2. Modelling Violations of EUT

Question 1

Give two restrictions of EUT

Answer 1

Preferences are transitive
Linearity in probabilities

Question 2

What are observed violations of EUT?

Answer 2

Things that have been observed in lab conditions and can’t be explained by EUT

Question 3

What are the 3 elements of prospect theory?

Answer 3

Editing
Probability-weighting
Reference dependence

Question 4

What are the two variants of Allais paradox?

Answer 4

Common ratio effect
Common consequence effect

Question 5

What is the common ratio effect?

Answer 5

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

Question 6

How can we prove the common ratio effect isn’t consistent with EUT?

Answer 6

Unit probability triangle. CRE preferences imply indifference curves can’t be straight parallel lines so CRE isn’t consistent with EUT

Question 7

Why can’t CRE and CCE be explained by linear indifference curves that fan out?

Answer 7

Further research (Starmer 2000) suggests ICs aren’t linear and there is fanning in as well as fanning out

Question 8

What are decision weights equal to in EUT?

Answer 8

Probabilities

Question 9

In the simple non linear probability weighting what do preferences over lotteries maximise?

Answer 9

U(L)= sum of pi(probability) x u(x)

Where pi(.) is a non linear function of probability

Question 10

When does the slope of the indifference curve vary across the triangle?

Answer 10

If pi(.) is non linear

Question 11

When can the simple non linear probability weighting explain common consequence effect?

Answer 11

If the probability weighting function displays sub certainty
pi(p) + pi(1-p) <1 with 1> p>0

Question 12

What is a drawback of simple non linear formulation?

Answer 12

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

Question 13

What do rank dependent theories make weighting depend on?

Answer 13

The position of xi in ordering of consequences as well as on probabilities

Question 14

Key steps of rank dependent/ cumulative decision weights

Answer 14

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

Question 15

Cumulative decision weighting formula in words

Answer 15

Wi= pi(probability of an outcome weakly preferred to xi) - pi(probability of an outcome strictly preferred to xi)

Question 16

How do dominated option and CRE fare under cumulative decision weighting?

Answer 16

Dominated option no longer picked
CRE easily explained by inverse-S probability weighting function

Question 17

What does a steeper indifference curve indicate

Answer 17

Greater risk aversion

Question 18

Explain how the phenomenon of fanning in and fanning out occurs in cumulative decision weighting?

Answer 18

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.

Question 19

What is a caveat to the inverse-s weighting function?

Answer 19

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

Question 20

What does Bardalo Et al 2012 propose?

Answer 20

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

Question 21

What is editing?

Answer 21

The idea that people simplify problems in their head before they apply any preference to it

Question 22

What is u(x2)/(1-u(x2)) equal to?

Answer 22

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

Question 23

In EUT when does capturing attitudes to risk only in the utility function work as a modelling strategy?

Answer 23

This only works as a modelling strategy if attitude to risk is uniform across the triangle

Question 24

Who postulated about overweighting of small probabilities and underweighting elsewhere?

Answer 24

Kahneman and Tversky 1979

Question 25

What does attitude to risk depend on in the simple non-linear probability weighting model?

Answer 25

Not only the shape of the utility function but also the shape of the probability weighting function (ie pi)

Question 26

What do some say the Allais paradox shows?

Answer 26

Dis-continuity of preferences in neighbourhood of certainty rather than the more general departures from EUT