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.

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