Sorted-pareto dominance and qualitative notions of optimality

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O'Mahony, Conor
Wilson, Nic
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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
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