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Regular version of the site
Bachelor 2019/2020

# Choice and Decision Theory

Category 'Best Course for Career Development'
Category 'Best Course for Broadening Horizons and Diversity of Knowledge and Skills'
Area of studies: Applied Mathematics and Information Science
When: 3 year, 1, 2 module
Mode of studies: offline
Language: English
ECTS credits: 5
Contact hours: 60

### Course Syllabus

#### Abstract

This course presents an introduction to individual and social choice and decision theory. We will introduce and analyse models of individual decision making in forms of binary relations and choice functions, their rationalization by utility functions and properties of rational choice, methods of collective decision making and their properties, problem of power evaluation and theory of matchings as an example of applied problem.

#### Learning Objectives

• to familiarize students with the basic concepts, models and statements of the theory of choice and decision making
• to familiarize students with the power assessment in voting and in network structures
• to familiarize students with the matching theory

#### 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 properties of social choice rules
• know the concept of manipulation in collective decision making
• know centrality measures in networks
• know the deferred acceptance algorithm and be able to use it in order to find a stable matching

#### Course Contents

• Mathematical Model of the Decision Making Situation
Decision making, its participants and stages. Mathematical Theory of Measurement.
• Utility, Preference and Choice
Utility function, value function. Binary relations of preference and indifference. Choice functions, their properties. Optimal and undominated alternatives. Context-dependent interval choice.
• Internal and External stability
Core. Some rules: position rules, rules based on majority relation, rules based on auxiliary number scale, rules based on tournament matrix. Threshold aggregation rule. Superposition of choice rules.
• Networks
Main notions. Classic centrality measures. Short- and Long-Range Interaction. Centralities. Applications.
• Political Decision Making
Downsian Analysis. Spatial Model of Voting. McKelvey’s Theorem. Manipulation of agents.
• Polarization in parliaments: uni- and multidimensional cases
Power distribution in electoral bodies. Classical power indices: Banzhaf index, Shapley-Shubik index, Johnston index, Deegan-Pakel index. Power indices taking into account agent’s preferences to coalesce. Applications.
• Assignment problem
Unicriterial assignment problem. Multicriterial assignment problem. Optimality criterion. Two-sided matchings. One-to-many matchings. Many-to-many matchings. Applications.

#### Assessment Elements

• homework
• mid-term exam
• final exam

#### Interim Assessment

• Interim assessment (2 module)
0.6 * final exam + 0.2 * homework + 0.2 * mid-term exam

#### Recommended Core Bibliography

• Aleskerov F., Bouyssou D., Monjardet B. ‘Utility Maximization, Choice and Preference’, Springer Verlag, Berlin, 2007
• Centrality measures in networks based on nodes attributes, long-range interactions and group infl..., Aleskerov, F., 2016
• 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
• Multidimensional polarization index and its application to an analysis of the russian state duma ..., Aleskerov, F., 2016
• Power and preferences : an experimental approach. Препринт WP7/2010/05, Aleskerov, F., 2010

#### Recommended Additional Bibliography

• Arrow, K. J. (2012). Social Choice and Individual Values (Vol. 3rd ed). New Haven, Conn: Yale University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=470436
• 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
• Network analysis of international migration. Препринт WP7/2016/06, Aleskerov, F., 2016
• Utility maximization, choice and preference : with 49 figures and 28 tables, Aleskerov, F., 2007