Sorted-pareto dominance and qualitative notions of optimality

Thumbnail Image
O'Mahony, Conor
Wilson, Nic
Journal Title
Journal ISSN
Volume Title
Research Projects
Organizational Units
Journal Issue
Pareto dominance is often used in decision making to compare decisions that have multiple preference values – however it can produce an unmanageably large number of Pareto optimal decisions. When preference value scales can be made commensurate, then the Sorted-Pareto relation produces a smaller, more manageable set of decisions that are still Pareto optimal. Sorted-Pareto relies only on qualitative or ordinal preference information, which can be easier to obtain than quantitative information. This leads to a partial order on the decisions, and in such partially-ordered settings, there can be many different natural notions of optimality. In this paper, we look at these natural notions of optimality, applied to the Sorted-Pareto and min-sum of weights case; the Sorted-Pareto ordering has a semantics in decision making under uncertainty, being consistent with any possible order-preserving function that maps an ordinal scale to a numerical one. We show that these optimality classes and the relationships between them provide a meaningful way to categorise optimal decisions for presenting to a decision maker.
Artificial intelligence (incl. robotics) , Information systems applications (incl. internet) , Logics and meanings of programs , Mathematical logic and formal languages , Information storage and retrieval , Computer communication networks
O’MAHONY, C. & WILSON, N. 2013. Sorted-Pareto Dominance and Qualitative Notions of Optimality. In: GAAG, L. (ed.) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. Utrecht, The Netherlands, 7-10 July. Berlin Heidelberg: Springer. pp 449-460
Link to publisher’s version
©Springer-Verlag Berlin Heidelberg 2013. The final publication is available at Springer via