Behavioral eco-lect 4: Choice under risk and uncertainty part 3 (Sure…
Behavioral eco-lect 4: Choice under risk and uncertainty part 3
Sure thing principle
A person who maximizes expected utility satisfies the sure thing principle:
If (p: x, p2: x2, … , pn: xn) ≽ (p: x, q2: y2, … , qn: yn)
then (p: α, p2: x2, … , pn: xn) ≽ (p: α, q2: y2, … , qn: yn) for all α.
If two lotteries have a common outcome that is received with equal probability, then replacing that common outcome by another common outcome does not affect preferences.
slide 24/55 : if .... then we can replace x by any other outcome without affecting the indifference
N.B. it is possible that x2=x, but y2 =/ x
Choice under risk: violations of expected utility
slide 26-27/55 Asian disease
Irrespective of your risk attitude, you should choose C if you have chosen A and you should choose D if you have chosen B
Reference points and the utility function (=value function) of prospect theory can explain the findings.
Asian disease problem explained
A vs B
reference point = ‘nobody will be saved’, so A and B are about gains
utility is concave for gains
→ risk averse in this case
C vs D
reference point = ‘nobody will die’, so A and B are about losses
utility is convex for losses
→ risk seeking in this case
Prospect theory utility function
a change from 0 to 10 appears larger than a change from 100 to 110, both for gains and for losses
concave utility for gains
convex utility for losses
– risk attitudes for gains are opposite of risk attitudes for losses – risk averse for gains and risk seeking for losses.
Prospect theory utility function cont.
Reflection effect is not due to loss aversion!
Loss aversion says that losses loom larger than gains
The Allais problem
The Allais problem is a violation of the
sure thing principle.
: people overweight outcomes that are certain.
In prospect theory this is captured by probability weighting – transforming probabilities before multiplying them with utilities – to be covered in future courses.
Prospect theory- summary
Prospect theory has several components
The utility function satisfies diminishing sensitivity and loss aversion.
Probability weighting – transforming probabilities
People evaluate outcomes relative to a reference point.
NB: Prospect theory does not say what the reference point is.