scholarly journals Range of Asymptotic Behaviour of the Optimality Probability of the Expert and Majority Rules

2006 ◽  
Vol 43 (01) ◽  
pp. 16-31
Author(s):  
Daniel Berend ◽  
Luba Sapir
Keyword(s):  
Group Decision ◽  
Choice Model ◽  
Correct Choice ◽  
Decision Makers ◽  
Independent Random Variables ◽  
Majority Rules ◽  
Uncertain Dichotomous Choice ◽  
The Individual ◽  
Two Alternatives ◽  
Asymptotic Behaviours

We study the uncertain dichotomous choice model. In this model, a group of expert decision makers is required to select one of two alternatives. The applications of this model are relevant to a wide variety of areas. A decision rule translates the individual opinions of the members into a group decision, and is optimal if it maximizes the probability of the group making a correct choice. In this paper, we assume the correctness probabilities of the experts to be independent random variables selected from some given distribution. Moreover, the ranking of the members in the group is (at least partly) known. Thus, one can follow rules based on this ranking. The extremes are the expert rule and the majority rule. The probabilities of the two extreme rules being optimal were compared in a series of early papers, for a variety of distributions. In most cases, the asymptotic behaviours of the probabilities of the two extreme rules followed the same patterns. Do these patterns hold in general? If not, what are the ranges of possible asymptotic behaviours of the probabilities of the two extreme rules being optimal? In this paper, we provide satisfactory answers to these questions.

scholarly journals Range of Asymptotic Behaviour of the Optimality Probability of the Expert and Majority Rules

2006 ◽  
Vol 43 (1) ◽  
pp. 16-31 ◽  
Author(s):  
Daniel Berend ◽  
Luba Sapir
Keyword(s):  
Group Decision ◽  
Choice Model ◽  
Correct Choice ◽  
Decision Makers ◽  
Independent Random Variables ◽  
Majority Rules ◽  
Uncertain Dichotomous Choice ◽  
The Individual ◽  
Two Alternatives ◽  
Asymptotic Behaviours

We study the uncertain dichotomous choice model. In this model, a group of expert decision makers is required to select one of two alternatives. The applications of this model are relevant to a wide variety of areas. A decision rule translates the individual opinions of the members into a group decision, and is optimal if it maximizes the probability of the group making a correct choice. In this paper, we assume the correctness probabilities of the experts to be independent random variables selected from some given distribution. Moreover, the ranking of the members in the group is (at least partly) known. Thus, one can follow rules based on this ranking. The extremes are the expert rule and the majority rule. The probabilities of the two extreme rules being optimal were compared in a series of early papers, for a variety of distributions. In most cases, the asymptotic behaviours of the probabilities of the two extreme rules followed the same patterns. Do these patterns hold in general? If not, what are the ranges of possible asymptotic behaviours of the probabilities of the two extreme rules being optimal? In this paper, we provide satisfactory answers to these questions.

scholarly journals AHP-Group Decision Making Based on Consistency

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 242 ◽  
Author(s):  
Juan Aguarón ◽  
María Teresa Escobar ◽  
José Moreno-Jiménez ◽  
Alberto Turón
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Real Life ◽  
Decision Makers ◽  
Local Context ◽  
Consensus Matrix ◽  
Stability Intervals ◽  
The Individual ◽  
Individual Consistency

The Precise consistency consensus matrix (PCCM) is a consensus matrix for AHP-group decision making in which the value of each entry belongs, simultaneously, to all the individual consistency stability intervals. This new consensus matrix has shown significantly better behaviour with regards to consistency than other group consensus matrices, but it is slightly worse in terms of compatibility, understood as the discrepancy between the individual positions and the collective position that synthesises them. This paper includes an iterative algorithm for improving the compatibility of the PCCM. The sequence followed to modify the judgments of the PCCM is given by the entries that most contribute to the overall compatibility of the group. The procedure is illustrated by means of its application to a real-life situation (a local context) with three decision makers and four alternatives. The paper also offers, for the first time in the scientific literature, a detailed explanation of the process followed to solve the optimisation problem proposed for the consideration of different weights for the decision makers in the calculation of the PCCM.

scholarly journals A multicriteria group decision model aggregating the preferences of decision-makers based on electre methods

2010 ◽  
Vol 30 (3) ◽  
pp. 687-702 ◽  
Author(s):  
Luciana Hazin Alencar ◽  
Adiel Teixeira de Almeida ◽  
Danielle Costa Morais
Keyword(s):  
Decision Model ◽  
Group Decision ◽  
Decision Makers ◽  
Relative Importance ◽  
Numerical Application ◽  
Second Stage ◽  
Individual Preferences ◽  
Third Stage ◽  
Three Stages ◽  
The Individual

Often decisions taken in organizations are made by a group of people, and in order to build a collective decision, the preferences of individuals must be considered. The two most useful approaches to aggregating individual preferences are the aggregation of individual judgments and the aggregation of individual priorities. This paper focuses on the latter approach and proposes a multicriteria group decision model in situations where there is no information with regard to the relative importance of the decision-makers. This model includes three stages. In the first, the ELECTRE II method is applied so as to obtain the individual rankings. In the second stage, a global matrix of alternatives versus decision-makers is built up using the results from the previous stage. Finally, the third stage aggregates the individual preferences by applying the ELECTRE IV method and the final collective evaluation is undertaken. A numerical application is presented to illustrate the model.

Multi-attribute Group Decision-making (MAGDM) using Fuzzy Linguistic Modeling Integrated with the VIKOR Method for Car Purchasing Model

2022 ◽  
Vol 14 (1) ◽  
pp. 0-0
Keyword(s):  
Decision Making ◽  
Group Decision ◽  
Decision Makers ◽  
Decision Making Process ◽  
Vikor Method ◽  
Decision Making Problem ◽  
Purchasing Model ◽  
The Individual ◽  
Fuzzy Linguistic

The change in the trend of transportation, increasing per capita income, expectation of better lifestyle, easy finance, and reduced cost of the automobile are some of the main factors that enable a commoner to have his/her own car. Therefore, it is essential to comprise such features in cars that offer qualities enabling the ease of consumer’s decision-making and comfort to purchase a car individually. Purchasing a car is a complicated multi-criteria decision-making problem as an individual may have different preferences for different criteria attributes. The attributes may be conflicting in nature depending on the need of the individual customer. Generally, it becomes quite difficult to assign ratings to these attributes based on numeric values. Therefore, the decision-making process relies on an idiosyncratic finding of the decision-makers which is in practice fuzzy with uncertainities. Hence, this article is a case study that deals with a hierarchy MCDM approach in accordance with the fuzzy logic and VIKOR method to solve a car purchasing problem.

A Novel Method for Fuzzy Multi-Criteria Decision Making

2014 ◽  
Vol 13 (03) ◽  
pp. 497-519 ◽  
Author(s):  
Meimei Xia ◽  
Zeshui Xu
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Weight Vector ◽  
Decision Makers ◽  
Decision Matrix ◽  
Novel Method ◽  
The Individual ◽  
Ideal Group ◽  
The Ideal

To determine the weight vector and to aggregate the individual opinions are necessary steps in the classical methods for multi-criteria group decision-making problems in which the weight vectors of the decision makers and the criteria are incompletely known. In this paper, we propose a simple but efficient approach which can avoid these steps by establishing some optimal models. To get the optimal group decision matrix, we first propose two kinds of models among which the former focuses on minimizing the deviations between individual decision matrix and the ideal group one, while the latter aims at minimizing the deviations between the estimated group opinion and the ideal group one. To get the overall performances of alternatives, another two types of models are further established, one of which is to minimize the distance between the evaluation value under each criterion and the ideal overall value for each alternative, and the other is to minimize the distance between the estimated overall value and the ideal overall one. The proposed models can be used to deal with group decision-making under intuitionistic fuzzy, interval-valued fuzzy or other fuzzy environments, and can also provide the decision makers more choices by containing the parameter which can be assigned different values according to different actual situations. Several examples illustrate the practicability of the proposed methods.

Research on the IAMM and IGMM Operators in Group Decision Making with Intuitionistic Preference Relations

2013 ◽  
Vol 753-755 ◽  
pp. 2806-2815
Author(s):  
Jun Ling Zhang ◽  
Jian Wu
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Geometric Mean ◽  
Arithmetic Mean ◽  
Decision Makers ◽  
Preference Relations ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
The Individual

Preference relations are the most common techniques to express decision makers preference information over alternatives or criteria. This paper focus on investigating effective operators for multiple attribute group decision making with intuitionistic fuzzy preference relations. Firstly, we extend arithmetic mean method operator and geometric mean method operator for accommodating intuitionistic fuzzy information to present the intuitionistic arithmetic mean method (IAMM) operator and the intuitionistic geometric mean method (IGMM) operator. Then the compatibility properties of intuitionistic preference relations obtained by IAMM and IGMM are analyzed, we found that aggregation of individual judgments and aggregation of individual priorities provide the same priorities of alternatives, and that if all the individual decision makers have acceptable consensus degree, then the collective preference relations obtained also are of acceptable consensus degree. Finally, the results are verified by an illustrative example carried out in the background of parts supplier selection.

scholarly journals GROUP INTERVAL WEIGHTS BASED ON CONJUNCTION APPROXIMATION OF INDIVIDUAL INTERVAL WEIGHTS

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Tomoe Entani
Keyword(s):  
Decision Maker ◽  
Group Decision ◽  
Decision Makers ◽  
Group Decisions ◽  
Trade Off ◽  
Proposed Model ◽  
The Individual ◽  
Interval Weight

<p>The individual and group decisions in this study are denoted as the normalized interval weights of alternatives as in Interval AHP. It assumes that a decision maker uses crisp values in the interval weights in giving comparisons. The interval weights reflect uncertainty in a decision maker’s mind. Then, the group interval weight is obtained as a conjunction approximation of the individual interval weights. For a consensus, the group interval weight is obtained so as to intersect with all the individual interval weights. In other words, the group interval weight has something in common with each individual interval weight. The group decision depends on how much the decision makers are satisfied or dissatisfied with it. The satisfaction of a decision maker is measured by the ranges of the group interval weights which s/he can support. Similarly, the decision maker’s dissatisfaction is defined by the ranges which are out of his/her decision. It is better to maximize the satisfaction and simultaneously to minimize the dissatisfaction. However, there is a trade-off between these two objectives. In the proposed model, the importance of the satisfaction or dissatisfaction is given. Then, the decision makers find not only the group decision but also their satisfaction and dissatisfaction with it. </p>

scholarly journals Expert rule versus majority rule under partial information, II

2002 ◽  
Vol 6 (2) ◽  
pp. 79-99 ◽  
Author(s):  
Daniel Berend ◽  
Luba Sapir
Keyword(s):  
Uniform Distribution ◽  
Group Size ◽  
Majority Rule ◽  
Partial Information ◽  
Distribution Parameter ◽  
Decision Makers ◽  
Independent Random Variables ◽  
Expert Rule ◽  
Distribution Rule ◽  
Two Alternatives

The main purpose of this paper is clarifying the connection between some characteristics of a deciding body and the probability of its making correct decisions. In our model a group of decision makers is required to select one of two alternatives. We assume the probabilities of the decision makers being correct are independent random variables distributed according to the same given distribution rule. This distribution belongs to a general family, containing the uniform distribution as a particular case. We investigate the behavior of the probability of the expert rule being optimal, as well as that of the majority rule, both as functions of the distribution parameter and the group size. The main result is that for any value of the distribution parameter the expert rule is far more likely to be optimal than the majority rule, especially as the deciding body becomes larger.

Aggregation cognitive maps procedure for group decision analysis

Kybernetes ◽  
2016 ◽  
Vol 45 (4) ◽  
pp. 589-603 ◽  
Author(s):  
Annielli Araújo Rangel Cunha ◽  
José Leao Silva Filho ◽  
Danielle Costa Morais
Keyword(s):  
Group Decision ◽  
Cognitive Maps ◽  
Relevant Information ◽  
Decision Makers ◽  
Problem Structuring Methods ◽  
Problem Structuring ◽  
Content Type ◽  
Individual Perceptions ◽  
Single Structure ◽  
The Individual

Purpose – Cognitive maps are used in group decision processes to structure problems. The problem structuring methods helps decision makers to improve the comprehension of the problem, identifying alternative actions and conflicts. However, represents the individual perceptions in a representative group decision into a single structure can be a complex task. The paper aims to discuss these issues. Design/methodology/approach – The objective of this paper is to improve the process of discussion, obtaining the interests and views of the participants and provide parameters to assist the analyst to guide the process. Furthermore, it is possible to analyze how participants are aligned or diverge from the group. The literature review presents some approaches for cognitive maps analysis, but there is a lack of structured methods to analyze them. This paper proposes a structure procedure for the aggregation of cognitive maps in three parts: workshop to generate individual maps, the aggregation of individual maps and the refinement of the global map. Findings – An example illustrates the application of the proposed method and shows the construction of a global map that summarizes the concepts that participants consider important. Originality/value – This paper presents a new procedure that allows reducing the bias of the analyst in the aggregation of individual cognitive maps maintaining the relevant information and allows decision makers know and approve the aggregation procedure.

Applications of Web-QFD and E-Delphi method in the higher education system

2004 ◽  
Vol 23 (4) ◽  
pp. 245-256
Author(s):  
Shun-Hsing Chen ◽  
Ching-Chow Yang
Keyword(s):  
Education System ◽  
Delphi Method ◽  
Quality Function Deployment ◽  
Decision Makers ◽  
The Internet ◽  
Total Quality ◽  
Web Based ◽  
Team Members ◽  
Higher Education System ◽  
The Individual

Quality function deployment (QFD) is an essential tool in implementing total quality management (TQM). This study applies a Web-QFD approach using group decision-making analysis in the Web environment to reduce the complicated data collection, aggregation and analysis processes. A Web-based questionnaire is designed by using an active service pages (ASP) involving the Internet relay chat (IRC) technique and the Delphi method with Internet (E-Delphi) to determine the importance degree of the customers' requirements. However, the traditional Delphi method is time-consuming mission. This study applies the proposed Web-QFD approach to efficiently gather the individual opinions of each team member, the requirements that are critical for customers, and then enables decision makers to accurately assess the priorities of these requirements. An empirical example of an education system in Taiwan is employed to demonstrate the practicability of the proposed Web-QFD model. This real world example involves team members communicating easily and quickly with other experts in the team through the Internet to accelerate the reaching of a consensus among multiple decision makers regardless of where their location. Customers' requirements can be rapidly prioritized based on the assessment results.

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