Manipulation of individual judgments in the quantitative pairwise comparisons method

Entities very often are referred to as alternatives, while the final result is in the form of a ranking. The first mention of pairwise comparison as a systematic ranking method comes from the 13th century and is attributed to Ramon Llull [7]. Lull proposed a procedure for selecting candidates based on comparing them in pairs. This technique might be viewed as in between the electoral system and a decisionmaking method in the modern sense. In later times, pairwise comparisons were used in the context of social choice and welfare theories [33, 25, 15], psychometric measurements [41, 16, 42] and decision-making methods [27]. In 1977, Saaty published his seminal paper introducing a new decision-making method: the Analytic Hierarchy Process (AHP) [34]. AHP is based on the quantitative pairwise comparison of alternatives. As a result, each of the considered entities is assigned a weight that determines its importance.