Prospect Theory

23A i 23B, reference point23A) Your country is plagued with an

outbreak of an exotic Asian disease, which may kill 600 people. You are responsible for making decision about two programs. Which program will you choose:

a) Program A: 200 people will be

saved for sureb) Program B: 600 will be saved

with probability 1/3, nobody will be saved with probability 2/3.

23B) Your country is plagued with an outbreak of an exotic Asian disease, which may kill 600 people. You are responsible for making decision about two programs. Which program will you choose:

a) Program A: 400 people will die for sureb) Program B: Nobody will die with

probability 1/3, 600 people will die with probability 2/3.

Kahneman, Tversky (1979) [framing, Asian disease]Lotteries in 23A) are exactly the same as lotteries in 23B).

Framing is different though. People often:

• Choose program A in 23A• Choose program B in 23B

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Gains and losses

• Which lottery would you choose– A) sure gain of $ 3 000 – B) 1:3 chance of getting $ 4 000 or nothing

• Which lottery would you choose– X) sure loss of $ 3 000– Y) 3:1 chance of losing $ 4 000 or nothing

Conclusion 1

• What matters is not final position, but changes relative to some reference point (status quo)

• Depending on the reference point a given consequence may be interpreted as gain or loss (framing)

• People are – Risk prone in the domain of losses– Risk averse in the domain of gains

20.1 i 20.2 (or how we perceive probabilities)

20.1) There is 90 balls in the urn – 30 blue balls and 60 that are either yellow or red. You pick a colour. Then one ball is drawn randomly from the urn. If the colour of the ball drawn and the colour of the ball you chose match, you will win $100. Which coloor do you pick? (One answer) a) Blueb) Yellow 20.2) Continuation: If the colour of the drawn ball is of one the colours you bet on, you win

$100. Which colours do you pick? (One answer) c) Blue and Redd) Yellow and Red

Ellsberg paradox (1962?) [uncertainty aversion]Many people choose:

• Blue in 20.1• Yellow and Red in 20.2

Why is it strange…

17.1 i 17.2 (or how we perceive objective probabilities)

17.1) Choose one lottery:

P=(1 mln, 1)Q=(5 mln, 0.1; 1 mln, 0.89; 0 mln, 0.01)

17.2) Choose one lottery:

P’=(1 mln, 0.11; 0 mln, 0.89)Q’=(5 mln, 0.1; 0 mln, 0.9)

Kahneman, Tversky (1979) [common consequence effect violation of independence]

Many people choose P over Q and Q’ over P’

• P better than Q• U(1)>0.1*U(5)+0.89*U(1)+0.01*U(0)• Substitute for U(0)=0 and rearrange:• 0.11*U(1)>0.1*U(5)• Hence P’ better than Q’

18.1 i 18.2 (or how we perceive objective probabilities)

18.1) Choose one lottery:

P=(3000 PLN, 1)Q=(4000 PLN, 0.8; 0 PLN, 0.2)

18.2) Choose one lottery:

P’=(3000 PLN, 0.25; 0 PLN, 0.75)Q’=(4000 PLN, 0.2; 0 PLN, 0.8)

Kahneman, Tversky (1979) [common ratio effect, violation of independence]

Many people choose P over Q and Q’ over P’

• P better than Q• U(3)>0.8*U(4)+0.2*U(0)• Divide by 4 and substitute for U(0)=0:• 0.25*U(3)>0.2*U(4)• Hence P’ better than Q’

Common consequence violates independence

P = (1 mln, 1)P’= (1 mln, 0.11; 0, 0.89)Q = (5 mln, 0.1; 1 mln, 0.89; 0, 0.01)Q’= (5 mln, 0.1; 0, 0.9)

• If we plug c = 1mln, we get P and Q respectively• If we plug c = 0, we get P’ and Q’ respectively

Common ratio violates independenceP=(3000 PLN, 1)P’=(3000 PLN, 0.25; 0 PLN, 0.75)Q=(4000 PLN, 0.8; 0 PLN, 0.2)Q’=(4000 PLN, 0.2; 0 PLN, 0.8)

p1

p2

1

1 1mln

05mln

17.1) Choose one lottery:

P=(1 mln, 1)Q=(5 mln, 0.1; 1 mln, 0.89; 0 mln, 0.01)

17.2) Choose one lottery:

P’=(1 mln, 0.11; 0 mln, 0.89)Q’=(5 mln, 0.1; 0 mln, 0.9)

Common consequence effect in the Machina triangle

Fanning out

p1

p2

1

1 1mln

05mln

Conclusion 2

• We often perceive probabilities as if they didn’t conform to the laws of probability– We prefer risk than uncertainty uncertainty

aversion (Ellsberg paradox)– Certainty effect - we attach to high a value to

certainty (Allais paradox)

• Maximizing utility may not describe many our choices

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11 (or endowment effect)11.1) You are given a new coffee mug (photo below). For what minimal price

would you sell it? Give a price between $1-$50. 11.2) There is a coffee mug for sale. For what maximal price would you buy it?

Give a price between $1-$50.

Kahneman, Knetsch, Thaler (1990) [endowment effect, WTA-WTP disparity]WTA>WTP

Conclusion 3

• We are reluctant to depart from the status quo

• We dont’t want to part with what’s ours or what we bought or acquired

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People usually pay more if n=1

Expected utility implies the opposite: 1/3 versus 1/6

Famous Zeckhauser’s paradox

Conclusion 4

• People do not weigh probabilities evenly– They overweigh low probabilities– They underweigh high probabilities

Recap

• Behavior– The context of decision is important (reference point, what is

gain, what is loss)– We perceive probabilities in the wrong way (e.g. attach too

much priority to a given event)– We are attracted too much to what we have (status quo bias)– We like sure gains, we dislike sure losses– We dislike losses more that we like gains (losses loom larger

than gains)

• Theory– Expected Utility Theory does not acommodate these features

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Probability weighting

Exercise