Using Pareto Optimal Choice Sets

In behavioral experiments the respondents make their choices based on several factors called attributes. When the attributes are related to benefits and costs and respondents choose one attribute at a time, the highest level for benefit attributes and the lowest level for cost attributes will be selected. The relative importance given by the respondents to the attributes is not determined. If a set of profiles (factorial treatment combinations) of the attributes is given to the respondents to choose, it is possible to determine the relative importance of the attributes under some conditions. If the choice set has a dominating profile (or dominated profile) almost surely that profile will be selected (or not selected). Thus the set of profiles given to the respondent known as the choice set should not have dominating or dominated profiles. Choice sets with no dominating or dominated profiles are called Pareto optimal subsets. In this paper, we consider the connectedness and optimality of designs with Pareto optimal choice sets for n attributes each at 2 levels. Balanced incomplete block designs are helpful to reduce the choice set sizes without sacrificing optimality and this paper shows some interesting application of them.