Decision Theory

Course Code : IA355

Time Hours : 18 hours

Time Period : not available yet

Lecturers :

Alexis Tsoukias, Research Director, Alexis.Tsoukias[at]lamsade.dauphine.fr

Elise Bonzon, Assistant Professor, elise.bonzon[at]parisdescartes.fr

Objective : The objectives of this course are to allow the students to

  •  Understand, model and resolve decision problems
  •  Handle more common models in decision theory and be able to propose extension in more complex situations
  •  Know about decision-making under uncertainty
  •  Know about Multi-Criteria Decision Analysis

Contents

  •  Preference modelling (2 sessions of 1h30) : ordering structures, preference structures, numerical representations, measurement theory
  •  Decision making under uncertainty (4 sessions of 1h30) : probabilities and values ; von Neuman and Morgenstern axioms ; expected utility ; conditional probability ; decision trees ; information value ; practical studies.
  •  Social choice theory (3 sessions of 1h30) : Introduction ; analysis of different election systems ; impossibility results (Condorcet paradoxe ; Arrow theorem) ; presentation of several methods of choice and aggregation (Borda, Condorcet …), and analysis of several properties (transitivity, monotonicity ; unanimity)
  •  Multi-Criteria Decision Analysis (3 sessions of 1h30) : scoring methods (utility theory ; elicitation of decision parameters ; analysis of these methods) ; Preferences for multi-attribute consequences ; meaningfulness

References

  •  Evaluation and decision models : a critical perspective by D. Bouyssou, T. Marchant, M. Pirlot, P. Perny, A. Tsoukiàs, and Ph. Vincke. Kluwer Academic, Dordrecht, 2000.
  •  Social Choice and Individual Values by K. J. Arrow. Second Edition, Wiley,1963.
  •  Collective Choice and Social Welfare by A. K Sen. 1970.
  •  Axioms of Cooperative Decision Making. by H. Moulin. Cambridge University Press, 1988.
  •  Arrow’s Impossibility Theorems. Academic Press by J. S. Kelly. 1978.
  •  Social Choice Theory : An Introduction by J. S. Kelly. Springer Verlag, 1988.
  •  Interval Orders and Interval Graphs by P.C. Fishburn. J.Wiley, New York, 1985.
  •  Preference modelling by M. Öztürk, A. Tsoukiàs, and Ph. Vincke.
  •  Multiple Criteria Decision Analysis : State of the Art Surveys, pages 27-73. by M. Ehrgott, S. Greco, and J. Figueira, editors, Springer, 2005
  •  Utility Theory for Decision Making by P.C. Fishburn. Wiley, New York, 1970.
  •  Measurement Theory, by F.S. Roberts, Addison Wesley, 1979.
  •  Deciding with Multiple Objectives by H. Raiffa, R., Keeney, J. Wiley, 1976
  •  Decision Theory : an introduction to the mathematics of rationality by S. French, Ellis Horwood, 1986
  •  Smart Choices by J.S. Hammond, R. Keeney, H. Raiffa, Harvard Business School Press, 1999
  •  Additive representations of preferences – A new foundation of decision analysis by P.P. Wakker, Kluwer Academic, 1989.
  •  Utility maximisation, choice and preference by F. Aleskerov, D. Bouyssou, B. Montjardet, Springer Verlag, 2006.