An introduction to optimal stable marriage problems and argumentation frameworks

In the Stable Marriage (SM) problem, given two sets of individuals partitioned into men and women, a matching is stable when there does not exist any matching man-woman by which both man and woman would be individually better off than they are with the person to which they are currently matched. In 1995, P.M. Dung modelled stable matchings as stable extensions in Abstract Argumentation Frameworks. In this paper we elaborate on the original formulation by using Weighted Abstract Argumentation to also represent optimality criteria in Optimal SM problems, where some matchings are better than others: criteria may consider only the preference of either men, or women, or a more balanced view obtained by differently combining the preferences of both of them.