The construction of designs in paired comparison experiments is considered. The procedures that are used in paired comparisons to estimate the parameters yield a covariance matrix that depends on the unknown parameters.
The assumption of no treatment differences is made to construct designs. By use of D-optimal discrete designs, exact designs are constructed with a high efficiency and a relatively small number of pairs. This is done for a quadratic model for 2, 3, 4 and 5 dimensions and hypercube as experimental region.
Key words: Paired comparison; Bradley-Terry model; Optimal designs; Factorials.