# A Simplified Algorithm for Dealing with Inconsistencies Using the Analytic Hierarchy Process
## 4 Discussion  
The automatic adjustment of inconsistent AHP matrixes is contentious, with some authors suggesting that, at best, the approaches should only be used to provide additional information to the original respondents, who should have the final say in how the matrix is to be adjusted [28; 29]. While this has advantages when dealing with small groups that will be directly affected by the outcomes of the management decision making, the shift to large online surveys of a broader stakeholder group makes such individual interactions difficult, particularly if data are collected anonymously. Several different approaches have been tried to avoid the problem of inconsistencies in online surveys. [PERSON], et al. [44] suggested an adaptive algorithm to reduce the number of pairwise comparisons a respondent is faced with given their initial consistency of response, with some combinations excluded from the survey and their values subsequently estimated  
Figure 3: The proportion of inconsistent observations after each iteration. based on the provided responses. While this approach has attractive features, programming of such an algorithm into an online survey would be complex. The problem of inconsistencies can also be minimized through appropriate hierarchy design. The number of comparisons required to be made by respondents increases substantially with the number of criteria to be compared: a survey with \(n\) criteria will require \(n(n-1)/2\) comparisons. [PERSON] and [PERSON] [45] suggest that the ability of respondents to be able to correct their own inconsistencies diminishes asymptotically to zero with an increasing number of criteria, with seven being an upper limit beyond which \"recovery\" is unlikely. With online surveys, the ability to return to respondents is limited (if not infeasible), so fewer comparisons are required to ensure inconsistencies are minimized in the first instance. The algorithm in this study is more readily applied in cases with four or less criteria being compared (after which some of the alternative approaches discussed in the earlier sections of the paper may be more suitable). Developing a hierarchy with four or less criteria in each level results in a manageable set of comparisons (i.e., \(4(4-1)/2=6\)) and a relatively straightforward process to adjust for any inconsistencies that emerge. Although this approach was motivated by a need to adjust inconsistencies observed in a large online survey, there are advantages also in considering the approach for smaller groups. Providing suggested modifications to the initial matrix to aid the respondents in reassessing stated preferences to improve their consistency is often undertaken, e.g., [28; 46]. However, in some cases, this can result in undesirable behavior. Recent experiences with deriving objective preference weightings in the marine and coastal environment from stakeholder groups, e.g., [14; 18], have found that some stakeholders felt that, by asking them to reconsider their preferences based on their level of inconsistency, the analyst was attempting to \"push\" their responses to a more desired (predefined) outcome and resisted changing their answers. Some also were offended by the idea that they were considered \"inconsistent\" in their views and insisted on maintaining their initial stated preferences. Even those who were prepared to change their responses exhibited undesirable behavior in some case, focusing more on trying to ensure consistency than on their actual preferences, effectively game playing to get the \"best\" score they could. This often resulted in these individuals moving their preferences closer to the center position in the bivariate comparisons (i.e., equal preference) to ensure a high consistency score. This satisficing response has been observed elsewhere and is a long-standing issue with attitudinal surveys [47]. Satisficing behavior particularly increases when the difficulty of the task increases (i.e., producing consistent preferences) and the respondent's motivation decreases.