### 2016　Graduate Lecture in Cognition, Mathematics and Information S1B

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Graduate major in Social and Human Sciences
Instructor(s)
Inohara Takehiro
Course component(s)
Lecture
Day/Period(Room No.)
Tue1-2(W9-707)
Group
-
Course number
SHS.M442
Credits
1
2016
Offered quarter
2Q
Syllabus updated
2016/4/27
Lecture notes updated
2016/7/14
Language used
English
Access Index

### Course description and aims

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.

### Student learning outcomes

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

### Keywords

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

### Competencies that will be developed

Intercultural skills Communication skills Specialist skills Critical thinking skills Practical and/or problem-solving skills
- - -

### Class flow

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

Course schedule Required learning
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

### Reference books, course materials, etc.

Course materials are posted on OCW-i and/or provided during the classes.

### Assessment criteria and methods

Assessment will be based on “summary reports” written during each class (50% in total) and the final examination (50%).

### Related courses

• SHS.M443 ： Graduate Lecture in Cognition, Mathematics and Information F1A
• SHS.M444 ： Graduate Lecture in Cognition, Mathematics and Information F1B
• SHS.M461 ： Graduate Methodologies in Cognition, Mathematics and Information S1
• SHS.L411 ： Trans-disciplinary Exercise in Social and Human Sciences S1A
• SHS.L412 ： Trans-disciplinary Exercise in Social and Human Sciences S1B

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students must have successfully completed “Graduate Methodologies in Cognition, Mathematics and Information S1” or have equivalent knowledge.

### Contact information (e-mail and phone)    Notice : Please replace from "[at]" to "@"(half-width character).

Takehiro Inohara, inohara.t.aa[at]m.titech.ac.jp

### Office hours

Instructor’s office: Rm. 813, 8 Fl., West Bldg. 9. Contact by e-mail in advance to schedule an appointment.

### Other

This course consists of the content of science.