This paper addresses the problem of multicriteria ordinal sorting through the lens of accountability, the ability of a human decision maker to own a recommendation made by the system. It proposes a number of model features that would favor the capability to support the recommendation with a convincing explanation, builds the only model possessing them all, discusses its aptitude at correctly representing some given preference information, and thoroughly describes the output recommendation, from mathematical and computational points of view. This recommendation is supported by an explanation, that takes the form of arguments implementing some specific argument schemes. Finally, it uncovers some flaws of the model, analyses their consequences, and proposes several directions for future research.