Incorporating within-pair order effects in the analytic hierarchy process

Analytic Hierarchy Process (AHP) has the objective of finding the priority weights of alternatives by using human judgments. A methodology that relies on human judgments should be capable of recognizing the complex behavioral or situational factors which contribute to the oder-dependent prioritizations. This dependence characterized as order effects is the effect of order of presentation within a pair of alternatives and should be removed before deriving the priority weights of alternatives. In the statistical approach to the AHP, a multiplicative model is provided for accommodating the order effects. These order effects being separate entities from the priority weights, they should be accounted in a proper model in the order-sensitive situations. If the order effects are not identified as separate entities, the estimated priority weights from the corresponding model do not yield pure priority weights-instead, they give the estimate of the parameters of priority weights in which order effects are confounded. Estimation of the parameters for the order effects does not have any significance as such. Instead, we propose a method for testing whether order effects are statistically significant in a typical situation. In case of the presence of these order effects, a method of estimation of priority weights is provided. Numerical examples are provided to illustrate the method proposed in the paper.