This course deals with basic concepts of theory of committees, which is a mathematical theory of group decision making situations, through discussion, group work, lectures, and working on exercise problems. Specifically, this course takes up: “simple games,” “committees,” “desirability relations on coalitions,” “cores of committees,” “consistent coalitions,” “permissible ranges of decision makers,” “permission games,” “hopefulness relations on coalitions,” “stable coalitions and stable alternatives,” “postulated permissible ranges,” “regretless alternatives,” and “characterizations of cores of committees.”
This course aims to cultivate the students’ abilities to understand basic concepts of theory of committees, and also to convey them to others concisely.
Upon completion of this course, students should be able to:
1) State the definitions of basic concepts used in the mathematical theories of group decision making situations; and
2) State the analysis methods in the mathematical theories of group decision making situations.
simple games, committees, desirability relations on coalitions, cores of committees, consistent coalitions, permissible ranges of decision makers, permission games, hopefulness relations on coalitions, stable coalitions and stable alternatives, postulated permissible ranges, regretless alternatives, and characterizations of cores of committees
|Intercultural skills||Communication skills||Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
One class deals with one basic concept.
The students examine definitions and analysis methods of basic concepts, first individually, second in pairs, then in groups of four, and finally with the class as a whole. Then a lecture on the basic concept 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|
|Class 1||Simple games||State the definition of simple games|
|Class 2||Committees||State the definition of committees|
|Class 3||Desirability relations on coalitions||State the definition of desirability relations on coalitions|
|Class 4||Cores of committees||State the definition of cores of committees|
|Class 5||Consistent coalitions||State the definition of consistent coalitions|
|Class 6||Permissible ranges of decision makers and permission games||State the definitions of permissible ranges of decision makers and permission games|
|Class 7||Hopefulness relations on coalitions||State the definition of hopefulness relations on coalitions|
|Class 8||Stable coalitions and stable alternatives||State the definitions of stable coalitions and stable alternatives|
|Class 9||Postulated permissible ranges||State the definition of postulated permissible ranges|
|Class 10||Regretless alternatives||State the definition of regretless alternatives|
|Class 11||A characterizations of cores of committees||State the content and the meanings of a characterizations of cores of committees|
|Class 12||A re-definition of committees with permissible ranges of decision makers||State the content and the meanings of a re-definition of committees with permissible ranges of decision makers|
|Class 13||A generalization of cores of committees||State the content and the meanings of a generalization of cores of committees|
|Class 14||Stability and regretless-ness of alternatives||State the definitions of stability and regretless-ness of alternatives|
|Class 15||A characterization of generalized core of committees||State the content and the meanings of a characterization of generalized core of committees|
Takehiro Inohara, “Rationality and Flexibility,” Keiso-syobo, 2002 (in Japanese) (Section 1.2, Section 2.1, Chapter 7, Chapter 8, Chapter 9）(ISBN-10: 4326502223, ISBN-13: 978-4326502226)
Takehiro Inohara, “Emotions and Perception,” Keiso-syobo, 2002 (in Japanese) (ISBN-10: 4326502231, ISBN-13: 978-4326502233). Course materials are found on OCW-i or provided during class.
Assessment will be based on “summary reports” written during each class (50% in total) and the final examination (50%).
Prospective students should have interests in decision making problems. Students must have successfully completed both “Decision Making A” and “Decision Making B” 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 includes the content of science.