Group Decision Making Under Multiple Criteria: Methods and Applications

I. Introduction.- II. Social Choice Theory.- 1. Voting.- 1.1 Nonranked Voting System.- 1.1.1 One Nember Elected From Two Candidates.- 1.1.2 One Nember Elected From Many Candidates.- (a) The First-Past-The-Post System.- (b) Majority Representation System.- Repeated Ballots.- The Second Ballot.- Note:.- Case 1 of Dodgson.- Case 2 of Dodgson.- Case 3 of Dodgson Modified.- 1.1.3 Election of Two or Nore Nembers.- 1.1.3.1 The Single Nontransferable Vote.- 1.1.3.2 Multiple Vote.- 1.1.3.3 Limited Vote.- 1.1.3.4 Cumulative Vote.- 1.1.3.5 List Systems.- (a) Highest Average.- (b) Greatest Remainder.- 1.1.3.6 Approval Voting.- 1.2 Preferential Voting System.- 1.2.1 Simple Majority Decision Rule.- 1.2.1.1 Two-Alternative Case.- 1.2.1.2 More Than Two Alternatives Case.- (a) Paradox of Voting.- Example 1 of Condorcet.- Example 2 of Condorcet.- (b) The Condorcet Effect.- Note: Nonminority Rule.- 2. Social Choice Function.- 2.1 Introduction.- Condorcet Principle.- 2.2 Notation, Definitions and Basic Properties.- 2.3 Condorcet's Function.- 2.4 Borda's Function.- 2.5 Copeland's Function.- 2.6 Nanson's Function.- 2.7 Dodgson's Function.- 2.8 Kemeny's Function.- 2.9 Cook and Seiford's Function.- 2.10 Fishburn's Function.- 2.11 Eigenvector Function.- 2.12 Bernardo's Assignment Approach.- 2.13 Cook and Seiford's Ordinal Intersection Method.- 3. Social Welfare Function.- 3.1 Introduction.- 3.2 Notation and Statement of Problem for Social Choice and Individual Values.- 3.3 Arrow's Conditions for Social Welfare Function.- 3.4 Arrow's Possibility Theorem for Two Alternatives.- 3.5 Arrow's General Possibility Theorem.- 3.6 Black's Single-Peaked Preferences.- 3.7 Bowman and Colantoni's Approach.- 3.8 Goodman and Markowitz's Approach.- 3.9 Cardinal Social Welfare Function.- 3.9.1 Value Function for Certainty Case.- 3.9.2 Utility Function for Uncertainty Case.- 3.9.2.1 Additive Group Utility Function.- 3.9.2.2 Multiplicative Group Utility Function.- 3.9.3 Some Applications.- 3.9.3.1 Gynnastics Conpetitions.- 3.9.3.2 Extended Contribution Rule Method (ECR Method).- 3.9.3.3 The Selection of Trajectories for the Marine Jupiter/Saturn 1977 Project.- 3.10 Comparison Between Arrow's Conditions for Social Welfare Function and Properties of Social Choice Function..- III. Experts Judgment and/or Group Participation.- 1. Introduction.- 2. Brainstorming.- 2.1 Introduction.- 2.2 Rules and Procedure for Brainstorming Method.- 2.3 Advantages and Disadvantages.- 2.4 Note on Various Modified Techniques.- 3. Brainwriting.- 3.1 Introduction.- 3.2 Procedure of Brainwriting Pool and Its Discussion.- 3.3 Brainwriting and Its Variations.- 4. The Nominal Group Technique (NGT).- 4.1 Introduction.- 4.2 The Nominal Group Technique Process.- 4.3 Advantages and Disadvantages of NGT.- 5. Synectics.- 5.1 Introduction.- 5.2 The Process of Synectics.- 5.3 Advantages and Disadvantages of Synectics.- Note.- 6. Surveys.- 6.1 Introduction.- 6.2 Survey Procedure.- 6.3 Advantages and Disadvantages of Surveys.- 7. Delphi Method.- 7.1 Introduction.- 7.2 The Procedure of Delphi Method.- 7.3 Advantages and Disadvantages of Delphi Method.- Note.- 7.4 Example.- 8. Conferences.- 8.1 Introduction.- 8.2 Planning and Conducting the Conference.- Note.- 9. Successive Proportional Additive Numeration or Social Participatory Allocative Network (SPAN).- 9.1 Introduction.- 9.2 The Procedure of SPAN Technique.- 9.3 Example.- 9.4 Advantages and Disadvantages of SPAN.- 10. Interpretive Structural Modeling (ISM).- 10.1 Introduction.- 10.2 The Procedure of ISM.- 10.3 Digraphs, Binary Matrices, and Computer Inplementation.- 10.4 Example: Urban Planning for Dayton, Ohio.- 10.5 Advantages and Disadvantages of ISM.- 11. Decision Making Trial and Evaluation Laboratory (Dematel).- 11.1 Introduction.- 11.2 Objectives, Ideas, and Goals.- 11.3 Procedure.- 11.3.1 Franework of the World Problematique.- 11.3.2 Participants.- 11.3.3 Questions Asked.- 11.3.4 Analysis of Individual Perceptions of World Problematique.- 11.3.5 Analysis of the Average Perceptions by Group of the World Problematique.- 11.3.6 Comparison of Individual Perceptions of the World Problematique.- 11.4 Example: Perception of the World Problematique.- Note.- 12. Cognitive Map.- 12.1 Introduction.- 12.2 Basic Elements of a Cognitive Map.- 12.3 Analysis of Signed Digraph.- 12.4 The Cognitive Map of Collectivities.- 12.5 Inferring the Properties of a Cognitive Map.- 12.6 Example: Building and Analyzing an Energy Demand Signed Digraph.- 12.7 The Limitation of the Cognitive Map.- 13. Kane's Simulation (KSIM).- 13.1 Introduction.- 13.2 The Procedure of KSIM.- 13.3 Example: Shall We Permit Bird Hunting in Eco Valley?.- 13.4 Advantages and Disadvantages of KSIM.- 13.5 Other Simulations.- Note.- 14. Implementing and Controlling a Project.- 14.1 Introduction.- 14.2 Gantt Chart.- 14.3 Program Evaluation Review Technique (PERT) and Critical Path Method (CPM).- 14.4 The Planning-Programming-Budgeting System (PPBS).- 14.5 DELTA Chart.- 15. Group Decision Making Under Multiple Criteria for Evaluation/Selection of Alternatives.- 15.1. Introduction.- 15.2. A General Formulation.- 15.3. The Ordinal Approach.- 15.3.1 The Agreed Criteria Approach.- 15.3.2 The Individual Approach.- 15.3.3 Numerical Example.- 15.4. The Cardinal Approach.- 15.4.1 The Agreed Criteria Approach.- 15.4.2 The Individual Approach.- 15.4.2.1 The Additive Weighted Value Approach.- 15.4.2.2 Topsis and Borda'S Function Approach.- 15.4.3 Example.- 15.5 Note.- 16. A Systems Approach to Expert Judgments and/or Group Participation Analysis.- 16.1 Introduction.- 16.2 Processes in the Systems Approach.- 16.3 Note.- IV. Game Theory.- 1. Introduction.- 2. Some Basic Concepts.- The Extensive Form of a Game.- The Normal Form of a Game.- The Characteristic Function Form of a Game.- Cooperative and Noncooperative Games.- Essential and Inessential Games.- Zero-Sum, Constant-Sum, General-Sum Games.- 3. The Normal form Payoff Function.- 3.1 Introduction.- 3.2 Pareto Optimal Set.- 3.3 The Nash-Harsanyi Arbitration Solution.- 3.4 Compromise Solution.- 4. The Characteristic Function Form.- 4.1 Introduction.- 4.2 Core Concept.- 4.3 Shapley Value.- 4.4 The Parametric Approach.- V. Concluding Remarks.- VI. References.