Experimental Strategies for Preference Information Acquisition: A Lattice Path Treatment

This paper investigates strategies for the acquisition of consumer preference information by a market researcher. Such preference information is obtained by the market researcher through an experimental process that entails polling consumers about their preference profiles with a view to completely specifying the preference order. In this paper, we limit the focus to one or two consumers. In this environment, the experiments are pairwise comparisons between resource bundles about which there is no a-priori preference information. Each such experiment can have three possible signals: one bundle is more preferred, indifferent, or less preferred over another. Choice of an experiment in the experimental sequence is important because different choices result in different average amounts of information. For the analysis the paper establishes a link between preference theory and lattice path counting. Combinatorial arguments that allow the market researcher to calculate quantities of information at the start of the information acquisition process are presented. A recursion for finding the impact of choosing different experiments on the average values of information gain is constructed. The paper studies how the experiments chosen subsequently can affect the elimination of other experiments from the experimental set and thus have an effect on the efficiency of information acquisition. The measures derived could be used by the market researcher as a benchmark with which to compare information gathering strategies.