3) Non Expected Utility

Question 1

Reflection Effect observed by Khanemann and Tversky

Answer 1

The authors conclude that investors have a changing risk aversion, showing a risk-averse behavior when facing possible gains and a risk-loving behavior when facing possible losses.

Question 2

Certainty Effect observed by Khanemann and Tversky

Answer 2

The authors conclude that there is a nonlinear consideration of probabilities with an over-consideration of events with probability one.

Question 3

Cos’è la prospect theory?

Answer 3

Teoria alternativa al modello dell’expected utility, caratterizzata da:
* sostituzione della tradizionale funzione d’utilità (u) con una value function (v) definita su profitti e perdite sulla ricchezza iniziale e non sulla ricchezza finale. La funzione è concava per i guadagni e convessa per le perdite.
* sostituzione delle probabilità tradizionali (p) con dei decision weights (π), una trasformazione non lineare delle probabilità.

La formulazione matematica è la seguente: consideriamo un giococ he produce n possibili scenari (di perdita o guadagno) xi con probabilità pi.

(Resto in foto)

Question 4

Preference for temporal resolution of uncertainty

Answer 4

Kreps and Porteus showed a deviation from the axioms of individual rationality that occurs when the agent in a position to choose between tables having the same expected utility, shows a systematic preference for situations in which the resolution of uncertainty is anticipated (or postponed).

Question 5

Problems with individual choice and collective decisions

Answer 5

Axioms on individual rationality require that preferences are transitive. While these axioms of rationality are quite reasonable to describe the choice of a single agent, they can be inadequate to represent the preferences of a community. Think to the so-called Condorcet paradox: suppose that voters express their preferences on candidates in a pattern like this:

• 1/3 of voters prefers A ≻ B ≻ C
• 1/3 of voters prefers B ≻ C ≻ A
• 1/3 of voters prefers C ≻ A ≻ B

Collectively we have that A ≻ B by 2/3 of voters, B ≻ C by 2 / 3 of the electorate, C ≻ A from 2/3 of voters and thus a preference based on democratic norms, or the preference of the majority of voters is inevitably intransitive (otherwise we fall into contradiction because
A ≻ A or A is strictly preferred to himself).