Course syllabus: Mathematics of decision making

An executive officer, who makes a decision, shall know whether his choice is adequate. What facts, data and expert estimations could prove the quality of a decision? This course presents methods of data and expert estimation collection, processing and modeling, which are necessary to make an adequate decision. The methods are intended to be used in the daily-routine practice and are supported by algorithms. The goal of the course is to learn how to state the problem of decision-making, where to collect necessary data, how to gather expert estimations and how to prove that the decision is optimal. The course includes 30 hours of lectures, 10 hours of workshops, one case test and the exam.

The feed-back management model
1. Decision problem understanding
2. Data understanding and collection
3. Data scales and admissible operations
Data preprocessing
1. General statistics
2. Data normalization and recoding
3. Data mining
4. Model selection
Collection of expert estimation
1. Who is an expert?
2. Psychology of expertise
3. How to make a questionnaire?
4. Delphi method
Voting systems
1. Voting procedures
2. Instant-runoff voting
3. Condorcet method
4. Kemeny-Young method
5. Arrow’s paradox of impossibility
Construction of integral indicators
1. Distance to the best
2. Linear models
3. Principal component analysis
4. Pareto optimal front and Pareto slicing
5. Non-parametric models
6. Pairwise comparison
Combining data and expert estimations
1. Linear-scale concordance
2. Ordinal-scale concordance
3. Multiple experts estimations
4. Statistical learning for indexes
Decision support systems
1. Specification of expert estimations
2. What index model we have to choose?
3. How to use expert estimations?
4. Quality of the decision
How to use indexes?
1. Error analysis
2. Model validation
3. Presentation of decision results

Prerequisites: Knowledge of linear algebra and mathematical statistics is required.

Grading:

Exam 80%
Case test 20%