Choice and Decision Theory
- 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
- 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
- Mathematical Model of the Decision Making SituationDecision making, its participants and stages. Mathematical Theory of Measurement.
- Utility, Preference and ChoiceUtility function, value function. Binary relations of preference and indifference. Choice functions, their properties. Optimal and undominated alternatives. Context-dependent interval choice.
- Internal and External stabilityCore. 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.
- NetworksMain notions. Classic centrality measures. Short- and Long-Range Interaction. Centralities. Applications.
- Political Decision MakingDownsian Analysis. Spatial Model of Voting. McKelvey’s Theorem. Manipulation of agents.
- Polarization in parliaments: uni- and multidimensional casesPower 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 problemUnicriterial assignment problem. Multicriterial assignment problem. Optimality criterion. Two-sided matchings. One-to-many matchings. Many-to-many matchings. Applications.
- Interim assessment (2 module)0.6 * final exam + 0.2 * homework + 0.2 * mid-term exam
- 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
- 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