This paper is about the Compromise Ranking Problem (CRP), a well-known problem in the social choice theory. According to the famous Arrow’s theorem there is no voting method which is entirely satisfying and fairness if one accepts Arrow’s axioms. In this paper we formalize the problem as a minimisation problem in a discrete finite search space. We attempt to solve it based on the Least Squares (LS) approach thanks to some appealing metrics to get the optimal CRP solution. Surprisingly, we show that the optimal consensus (compromise) ranking solution disagrees with the commonsense solutions in four simple interesting examples. The search for an optimal solution in agreement with the commonsense appears to be an open very challenging question and our paper warns the users about the impossibility of the main current methods to provide acceptable solutions even for the rather simple examples considered in this work.

In today's world, addressing multi-criteria decision problems presents a considerable challenge due to their inherent complexity. Decision-makers face diverse and often conflicting factors that exceed their analytical capabilities and complicate the identification of the best solutions. Within this intricate field, Multi-Criteria Decision Analysis (MCDA) serves as an important decision support tool. The complex nature of these problems introduces numerous variables that influence the final choice. This complexity requires sensitivity analysis as an indispensable part of the assessment process. It allows for an examination of how changes in input data can affect the outcomes, providing valuable insights into the stability and reliability of the decision-making process. Based on the state-of-the-art, this study identifies a gap in sensitivity analysis, particularly in assessing the impact of modifications to the decision matrix. Although one-at-a-time (OAT) modification is efficient, simultaneously changing multiple elements provides nuanced insights into decision-matrix interdependencies. Therefore, this research introduces a novel sensitivity analysis method, the COMprehensive Sensitivity Analysis Method (COMSAM), which systematically modifies multiple values within the decision matrix. The COMSAM allows for a detailed problem space exploration, providing insights into alterations across criteria values. Furthermore, the method represents the preferences obtained from the evaluations as interval numbers, offering decision makers additional knowledge about the uncertainty of the analyzed problem. This study advances the field of sensitivity analysis, providing a new perspective on changes in multiple values' simultaneous influence on the robustness of the MCDA result.

This study introduces an extension of the Characteristic Objects Method (COMET) by incorporating the Expected Solution Point (ESP) approach to enhance individual decision-making. By integrating the ESP methodology, we aim to simplify decision-making, particularly when facing a vast decision matrix concerning multiple criteria. We demonstrate the efficacy of the proposed ESP-COMET method by applying it with one or two ESPs, thereby examining its impact on ranking alternatives according to personal customer preferences. In order to provide a practical example, we use a dataset of used cars to show how the proposed method facilitates the selection of the most suitable vehicle based on individual needs. The main goal of this paper is to show how the ESP-COMET method can help to adapt decisions to individual needs and expectations. We also introduce a novel and efficient approach for determining characteristic values in personalized decision-making, which plays a crucial role in ensuring the higher accuracy of the ESP-COMET method. Additionally, we compare the proposed approach with such methods as Stable Preference Ordering Toward the Ideal Solution (SPOTIS) and Reference Ideal Method (RIM). This study addresses the research gap by introducing an easy way to define customer preferences within COMET, enabling responsible decision-making.