and explanatory coverage of case-bases that were
previously found wanting.
