Almost optimal manipulation of pairwise comparisons of alternatives

The role of an expert in the decision-making process is crucial. If we ask an expert to help us to make a decision we assume their honesty. But what if the expert is dishonest? Then, the answer on how difficult it is for an expert to provide manipulated data in a given case of decision-making process becomes essential. In the presented work, we consider manipulation of a ranking obtained by the Geometric Mean Method applied to a pairwise comparisons matrix. More specifically, we propose an algorithm for finding an almost optimal way to swap the positions of two selected alternatives in a ranking. We also define a new index which measures how difficult such manipulation is in a given case.