Теория выбора и принятия решений

Бакалавриат 2019/2020

Лучший по критерию «Полезность курса для Вашей будущей карьеры»

Лучший по критерию «Полезность курса для расширения кругозора и разностороннего развития»

Статус: Курс по выбору (Прикладная математика и информатика)

Направление: 01.03.02. Прикладная математика и информатика

Кто читает: Департамент математики

Где читается: Факультет компьютерных наук

Когда читается: 3-й курс, 1, 2 модуль

Формат изучения: Full time

Преподаватели: Алескеров Фуад Тагиевич, Доган Эмре, Егорова Людмила Геннадьевна

Язык: английский

Кредиты: 5

Полная версия программы учебной дисциплины

Аннотация

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.

Цель освоения дисциплины

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

Результаты освоения дисциплины

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

Содержание учебной дисциплины

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.