AHP applied to binary and ternary comparisons

This paper confines the values of the components of comparison matrix of AHP, to two (θ,θ’-¹) or three (θ,1,θ’-¹) distinct values. The former is called ‘binary case’ and the latter ‘ternary case’. Then it has some beautiful theoretical results if comparison matrices have some regularity conditions. In sports games ‘win, defeated, tied’ just means to ternary case, and the present method serves to estimate true strength of teams from the results of ‘win, defeated, tied’ in a league tournament game.