Pairwise agreement of gradient directions in interactive multicriterion optimization

Statistical tests involving mean directions have in the past been limited to two- and three-dimensional settings, perhaps owing to their primary applications to such fields as geology, meteorology and related earth sciences. In the study of interactive multicriterion optimization it becomes necessary to compare gradient directions obtained from decision makers by two or more methods. Typically these direction vectors are in a higher-dimensional space. This paper provides a general procedure based on Householder transformations which is potentially suitable for any finite dimension. An illustration and comparison of the method are provided.