On the theoretical incorrectness of the analytic hierarchy process

The paper considers the basic statement of the analytic hierarchy process (AHP), that the priorities of decision variants on individual criteria are compared on the ratio scales that are not linked to each other and are also independent of the priorities of criteria. According to the mathematical theory of measurement this approach is incorrect. To demonstrate its potential consequences a simple example in which the use of the AHP procedure leads to a clearly erroneous result is provided.