Polyhedral sampling for multiattribute preference elicitation

A basic requirement for running multiattribute auctions is knowledge of the utility function of the buyer that trades off nonprice attributes against price. We present and study an approach that elicits this preference structure based on a markovian polyhedral sampling scheme called the " Hit-and-Run" algorithm. An advantage of this technique is its relative simplicity - it relies only on matrix algebra as opposed to the use of nonlinear optimization techniques by other methods in the literature. Computational results suggest that this method is fast and accurate.