Voting and MCDM: the pedagogy of the Saari triangle

Multi-criteria decision making (MCDM) is represented by utility and outranking methods. Of the utility models, the analytic hierarchy process (AHP) is probably the most popular in group-decision support. The social choice theory (SCT) with its voting systems can be efficiently combined with MCDM, and AHP in particular, in various group-decision contexts. This paper investigates two possible contexts where modeling group decision-making processes in the field of human---computer interaction (HCI) takes place. Being an important part of universal access in the information society, the first context assumes the use of AHP only, associated with two different aggregating techniques to derive the group decision, with and without a consensus. The second context is based on using only SCT systems, i.e., preferential and non-preferential voting systems. The third, novel, approach that is proposed assumes a full AHP application in the first stage to obtain the weights of alternatives and, in the second stage, an interpretation of the AHP's cardinal information as being the ordinal one and the direct application of the SCT voting systems. Comparative analyses show good agreement for the results when the three methodologies are applied as the decision support to ranking by importance (for a group of 14 PhD students) several widely used sources of information for the internet. The method of virtually combining the AHP and SCT voting systems could be efficiently implemented in real decision-making situations in HCI and related sectors, as well as in cross-sector settings.

The theory of social choice is the study of voting methods. In the literature manystudies have been conducted for the development of a fair voting system, that is to say a voting method that allows to aggregate the individual preferences in a collective preference representing in the most possible faithfull way individual preferences. Yet some voting methods do not allow to obtain a consensus. So there are a lot of paradoxes in electoral systems and related results in the theory of social choice are also paradoxical. This is the case, for example, with Arrow’s theorem showing that no voting method can simultaneously verify a restricted list of roperties that are desirable in a democratic political system. That is to mean that the search for a system that makes it possible to reach a consensus remains a concern in the theory of social choice. In this article we have combined various voting methods based on grading, scoring or approving to contribute to literature with a new voting system filling fair properties.

Contributors To This Issue

A group package recommender based on learning group preferences, multi-criteria decision analysis, and voting

Multicriteria Decision Analysis to Support Health Technology Assessment Agencies: Benefits, Limitations, and the Way Forward

Multicriteria decision making (MCDM) methods generally require information that is difficult and expensive to obtain. It is shown in this paper that given an ordering of criteria by importance, and whether each alternative is above the average evaluation of the alternatives for each criterion, considerable information can be extracted concerning the overall rankings of the alternatives. This is done by recognizing the similarity between criteria in MCDM, and voters in social choice theory. Multicriteria approval, proposed in this paper, is an MCDM adaptation of approval voting which can be used to classify decisions into one of several categories, depending on whether, and the manner in which, a superior alternative can be identified. An exhaustive examination of all possible decision situations of tractable size is made to measure the applicability of multicriteria approval, and the approach is demonstrated in an industrial procurement case. In addition to requiring minimal information from a decision maker, multicriteria approval satisfies several desirable criteria for MCDM techniques. © 1998 John Wiley & Sons, Ltd.

Multicriteria decision making (MCDM) methods generally require information that is difficult and expensive to obtain. It is shown in this paper that given an ordering of criteria by importance, and whether each alternative is above the average evaluation of the alternatives for each criterion, considerable information can be extracted concerning the overall rankings of the alternatives. This is done by recognizing the similarity between criteria in MCDM, and voters in social choice theory. Multicriteria approval, proposed in this paper, is an MCDM adaptation of approval voting which can be used to classify decisions into one of several categories, depending on whether, and the manner in which, a superior alternative can be identified. An exhaustive examination of all possible decision situations of tractable size is made to measure the applicability of multicriteria approval, and the approach is demonstrated in an industrial procurement case. In addition to requiring minimal information from a decision maker, multicriteria approval satisfies several desirable criteria for MCDM techniques. © 1998 John Wiley & Sons, Ltd.

Linking analytic hierarchy process and social choice methods to support group decision-making in water management

The influence of the ongoing COVID-19 pandemic that is being felt in all spheres of our lives and has a remarkable effect on global health care delivery occurs amongst the ongoing global health crisis of patients and the required services. From the time of the first detection of infection amongst the public, researchers investigated various applications in the fight against the COVID-19 outbreak and outlined the crucial roles of different research areas in this unprecedented battle. In the context of existing studies in the literature surrounding COVID-19, related to medical treatment decisions, the dimensions of context addressed in previous multidisciplinary studies reveal the lack of appropriate decision mechanisms during the COVID-19 outbreak. Multiple criteria decision making (MCDM) has been applied widely in our daily lives in various ways with numerous successful stories to help analyse complex decisions and provide an accurate decision process. The rise of MCDM in combating COVID-19 from a theoretical perspective view needs further investigation to meet the important characteristic points that match integrating MCDM and COVID-19. To this end, a comprehensive review and an analysis of these multidisciplinary fields, carried out by different MCDM theories concerning COVID19 in complex case studies, are provided. Research directions on exploring the potentials of MCDM and enhancing its capabilities and power through two directions (i.e. development and evaluation) in COVID-19 are thoroughly discussed. In addition, Bibliometrics has been analysed, visualization and interpretation based on the evaluation and development category using R-tool involves; annual scientific production, country scientific production, Wordcloud, factor analysis in bibliographic, and country collaboration map. Furthermore, 8 characteristic points that go through the analysis based on new tables of information are highlighted and discussed to cover several important facts and percentages associated with standardising the evaluation criteria, MCDM theory in ranking alternatives and weighting criteria, operators used with the MCDM methods, normalisation types for the data used, MCDM theory contexts, selected experts ways, validation scheme for effective MCDM theory and the challenges of MCDM theory used in COVID-19 studies. Accordingly, a recommended MCDM theory solution is presented through three distinct phases as a future direction in COVID19 studies. Key phases of this methodology include the Fuzzy Delphi method for unifying criteria and establishing importance level, Fuzzy weighted Zero Inconsistency for weighting to mitigate the shortcomings of the previous weighting techniques and the MCDM approach by the name Fuzzy Decision by Opinion Score method for prioritising alternatives and providing a unique ranking solution. This study will provide MCDM researchers and the wider community an overview of the current status of MCDM evaluation and development methods and motivate researchers in harnessing MCDM potentials in tackling an accurate decision for different fields against COVID-19.

This study hopes to develop a multi-criteria decision-making (MCDM) method for equitable and efficient allocation of water resources under scarcity. Based on the Bankruptcy problems, five classic plus one proposed allocation rules are introduced to generate water distribution alternatives. The “Core” solution of Cooperative Game Theory (CGT) and the Security Restriction have been used to select feasible alternatives. Additionally, five voting methods in Social Choice Theory (SCT) are launched to aggregate preferences and obtain a “win” alternative. Apply this model to the 2030 water allocation planning project of Ezhou City, China, as a case study. Under the proposed rule, Adjust minimal overlap rule (AMO), five regions, Urban Area, Gedian DZ, and three counties, hold the water deficit rate of 5.9%, 15.8%, and 4.7%-6.1%, respectively. In aggregating preferences by voting, AMO wins four out of five methods and takes second place in the last one, which provides some insights for allocating water fairly and feasibly.

Voting plays a vital role in any society. Indeed the votes involve decision making especially and the more in the decision of group. Thanks to the opinions expressed by a group of people, an opinion representing the preference of the group is determined. But most often some voting methods seem to distance the result from a vote of the general opinion. The study of voting methods is based on the theory of social choice. For several years, in the literature on the theory of social choice, many theorists have contributed trying to find a representative voting method.It seems that there is no totally satisfactory way of voting.Thus we have tried, through this article, to design a voting method based on approval voting and the arithmetic mean that leads to goodcompromise results.In contrast to the other methods, the new method takes into account the choice of each voter and allows to obtain a result which represents the choice of the majority of the voters.

Empirical study on voting power in participatory forest planning

n modern aircraft design, increased attention is being paid to the conceptual and preliminary design phases so as to increase the odds of creating a design that will ultimately be successful at the completion of the design process. Since aerospace systems are complex systems with interacting disciplines and technologies, the decision makers dealing with such design problems are involved in balancing multiple, potentially conflicting attributes/criteria, transforming a large amount of customer supplied guidelines into a solidly defined set of requirement definitions. As a result, the criteria have to be all simultaneously taken into account and a compromise essentially becomes part of the decision making process. Various methods and techniques are available to deal with such sort of multi-criteria decision making (MCDM) problems. In the 1970’s, Saaty proposed the Analytic Hierarchy Process (AHP), which facilitates the MCDM problems that have a hierarchical structure of attributes by reducing complex decisions to a series of pair-wise comparisons. In this method, the preference information is elicited as the pair-wise comparisons between attributes or alternatives and treated using the eigenvector method. The other straightforward method to handle the MCDM problem is the Overall Evaluation Criterion (OEC) technique, presented in Ref 3. The OEC is a single metric and is obtained by summing multiple non-dimensional attribute metrics normalized by the metric values of a relevant baseline. Another commonly used MCDM technique is the Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS). The “best” solution chosen by TOPSIS is the alternative that is the closest to the positive ideal solution and the furthest from the negative ideal solution. The separation between each alternative solution and the ideal solution, which is determined by the weighted criteria, is rather sensitive to criterion weights, so typically several weighting scenarios are investigated to determine the final solution. Among these developed MCDM methods, different methods have different underlying assumptions, information requirements, analysis models, and decision rules that are designed for solving a certain class of decision making problems. This implies that it is critical to use the most appropriate method to solve the problem under consideration since the use of unsuitable method always leads to misleading design decisions. Consequently, bad design decisions will result in big loss to the society, such as property damage or personal injury. Thus, it is necessary to review the existing MCDM methods, discuss in depth their advantages, disadvantages, applicability, computational complexity, etc. in order to make right decision when choosing the right method for the given problem. In this paper a hybrid MCDM method is developed to deal with the problem under consideration. Relative weights of the evaluation criteria are elicited by using the eigenvector method to describe the decision maker’s preference information. The TOPSIS method is used to analyze the qualitative and quantitative data of input parameters and find the solution to the given problem. An aircraft technology selection problem is conducted as a proof of implementation to demonstrate the functionality and effectiveness of the proposed methodology.

Voting rules allow multiple agents to aggregate their preferences in order to reach joint decisions. Perhaps one of the most important desirable properties in this context is Condorcet-consistency, which requires that a voting rule should return an alternative that is preferred to any other alternative by some majority of voters. Another desirable property is participation, which requires that no voter should be worse off by joining an electorate. A seminal result in social choice theory by Moulin (1988) has shown that Condorcet-consistency and participation are incompatible whenever there are at least 4 alternatives and 25 voters. We leverage SAT solving to obtain an elegant human-readable proof of Moulin's result that requires only 12 voters. Moreover, the SAT solver is able to construct a Condorcet-consistent voting rule that satisfies participation as well as a number of other desirable properties for up to 11 voters, proving the optimality of the above bound. We also obtain tight results for set-valued and probabilistic voting rules, which complement and significantly improve existing theorems.

Social Choice and Game Theory: Recent Results with a Topological Approach