A Probabilistic Approach for Indirect Elicitation of the Preferences of a Decision Maker

Eliciting the preferences of a Decision Maker (DM) is a challenging task in multi criteria-decision making problems. DM preferences can be represented in the form of weights for criteria. Direct elicitation methods can be cognitively difficult for the DM especially when a large number of weights with close values are available. Indirect methods are beneficial in this regard as they use decision alternatives rather than weights for elicitation. However, the accuracy of these approaches can vary depending on consistency of the DM and the similarity of the alternatives shown the DM. We propose a probabilistic approach for indirect elicitation of preferences. Our approach assumes that preferences of the DM are represented by a weighted utility function. It estimates the probability distribution of these weights by asking the DM to rank multiple sets each containing a small number of decision alternatives. The answers of the DM are inputted to a graphical probabilistic model to compute the posteriors of the weight distributions. The benefits of the proposed approach include estimation of uncertainty regarding the preferences and decreased cognitive difficulty due to ranking small number of alternatives. The proposed approach is also able to incorporate expert knowledge in the elicitation in terms of prior distributions or constraints between the parameters. We illustrate the use of the method by using two case studies and evaluate the performance of the method by using a simulated DM. Possible approaches to obtain better information from the DM in the preference elicitation process are considered. Approaches to put alternatives in ranking orders or to establish outranking relations using the probability distributions are also discussed