Sorted-Pareto dominance and qualitative notions of optimality

  • Authors:

  • Conor O'Mahony;Nic Wilson

  • Affiliations:

  • Cork Constraint Computation Centre, University College Cork, Ireland;Cork Constraint Computation Centre, University College Cork, Ireland

  • Venue:
  • ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
  • Year:
  • 2013

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Abstract

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.