The theme of this course is “Advanced Analysis of Decision Making.” This course deals with advanced methods of mathematical decision making analysis and primary propositions in mathematical social choice theory through discussion, group work, lectures and working on exercise problems. Specifically, this course takes up: “coalition analysis” and “attitude analysis” in “the Graph Model for Conflict Resolution (GMCR),” “comparison between majority decision and consensus decision,” “characterization of the Condorcet situation with respect to misperception correction,” “Arrow’s theorem”, “Sen’s theorem,” “Gibbard-Sattarthwaite’s theorem,” and “Nakamura’s theorem.”
This course aims to cultivate the students’ abilities to understand advanced methods of mathematical decision making analysis and primary propositions in mathematical social choice theory and to convey them to others concisely.
Upon completion of this course, students should be able to:
1) State the procedures and the meanings of advanced methods of mathematical decision making analysis; and
2) State the contents and the meanings of primary propositions in mathematical social choice theory
coalition analysis, attitude analysis, the Graph Model for Conflict Resolution (GMCR), majority decision, consensus decision, the Condorcet situation, misperception correction, Arrow’s theorem, Sen’s theorem, Gibbard-Sattarthwaite’s theorem, Nakamura’s theorem
Intercultural skills | Communication skills | Specialist skills | Critical thinking skills | Practical and/or problem-solving skills |
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- | ✔ | ✔ | - | - |
One class deals with one analysis method or one primary proposition.
The students examine an analysis method or a primary proposition, first individually, second in pairs, then in groups of four, and finally with the class as a whole. Then a lecture on the analysis method or the primary proposition is presented, and the students work on exercise problems. At the end of the class, each student writes and submits a “summary report” on what he/she learned through individual observation, other students’ ideas, the lecture, and exercise problems.
Course schedule | Required learning | |
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Class 1 | Coalition analysis in the Graph Model for Conflict Resolution (GMCR) | State the procedure and the meanings of coalition analysis |
Class 2 | Attitude analysis in the GMCR | State the procedure and the meanings of attitude analysis |
Class 3 | Comparison between majority decision and consensus decision | State the procedure and the meanings of comparison between majority decision and consensus decision |
Class 4 | A characterization of the Condorcet situation with respect to misperception correction | State the procedure and the meanings of a characterization of the Condorcet situation with respect to misperception correction |
Class 5 | Arrow’s theorem | State the content and the meanings of Arrow’s theorem |
Class 6 | Sen’s theorem | State the content and the meanings of Sen’s theorem |
Class 7 | Gibbard-Sattarthwaite’s theorem | State the content and the meanings of Gibbard-Sattarthwaite’s theorem |
Class 8 | Nakamura’s theorem | State the content and the meanings of Nakamura’s theorem |
None required
Course materials are posted on OCW-i and/or provided during the classes.
Assessment will be based on “summary reports” written during each class (50% in total) and the final examination (50%).
Students must have successfully completed “Graduate Methodologies in Cognition, Mathematics and Information S1” or have equivalent knowledge.
Takehiro Inohara, inohara.t.aa[at]m.titech.ac.jp
Instructor’s office: Rm. 813, 8 Fl., West Bldg. 9. Contact by e-mail in advance to schedule an appointment.
This course consists of the content of science.