A technical note on two inconsistency indices for preference relations: A case of functional relation

Different representations of valued preferences have been studied and used over the years; however, one common factor has been the prominence of the concept of consistency. Inconsistency indices have been introduced to estimate the deviation of preferences from a fully consistent form. In this note we shall recall two types of preference relations (reciprocal relations and multiplicative preference relations) and show that two inconsistency indices introduced in these two different frameworks are functionally related. Besides this main result, some reflections on the consequences of being functionally related are presented.