The course "Normative Decision Theory" was conveyed by discusing on seminars different topics taken out from the book "Decision, probability and utility" by Peter Gärdenfors and Nils-Eric Sahlin.
I considered important the following topics:
- Bayesian decision theory
The four original statements of decision theory are presented :
A1- The values of the outcomes in a decision situation are determined by a utility measure which assigns numerical values to the outcomes.
A2 - In arriving to a decision, the only information exploitable by the decision's maker is the utilities of the possibles outcomes of the alternatives.
A3 - The beliefs about the states of the world are represented by a unique probability measure defined over the states.
A4 - For all states and all alternatives, the probability of the states are independent of the act chosen.
In this traditional theory the evaluation criteria is driven by the principle of maximal expected utility
The expected utility is expressed this way :
EU(Ai) = P(S1)xU(Oi1) + ... +P(Sm)xU(Oim),
where Ai is the ith alternative, P(Si) is the probability assigned to the state Si (subjective), and U(Oij) is the utility value assigned to the outcome Oij.
Observe that here is supposed that the decision maker knows the probability of the states. This situation is known as decision making under risk. When the probability of the states are unknown then we have a decision situation under uncertainty. These are considered the two extrem points of decision situations.
In order to give an axiomatic form to the Bayesian theory, Savage proposes a system of preferences, so the different alternatives can be ordered. To do that, Savage issues the sure-thing principle which stablish the existence of a preference order between two sets of alternatives, no matter the occurrence of some set of events.
- Unreliable probabilities, risk taking, and decision making.
Is usual to think that the Bayesian proposal is too restrictive, and many experiments show that fact. Peter and Sahlin, the authors of the book, present a theory of decision, where, instead of considering a unique probability distribution, a set of distribution is proposed in order for the decision maker to arrive to a decision. In this way, intervals of probabilities result, and the range from decision under risk and decision under uncertainty is covered. Observe that when an interval is reduced to one point, decision under risk (traditional theory) is obtained, and when the whole interval or a subinterval of (0,1) result, then decision under uncertainty is obtained.
- My opinion is :
Through the book, a special attention is payed to the state of the world and the beliefs on them. My opinion is that there is no intention to assume a general structure of the world in order to attack the states. I do think there is a general structure of the world, one unconscientiously assumes in taking decisions. Another problem is that the analysis is too centered on simple situation games. Is true that life is like a game, but is not such a simple game; many factors and combination of them get into the field. I also think that a superficial analysis was made when discussing the Allais' paradox against the sure-thing principle , which I see as an asymptotic behavior in the beliefs.
However, the book encouraged me to get a little bit more into the subject of agents involved in decision situations; it was my first trip.