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Rationalising Concavifiable Preferences

Wednesday 02 February 2011, 4.30pm-6.00pm
NAB 1.07, New Academic Building

Dr Nikolaos Argyris
Fellow, Management Science Group
London School of Economics

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The typical way to deal with problems involving multiple criteria is to aggregate these via a utility function that represents the underlying preferences. Obtaining the utility function, however, often requires that we accept restrictive assumptions on the nature of these preferences. In applications of multi-criteria decision analysis and multi-objective optimisation, it is particularly common to use additively separable utility functions, which require independence among attributes. In this talk, we consider how we may lift the assumption of additivity and impose instead a concavity assumption on the utility function. We take an axiomatic approach and consider under what conditions on the underlying preferences we may reasonably assume that the representing utility function is concave and nondecreasing. We then consider the general problem of rationalising partial preference information by means of a concave and nondecreasing utility function. We introduce a complete characterisation of all utility functions compatible with the partial preference information. Finally, we consider how these results may be utilised in several multi-criteria problem settings, namely pre-ordering (ranking), 1-out-of-n choice and multi-objective optimisation.

Joint work with Alec Morton and Jose Rui Figueira

Nikos Argyris