Decision analysis has been with us for at least half a century. Over that time it has developed from a theoretical paradigm for individual rational choice to a practical tool for individuals, small groups and 'unitary' organisations, which helps them towards a sound decision-making mindful of the behavioural characteristics of individuals and group dynamics. Decision analysis has also shown its worth in the context of stakeholder engagement and public participation. The time is right for it to be more widely used in making societal decisions. However, to achieve that we need to realise that in many circumstances it will only be one input to the political process that leads to the actual decision. Recognising that suggests that our community of decision analysts needs to deconstruct our paradigm and attend more to communicating the result of the analysis in comparison with other inputs to the societal decision.
We consider the problem of helping a decision maker (DM) choose from a set of multiattributed objects when her preferences are "concavifiable", i.e. representable by a concave value function. We establish conditions under which preferences or preference intensities are concavifiable. We also derive a characterization for the family of concave value functions compatible with a set of such preference statements expressed by the DM. This can be used to validate dominance relations over discrete sets of alternatives and forms the basis of an interactive procedure. We report on the practical use of this procedure with several DMs for a flat-choice problem and its computational performance on a set of project-portfolio selection problem instances. The use of preference intensities is found to provide significant improvements to the performance of the procedure.
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