# Detection of Decision-Making Manipulation in the Pairwise Comparison Method
## 2 Motivation  
It is widespread among those concerned with decision-making methods to believe that decision-makers, sometimes equated with experts, are honest. i.e., they express their opinions according to their most profound conviction and knowledge within a defined decision model. Hence, even when inconsistencies appear in judgments, they are most often explained by simple human frailities. This somewhat romantic assumption comes from decision-makers usually being experts in the field. Consequently, it is inappropriate for an expert to say something incompatible with their knowledge. Interestingly, in the case of electoral systems and social choice methods, expectations of decision-maker honesty are much lower. This is perhaps because the decision-makers are equated with the politicians, and the general perception is that both honesty and integrity among politicians are low (for example, a survey conducted during the 2010 general election in the UK found that 58% of respondents thought the honesty and integrity of elected politicians were low or very low [37]). Nevertheless, these two approaches have resulted in quite a lot of work on the manipulation of electoral systems ([12], pp. 127-169, [38]) and a relatively moderate number of studies on the manipulation of decision-making methods, including the method of pairwise comparison of alternatives. By addressing the topic of manipulation in the pairwise comparison method, we want to enter this gap. Research on manipulation within decision-making methods often concerns group decision-making (GDM). In such a context, it is easier to identify strategic behaviors that may suggest a desire to influence the outcome directly. [PERSON] et al. [39] propose a consensus model that takes into account possible manipulations and uses several heuristics to identify them, such as an overly strong preference for the chosen alternative or a decision-maker's different preferences compared to the rest of the group. An approach to prevent priority manipulation using minimum adjustment and maximum entropy methods in GDM in social networks is presented in the paper [40]. [PERSON] et al. [41] study a framework preventing manipulations during consensus-finding processes in social network GDM. [PERSON] et al. [42] propose a consensus framework using historical data and employing several heuristics to help identify manipulation. Interestingly, manipulations can involve both preferences and trust relationships. Detecting a manipulation entails a penalty that reduces the influence of a given expert or group (cluster) of experts on the outcome. [PERSON] et al. deal with consensus finding and potential manipulative behavior using the example of the social network WeChat [43]. [PERSON] et al. [44] established guidelines for identifying non-cooperative behaviors among DMs and utilized social network analysis to manage these behaviors effectively. [PERSON] and [PERSON] [45] explore such behaviors during the aggregation process using optimization techniques to counteract the adverse effects of manipulation behaviors. [PERSON] [46,47] delves into strategic preference manipulation behaviors primarily within the selection process. [PERSON] [13] defines a game-theoretical GDM model based on aggregating individual judgments with strategic manipulation in mind. [PERSON] et al. [48] suggest using uniform aggregation operators to manage non-cooperative behaviors. [PERSON] et al. [49] introduce a consensus model that handles non-cooperative behaviors and minority opinions. Although there are statistical methods (not necessarily related to GDM) used to detect fraudulent behavior in addition to GDM [50], most studies focus on group decision-making. The question arises, however, of whether expert dishonest behavior can only be investigated and detected in the context of group decision-making. The answer is of course not, and some indication may be the ways (heuristics) used in GDM to identify manipulative behavior.