4 - Expected utility theory and what might be wrong with it

Question 1

what is the standard model of decision making under risk

Answer 1

expected utility theory

Question 2

what is the BE model of decision making under risk

Answer 2

prospect theory

Question 3

what is EUT

Answer 3

framework in economics and decision theory that describes how rational individuals make choices under uncertainty by maximizing their expected utility

Question 4

what are the 2 forms of uncertainty

Answer 4

risk
ambiguity

Question 5

what is risk

why is this good way to use for economists

Answer 5

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

Question 6

what is a lottery

Answer 6

defined by its prizes and their probabilities
{100, 0.5 ; 0, 0.5}
lottery between 100 50% and 0 50%

Question 7

what is the definition of expected value

Answer 7

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

Question 8

what is the definition of expected utility

Answer 8

the probability weighted sum of utilities of consequences

Question 9

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

Answer 9

• risk neutral = indifferent
• risk seeking = prefers lottery
• risk averse = prefers certain money

Question 10

what is the difference between EV and EU

Answer 10

EU
- incorporates preferences and attitudes towards risk

Question 11

under what condition must decision makers preferences satisfy EUT

what does this lead to

Answer 11

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

Question 12

how are different attitudes to risk represented in EUT

Answer 12

by different shapes of utility function
- risk neutral = linear
- risk seeking = convex
- risk averse = concave (U(EV(l) > EU(l)

Question 13

what does EU impose

Answer 13

it can capture attitude with shape of utility function

but EU is always linear in probabilities

Question 14

what does EU being linear in probabilities mean

Answer 14

the impact on EU of given change in some probability does not vary with level of probability
- impact is independent of level of probability

Question 15

what are the 2 psychological features that EUT relies on

Answer 15

1. EU is linear in probabilities
2. relative weight of 2 utilities is ratio of their probabilities

Question 16

what are the allais paradoxes explain

Answer 16

2 empirical phenomena that the classic form of EUT cant explain
- found in lab experiments

Question 17

what is the classic form of EUT

Answer 17

assumes that people have EU representable preferences and always choose option that maximises EU

Question 18

what are the 2 Allais paradoxes

Answer 18

CCE = common consequence effect
CRE = common ratio effect

Question 19

what is the CCE lab experiment

• CC differs across problems

Answer 19

• 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

Question 20

what did CCE lab experiment find

1 choice problem
2 choice problem

Answer 20

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

Question 21

what does EUT predict will happen in CCE lab experiment

and why does this happen

Answer 21

• 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

Question 22

why would changing the CC between 2 problems not make a difference

Answer 22

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

Question 23

why does EUT fail to explain CCE

Answer 23

• 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

Question 24

what is the lab experiment for CRE common ratio effect

Answer 24

2 choice problems that are the same but the 2nd the good outcomes have been multiplied by a common ratio of 0.25

Question 25

what is the results of CRE lab experiement

Answer 25

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

Question 26

what is CRE not consitent with in EUT

what does EUT expect from CRE

Answer 26

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

Question 27

are the CCE and CRE effects real?

Answer 27

many experiments have found evidence of the effects, but not all
CRE
- not all subjects display the effect

Question 28

what doe CCE and CRE prove about EUT

Answer 28

that people arent always rational
- casts doubt on classic form of EUTs modelling

• linear probability
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