Ordered weighted averaging (OWA) functions, a.k.a. Generalised Gini Index, are routinely used to obtain fair solutions. However, while they ensure some level of fairness in the result, two remaining questions are why they recommend a given alternative, and how robust is this recommendation. We bring practical and theoretically grounded solutions to these questions, by providing an explanation engine for robust OWA that consists in a normative transitive chain of self-evident arguments, themselves based on the normative properties of the model. We provide a thorough theoretical study of the engine, showing that it is sound and complete with respect to the model, with a theoretical upper bound on the length of the explanation and a tractable algorithm (even though minimizing the length is NP-hard). We also provide experimental evidence that the engine performs well on synthetic data. Thus, we guarantee that an explanation can always be found, and that reasoning according to the provided scheme always produces a valid statement. Moreover, the explanations allow to probe the normative requirements of the model, so as to allow validation, accountability and recourse, that are key components of trustworthy AI.

Despite their expressive power in representing alternatives or beliefs tainted by incomparabilities, it is often difficult to use generic partial orders. Hence, various structures have been historically studied in the literature, such as weak orders, semiorders or interval orders, each capturing a different fragment of partial orders. In this article, we propose and study in detail a fragment rich enough to represent some highly intuitive patterns involving incomparable elements that cannot be captured by the aforementioned fragments: partitioned linear orders (PLOs). These structures can be viewed as split independent linear orders, each one of them representing a local totally ranked situation. Then, we show how they can be used in Katsuno-Mendelzon-style belief revision. We propose a set of postulates, a representation theorem and a family of concrete operators.

We consider the problem of the conjoint selection and allocation of projects to a population of agents, e.g. students are assigned papers and shall present them to their peers. The selection can be constrained either by quotas over subcategories of projects, or by the preferences of the agents themselves. We explore fairness and optimality issues and refine the analysis of the rank-maximality and popularity optimality concepts. We show that they are compatible with reasonable fairness requirements related to rank-based envy-freeness and can be adapted to select globally good projects according to the preferences of the agents.

Integer models are of particular interest for applications where predictive models are supposed not only to be accurate but also interpretable to human experts. We introduce a novel penalty term called Facets whose primary goal is to favour integer weights. Our theoretical results illustrate the behaviour of the proposed penalty term: for small enough weights, the Facets matches the L1 penalty norm, and as the weights grow, it approaches the L2 regulariser. We provide the proximal operator associated with the proposed penalty term, so that the regularised empirical risk minimiser can be computed efficiently. We also introduce the Strongly Convex Facets, and discuss its theoretical properties. Our numerical results show that while achieving the state-of-the-art accuracy, optimisation of a loss function penalised by the proposed Facets penalty term leads to a model with a significant number of integer weights.

We introduce a way of reasoning about preferences represented as pairwise comparative statements, based on a very simple yet appealing principle: cancelling out common values across statements. We formalize and streamline this procedure with argument schemes. As a result, any conclusion drawn by means of this approach comes along with a justification. It turns out that the statements which can be inferred through this process form a proper preference relation. More precisely, it corresponds to a necessary preference relation under the assumption of additive utilities. We show the inference task can be performed in polynomial time in this setting, but that finding a minimal length explanation is NP-complete.

We consider decision situations in which a set of points of view (voters, criteria) are to sort a set of candidates to ordered categories (Good/Bad). Candidates are judged good, when approved by a sufficient set of points of view; this corresponds to NonCompensatory Sorting. To be accountable, such approval sorting should provide guarantees about the decision process and decisions concerning specific candidates. We formalize accountability using a feasibility problem expressed as a boolean satisfiability formulation. We illustrate different forms of accountability when a committee decides with approval sorting and study the information that should be disclosed by the committee.

We address the problem of multicriteria ordinalsorting through the lens of accountability, i.e. theability of a human decision-maker to own a recommendationmade by the system. We put forward anumber of model features that would favor the capabilityto support the recommendation with a convincingexplanation. To account for that, we designa recommender system implementing and formalizingsuch features. This system outputs explanationsdefined under the form of specific argumentschemes tailored to represent the specific rules ofthe model. At the end, we discuss possible andpromising argumentative perspectives.