Bachelor 2020/2021

Individual and Social Choice

Type: Elective course (Applied Mathematics and Information Science)

Area of studies: Applied Mathematics and Information Science

Delivered by: Department of Mathematics

Where: Faculty of Computer Science

When: 4 year, 1, 2 module

Mode of studies: offline

Instructors: Emre Dogan

Language: English

ECTS credits: 5

Contact hours: 60

Course Syllabus

Abstract

The course includes main notions and stages of decision making, uni- and multicriterial models, rationality of individual and social decisions, main notions of utility theory, choice models, and their use in applied problems

Learning Objectives

• To familiarize students with the concepts, models and statements of the theory of individual and collective decision making

Expected Learning Outcomes

• know properties and special classes of binary relations
• know the concept of ordinal utility
• know choice functions and their rationalization by utility functions and binary relations
• know the concept of expected utility and its axiomatization
• know properties of social choice rules
• know the concept of manipulation in collective decision making
• know principles of models construction in decision analysis
• be able to choose rational options in practical decision-making problems

Course Contents

• Introduction to decision making problem. Binary relations and their properties. Main classes of binary relations: linear orders, weak orders, partial orders
• Individual decision making. Preferences, utility functions and their relation to binary relations. Ordinal utility. Choice functions and their properties.
• Interval choice. Interval orders and semiorders and their properties. Interval orders and semiorders representation theorem.
• Theory of expected utility. Lotteries. Fon Neumann-Morgenstern axioms. Violation of expected utility principles: May paradox, Allais paradox, Ellsberg paradox. Saint-Petersburg paradox.
• Collective decision making. Local aggregation models PP. Rationality of individual behavior. Independence of irrelevant alternatives axiom. List representation of procedures. Normative properties of social choice procedures. Rationality restrictions. Federation rules and its cases: dictatorship, oligarchy and collegium.
• Local aggregation models CC and PC. Normative properties of functional aggregation rules and social choice correspondence. Rationality restrictions. Q-federation rules and its cases.
• Non-local aggregation. Positional rules. Threshold aggregation. Axioms of threshold aggregation. Application of these rules.
• Manipulation in social choice. Degree of manipulability of rules. Gibbard-Satterthwaite theorem.

Assessment Elements

• homework
  The homework consisting of several tasks. Students are encouraged to work together to help each other in understanding the course material and completing the homework problems. However, everybody has to write up his/her own solutions. Late homework will not be accepted. The common mistakes made in the homework will be discussed during the seminars.
• midterm
• final exam
• attendance

Interim Assessment

• Interim assessment (2 module)
  0.3 * midterm + 0.1 * attendance + 0.4 * final exam + 0.2 * homework

Bibliography

Recommended Core Bibliography

• Aleskerov F., Bouyssou D., Monjardet B. ‘Utility Maximization, Choice and Preference’, Springer Verlag, Berlin, 2007
• Fuad Aleskerov, Denis Bouyssou, & Bernard Monjardet. (2007). Utility Maximization, Choice and Preference. Post-Print. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsrep&AN=edsrep.p.hal.journl.halshs.00197186

Recommended Additional Bibliography

• Fuad Aleskerov, & Andrey Subochev. (2013). Modeling optimal social choice: matrix-vector representation of various solution concepts based on majority rule. Journal of Global Optimization, (2), 737. https://doi.org/10.1007/s10898-012-9907-2