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.
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
Expected utility theory, Arrowʼs possibility theorem, Gibbard-Sattarthwaiteʼs theorem, Nakamuraʼs theorem, Senʼs possibility theorem, and Sen’s liberal paradox
|Intercultural skills||Communication skills||Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
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|
|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.|
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, inostaff[at]shs.ens.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.