4 - Expected utility theory and what might be wrong with it Flashcards
what is the standard model of decision making under risk
expected utility theory
what is the BE model of decision making under risk
prospect theory
what is EUT
framework in economics and decision theory that describes how rational individuals make choices under uncertainty by maximizing their expected utility
what are the 2 forms of uncertainty
risk
ambiguity
what is risk
why is this good way to use for economists
decision maker knows the possible outcomes of a choice and their probabilities
- can create environments in lab - that know all the probabilities - to match the problems of economic theory
- can easily test theories of risky choice
what is a lottery
defined by its prizes and their probabilities
{100, 0.5 ; 0, 0.5}
lottery between 100 50% and 0 50%
what is the definition of expected value
the probability weighted sum of its consequences
- what it would yield on average
- EV(L) = sum of money
- {EV(L), 1} = lottery of getting that sum for sure
what is the definition of expected utility
the probability weighted sum of utilities of consequences
how does EV relate to risk preferences
do you prefer L or {EV(L), 1}
do you prefer a lottery, or getting the EV of the lottery for sure
- risk neutral = indifferent
- risk seeking = prefers lottery
- risk averse = prefers certain money
what is the difference between EV and EU
EU
- incorporates preferences and attitudes towards risk
under what condition must decision makers preferences satisfy EUT
what does this lead to
they must have complete and transitive preferences
then utility function can be used to represent their preferences
- if preferences satisfy EUT then they make choices that max EU
how are different attitudes to risk represented in EUT
by different shapes of utility function
- risk neutral = linear
- risk seeking = convex
- risk averse = concave (U(EV(l) > EU(l)
what does EU impose
it can capture attitude with shape of utility function
but EU is always linear in probabilities
what does EU being linear in probabilities mean
the impact on EU of given change in some probability does not vary with level of probability
- impact is independent of level of probability
what are the 2 psychological features that EUT relies on
- EU is linear in probabilities
- relative weight of 2 utilities is ratio of their probabilities
what are the allais paradoxes explain
2 empirical phenomena that the classic form of EUT cant explain
- found in lab experiments
what is the classic form of EUT
assumes that people have EU representable preferences and always choose option that maximises EU
what are the 2 Allais paradoxes
CCE = common consequence effect
CRE = common ratio effect
what is the CCE lab experiment
- CC differs across problems
- choice problem between 2 lotteries A and B
- A is a safer choice = more of a chance of getting an outcome > 0
- B is a risky choice = higher best option but more chance of worst option
a second choice problem that is the same as the first - has a safer option and a risky option
- differs by a different CCE, in the second problem it is 0
what did CCE lab experiment find
1 choice problem
2 choice problem
1
- majority of individuals choose the safe option
- choose safe when CCE is 2400
2
- majority of individuals choose the risky option
- choose risky when CCE is 0
what does EUT predict will happen in CCE lab experiment
and why does this happen
- all individuals should stay consistent and not switch - should choose either safe in both problems, or risk in both problems
- the CCE has no impact on the comparison of EUs between the 2 problems
why would changing the CC between 2 problems not make a difference
because the CC is not considered when comparing the EU’s of the different options within each problem
- so changing the CC should have no effect
- not considered when choosing between which option A or B in problem 1 has higher utility
- should be the same outcome in problem 2 because we should ignore the CC
- but it isnt the same - most people switch
why does EUT fail to explain CCE
- in both problems option B has 1% higher chance of getting 0 than option A
- but the level of probabilities this is evaluated at is different
- EUT = this shouldnt make a difference because EU is linear in probability
- responses to increase in 1% should be the same in both problems
- but this is evidence that it does make a difference
what is the lab experiment for CRE common ratio effect
2 choice problems that are the same but the 2nd the good outcomes have been multiplied by a common ratio of 0.25
what is the results of CRE lab experiement
tendency for subjects to choose safe option in problem 1
but switch to risky option in problem 2
- switch from safe to risky when the probabilities of good outcomes are scaled down by common ratio
what is CRE not consitent with in EUT
what does EUT expect from CRE
the idea that relative weight on different utilities is just ration of probabilities
expects that people stay consistent
when multiplying by CR preferences shouldnt change
are the CCE and CRE effects real?
many experiments have found evidence of the effects, but not all
CRE
- not all subjects display the effect
what doe CCE and CRE prove about EUT
that people arent always rational
- casts doubt on classic form of EUTs modelling
- linear probability
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