Capturing preferences for inequality aversion in decision support

Abstract

We investigate the situation where there is interest in ranking distributions (of income, of wealth, of health, of service levels) across a population, in which individuals are considered preferentially indistinguishable and where there is some limited information about social pref- erences. We use a natural dominance relation, generalized Lorenz dominance, used in welfare comparisons in economic theory. In some settings there may be additional information about preferences (for example, if there is policy statement that one distribution is preferred to an- other) and any dominance relation should respect such preferences. However, characterising this sort of conditional dominance relation (specifically, dominance with respect to the set of all symmetric increasing quasiconcave functions in line with given preference information) turns out to be computationally challenging. This challenge comes about because, through the as- sumption of symmetry, any one preference statement (“I prefer giving $100 to Jane and $110 to John over giving $150 to Jane and $90 to John”) implies a large number of other preference statements (“I prefer giving $110 to Jane and $100 to John over giving $150 to Jane and $90 to John”; “I prefer giving $100 to Jane and $110 to John over giving $90 to Jane and $150 to John”). We present theoretical results that help deal with these challenges and present tractable linear programming formulations for testing whether dominance holds between any given pair of distributions. We also propose an interactive decision support procedure for ranking a given set of distributions and demonstrate its performance through computational testing

Solution approaches for equitable multiobjective integer programming problems

“…The interactive algorithm gets preference information in terms of pairwise comparisons and at each iteration it generates an equitably nondominated point that is not inferior to the convex cones generated based on preference information. We first briefly introduce the convex cones concept in the multicriteria decision making settings: both the classical settings where there is no symmetry assumption (see Korhonen et al 1984;Hazen 1983;Karsu 2013 for more information) and the symmetric setting where the alternatives are explicitly given (see Karsu et al 2018). We then discuss use of convex cones in the classical optimization settings, where the underlying preference relation is rational.…”

“…The definition of the cone dominated region implies that we need to perform checks by taking into account every permutation of the distributions over which preferences are provided, which may lead to prohibitively large computational effort. Karsu et al (2018) provide a compact characterization of the cone dominated region which avoids the need for considering all permutational checks, and in some cases avoid them altogether, thus affording tractability by proving the following:…”

Advances in Spatial Risk Analysis

“…Second, the comparison of spatial alternatives typically requires an overall assessment of maps (with an aggregation of spatially distributed values into a single value index), which is complex due to such spatial relations (Metchebon, Brison, & Pirlot, 2013). Third, potential variation among the effects of different hazards across regions, areas, or groups of people may bring out concerns about equitability and fairness in remediation strategies, which need to be appropriately captured in preference modeling and decision making (see, e.g., Karsu, Morton, & Argyris, 2018).…”

Using convex preference cones in multiple criteria decision making and related fields

“…Capturing preferences for inequality aversion: Karsu et al ( 2018) Karsu et al (2018) considered fairness problems, which occur widely in the public sector. In these problems the DM has both efficiency as well as equity or fairness concerns.…”