We have to make a decision even if utility functions and measurement procedures of alternatives are not given clearly. The Analytic Hierarchy Process (AHP) is a multi-criteria decision-making process in transdisciplinary areas. The process does not assume linear order of utility and priorities of alternatives; they are given as ratios from pairwise comparisons with regards on each criterion. This study is on the pairwise comparisons. First, I introduce a criterion, called naturality in this article. It is a generalized concept of Condorcet’s principle. And I provide a link diagram to confirm naturality. Finally, I describe a rating procedure to aggregate weights which satisfy naturality.