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- 工学院，物質理工学院，環境・社会理工学院共通科目
- Liberal arts and basic science courses
- First-Year Courses
- School of Science
- School of Engineering
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- School of Life Science and Technology
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School of Environment and Society
- Department of Architecture and Building Engineering
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- Department of Social and Human Sciences
- Department of Innovation Science
- Graduate major in Technology and Innovation Management
- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Social and Human Sciences
- Instructor(s)
- Inohara Takehiro
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Tue1-2(W9-707)
- Group
- -
- Course number
- SHS.M442
- Credits
- 1
- Academic year
- 2017
- Offered quarter
- 2Q
- Syllabus updated
- 2017/9/6
- Lecture notes updated
- 2017/7/3
- Language used
- English
- Access Index
-
Course description and aims
The theme of this course is “Mathematical Decision Making.” This course deals with primary propositions in mathematical decision making theory and mathematical social choice theory through discussion, group work, lectures and working on exercise problems. Specifically, this course takes up: “Expected utility theory,” “Arrowʼs possibility theorem,” “Gibbard-Sattarthwaiteʼs theorem,” “Nakamuraʼs theorem,” “Senʼs possibility theorem,” and “Sen’s liberal paradox.” This course aims to cultivate the studentsʼ abilities to understand primary propositions in mathematical decision making theory and 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 contents and the meanings of primary propositions in mathematical decision making theory; and
2) State the contents and the meanings of primary propositions in mathematical social choice theory
Keywords
Expected utility theory, Arrowʼs possibility theorem, Gibbard-Sattarthwaiteʼs theorem, Nakamuraʼs theorem, Senʼs possibility theorem, and Sen’s liberal paradox
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | ✔ Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
One class deals with one primary proposition.
The students examine 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 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 studentsʼ ideas, the lecture, and exercise problems.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Guidance and introduction | State the definitions of “decision making” and “social choice.” |
| Class 2 | Expected utility theory | State the content and the meanings of expected utility theory. |
| Class 3 | Arrowʼs possibility theorem | State the content and the meanings of Arrowʼs possibility theorem. |
| Class 4 | Gibbard-Sattarthwaiteʼs theorem | State the content and the meanings of Gibbard-Sattarthwaiteʼs theorem. |
| Class 5 | Nakamuraʼs theorem | State the content and the meanings of Nakamuraʼs theorem. |
| Class 6 | Senʼs possibility theorem | State the content and the meanings of Senʼs possibility theorem. |
| Class 7 | Sen’s liberal paradox | State the content and the meanings of Sen’s liberal paradox. |
| Class 8 | Review | Explain the outline of the knowledge structure on mathematical decision making to others. |
Textbook(s)
Not 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, inostaff[at]shs.ens.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.
