## 5 Discussion  
In this section, we discuss the outcomes of this paper with respect to the premises presented in the introduction. First, in the framework of the assessment of LF throughout Sardinian LUs, we are interested to check whether the weighted versions of the CILF perform better--i.e., add more information--than its unweighted releases (all weights equal). We would like to stress that the development of both weight assessments implies demanding and time-consuming activities, such as the mobilization of scientific knowledge, the application of sophisticated methods and algorithms, the design, test, and submission of ad hoc questionnaires, the selection of the target audience, etc. Weighting is never for free because it implies costs,  
Figure 3: Sensitivity analysis chart of CILF (2003). Rankings are compared pairwise keeping fixed the weighting patterns and changing the aggregation rules. which are also difficult to evaluate precisely in advance. Thus, it is not surprising that scientists question the worthiness of the weighting effort. In our exercise, we obtained the weights following two streams of research. According to the first set of contributions (for instance, [PERSON] et al. [15]), we opted for an \"objective\" quantitative assessment of the importance of the indicators, which are calculated as the percentage of variance (information) explained. This is an informational weighting method that yields values by processing characteristics embedded in the indicators' dataset. The PCA-based triplet of weights reported in Table 4 signs a clear prevalence of IFI and UFI with respect to the \(S_{\textit{eff}}\). This per se diverges from the scenario represented by the equalization of the weights. According to a stream of contributions (see [43; 46]), we have calculated another weight triplet applying a \"subjective\" assessment that considers the judgment of a set of selected experts. This triplet is representative of the average judgment of the experts and may vary when considering a different set of participants. The endorsers of subjective assessment frameworks question that quantitative PCA-based methods may be too neutral and abstract for policy and decision makers. In addition, they point out that a clear presentation of subjective assessment methods may strengthen the acceptability and viability of weighted CIs. In our case, the expert judgment-based weight triplet (see Table 4) converges to the scenario with all weights equal. Therefore, an argument purely focused on the values of the weight triplets would suggest that the first process of weighting was more worthwhile than the second because the first one potentially leads to a different picture with respect to the situation described by the unweighted CLIF (all weights equal). However, we need to widen our perspective to complete the assessment of the influence of the algorithm on the new release of the CLIF. Thus, we have jointly analyzed the combined impacts of both the weighting pattern and the aggregation rule. Therefore, as for the argument concerning the evidence of the complete sensitivity analysis, it does not show us a monochrome picture and needs to be carefully interpreted. If we consider the outcomes reported in Tables 7 and 8, the figures do not address a monolithic message. In the first case, figures suggest that sensitivity is overall contained (\(\,\mid\,\mid\,\mid\,\mid\,\mid\,\mid\,\mid\,\mid\,\mid\,\mid\,\mid\,\mid\,\mid \,\mid  
versions of the CILF embed new information and lead to different rankings--a circumstance that justifies the adoption of the composites and the effort for introducing the weights. The cases reported in Table 7 describe a panorama, in which low sensitivity values would support that the new weighted composites do not add much to the information provided by the original CILF and that the weighting has not been worthwhile. However, this can be questionable since weighting per se adds advantages, as intangible as they may be.