How much informative is your XAI? A decision-making assessment task to objectively measure the goodness of explanations

There is an increasing consensus about the effectiveness of user-centred approaches in the explainable artificial intelligence (XAI) field. Indeed, the number and complexity of personalised and user-centred approaches to XAI have rapidly grown in recent years. Often, these works have a two-fold objective: (1) proposing novel XAI techniques able to consider the users and (2) assessing the \textit{goodness} of such techniques with respect to others. From these new works, it emerged that user-centred approaches to XAI positively affect the interaction between users and systems. However, so far, the goodness of XAI systems has been measured through indirect measures, such as performance. In this paper, we propose an assessment task to objectively and quantitatively measure the goodness of XAI systems in terms of their \textit{information power}, which we intended as the amount of information the system provides to the users during the interaction. Moreover, we plan to use our task to objectively compare two XAI techniques in a human-robot decision-making task to understand deeper whether user-centred approaches are more informative than classical ones.