2. Modelling Violations of EUT Flashcards
Give two restrictions of EUT
Preferences are transitive
Linearity in probabilities
What are observed violations of EUT?
Things that have been observed in lab conditions and can’t be explained by EUT
What are the 3 elements of prospect theory?
Editing
Probability-weighting
Reference dependence
What are the two variants of Allais paradox?
Common ratio effect
Common consequence effect
What is the common ratio effect?
The systematic tendency to prefer L2 in problem 1 and L3 in problem 2. Where problem 2 comes from 1 by scaling down probabilities of all non zero outcomes by common ratio
How can we prove the common ratio effect isn’t consistent with EUT?
Unit probability triangle. CRE preferences imply indifference curves can’t be straight parallel lines so CRE isn’t consistent with EUT
Why can’t CRE and CCE be explained by linear indifference curves that fan out?
Further research (Starmer 2000) suggests ICs aren’t linear and there is fanning in as well as fanning out
What are decision weights equal to in EUT?
Probabilities
In the simple non linear probability weighting what do preferences over lotteries maximise?
U(L)= sum of pi(probability) x u(x)
Where pi(.) is a non linear function of probability
When does the slope of the indifference curve vary across the triangle?
If pi(.) is non linear
When can the simple non linear probability weighting explain common consequence effect?
If the probability weighting function displays sub certainty
pi(p) + pi(1-p) <1 with 1> p>0
What is a drawback of simple non linear formulation?
Sub certainity pi(p) + pi(1-p) < 1
This may be a psychologically plausible feature of how agents perceive probabilities if probability weighting function pi(p) interpreted in that way. But it is arguably unattractive for decision weights to sum to less than unity. This can allow the choice of a dominated gamble
What do rank dependent theories make weighting depend on?
The position of xi in ordering of consequences as well as on probabilities
Key steps of rank dependent/ cumulative decision weights
Impose pi(1)=1 and pi(0)=0
Distinguish decision weights from probability weights
Make decision weights depend on i’s place in ordering of consequences in a way that forces decision weights to sum to 1
Cumulative decision weighting formula in words
Wi= pi(probability of an outcome weakly preferred to xi) - pi(probability of an outcome strictly preferred to xi)
How do dominated option and CRE fare under cumulative decision weighting?
Dominated option no longer picked
CRE easily explained by inverse-S probability weighting function
What does a steeper indifference curve indicate
Greater risk aversion
Explain how the phenomenon of fanning in and fanning out occurs in cumulative decision weighting?
Along a “long” vertical line (starting at bottom) numerator of second term is constant but denominator starts high, falls, then rises again.
Along a “long” horizontal line (starting at left) denominator of second term is constant but numerator starts high, falls, then rises again.
What is a caveat to the inverse-s weighting function?
Estimates of the inverse -s weighting function are mainly from experiments with stated probabilities. Things may be different if probabilities have to be learned by experience or are ambiguous
What does Bardalo Et al 2012 propose?
Uncertainty represented by states which have weights. Decision weight on a state depends not only on its probability but also on difference in possible outcomes in that state
What is editing?
The idea that people simplify problems in their head before they apply any preference to it
What is u(x2)/(1-u(x2)) equal to?
The slope of the indifference curve and attitudes to risk embedded in the utility function of EUT when we scale u(x1)=1 and u(x3)=0
In EUT when does capturing attitudes to risk only in the utility function work as a modelling strategy?
This only works as a modelling strategy if attitude to risk is uniform across the triangle
Who postulated about overweighting of small probabilities and underweighting elsewhere?
Kahneman and Tversky 1979
What does attitude to risk depend on in the simple non-linear probability weighting model?
Not only the shape of the utility function but also the shape of the probability weighting function (ie pi)
What do some say the Allais paradox shows?
Dis-continuity of preferences in neighbourhood of certainty rather than the more general departures from EUT
