The paper deals with a step-wise HAP, applied by a group of decision makers, wherein nobody has a dominant position and it is unlikely to come to terms with respect to either the weights of different objectives or expected utilities of different alternatives. One of HAP outcome, namely the consistency index, is computed for each decision maker, for all other decision makers but that one, and for the whole group. Doing so, the group is able to assess to which extent each decision maker alters the group consistency index and a better consistency index could be achieved if the assessment procedure is being resumed by the most influential decision maker in terms of consistency. A case study is used to demonstrate how the step-wise process succeeds in improving the group's consistency index and how the weights of criteria are being changed during the negotiation process. The main contribution of the new approach is the algorithm presented in the figure of the paper where the condition to stop the process might be either a threshold value for the consistency index, or a given number of iterations per group or per person.
Keywords: managerial decision, HAP, PAI method