Identifying non-additive multi-attribute value functions based on uncertain indifference statements

Multi-criteria decision analysis (MCDA) requires an accurate representation of the preferences of decision-makers, for instance in the form of a multi-attribute value function. Typically, additivity or other stringent assumptions about the preferences are made to facilitate elicitation by assuming a simple parametric form. When relaxing such assumptions, parameters cannot be elicited easily with standard methods. We present a novel approach for identifying multi-attribute value functions which can have any shape. As preference information indifference statements are used that can be elicited by trade-off questions. Instead of asking one indifference statement for each pair of attributes, we ask for multiple trade-offs at different points in the attribute space. This allows inferring parameters of complex value functions despite the simplicity of the preference statements. Parameters are estimated by taking into account preference and elicitation uncertainty with a probabilistic model. Statistical inference supports identifying the most adequate preference model out of several candidate models through quantifying the uncertainty and assessing the need for non-additivity. The approach is elaborated for determining value functions by hierarchical aggregation. We apply it to an assessment of the ecological state of rivers, which is used to support environmental management decisions in Switzerland. Preference models of four experts were quantified, confirming the feasibility of the approach and the relevance of considering non-additive functions. The method suggests a promising direction for improving the representation of preferences.