Classification Aggregation without Unanimity

A classification is a surjective mapping from a set of objects to a set of categories. A classification aggregation function aggregates every vector of classifications into a single one. We show that every citizen sovereign and independent classification aggregation function is essentially a dictatorship. This impossibility implies an earlier result of Maniquet and Mongin (2016), who show that every unanimous and independent classification aggregation function is a dictatorship. The relationship between the two impossibilities is reminiscent to the relationship between Wilson's and Arrow's impossibilities in preference aggregation. Moreover, while the Maniquet-Mongin impossibility rests on the existence of at least three categories, we propose an alternative proof technique that covers the case of two categories, except when the number of objects is also two. We also identify all independent and unanimous classification aggregation functions for the case of two categories and two objects.

A formal framework for deliberated judgment

While the philosophical literature has extensively studied how decisions relate to arguments, reasons and justifications, decision theory almost entirely ignores the latter notions and rather focuses on preference and belief. In this article, we argue that decision theory can largely benefit from explicitly taking into account the stance that decision-makers take towards arguments and counter-arguments. To that end, we elaborate a formal framework aiming to integrate the role of arguments and argumentation in decision theory and decision aid. We start from a decision situation, where an individual requests decision support. In this context, we formally define, as a commendable basis for decision-aid, this individual's deliberated judgment, popularized by Rawls. We explain how models of deliberated judgment can be validated empirically. We then identify conditions upon which the existence of a valid model can be taken for granted, and analyze how these conditions can be relaxed. We then explore the significance of our proposed framework for decision aiding practice. We argue that our concept of deliberated judgment owes its normative credentials both to its normative foundations (the idea of rationality based on arguments) and to its reference to empirical reality (the stance that real, empirical individuals hold towards arguments and counter-arguments, on due reflection). We then highlight that our framework opens promising avenues for future research involving both philosophical and decision theoretic approaches, as well as empirical implementations.

Reasons and Means to Model Preferences as Incomplete

Literature involving preferences of artificial agents or human beings often assume their preferences can be represented using a complete transitive binary relation. Much has been written however on different models of preferences. We review some of the reasons that have been put forward to justify more complex modeling, and review some of the techniques that have been proposed to obtain models of such preferences.