  In the field of Explainable Artificial Intelligence (XAI), counterfactual
examples explain to a user the predictions of a trained decision model by
indicating the modifications to be made to the instance so as to change its
associated prediction. These counterfactual examples are generally defined as
solutions to an optimization problem whose cost function combines several
criteria that quantify desiderata for a good explanation meeting user needs. A
large variety of such appropriate properties can be considered, as the user
needs are generally unknown and differ from one user to another; their
selection and formalization is difficult. To circumvent this issue, several
approaches propose to generate, rather than a single one, a set of diverse
counterfactual examples to explain a prediction. This paper proposes a review
of the numerous, sometimes conflicting, definitions that have been proposed for
this notion of diversity. It discusses their underlying principles as well as
the hypotheses on the user needs they rely on and proposes to categorize them
along several dimensions (explicit vs implicit, universe in which they are
defined, level at which they apply), leading to the identification of further
research challenges on this topic.
