Optimal designs for main effects in linear paired comparison models

In psychology, marketing research and sensory analysis paired comparisons which demand judges to evaluate the trade-off between two alternatives constitute a popular method of data collection. For this situation we present optimal designs in a discrete setting when the alternatives are specified by an analysis of variance model with main effects only. We employ combinatorial tools to achieve optimal designs which have sufficiently small sample sizes. Moreover, optimal designs are constructed when the number of factors presented is restricted for each pair of alternatives.