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Prospect Theory

Prospect Theory. 2 3 A i 2 3 B , reference point. 23A) 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: Program A: 200 people will be saved for sure

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Prospect Theory

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  1. ProspectTheory

  2. 23A i 23B, reference point 23A) 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: • Program A: 200 people will be saved for sure • 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: • Program A: 400 people will die for sure • 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

  3. Gains and losses • Whichlotterywouldyouchoose • A) suregain of $ 3 000 • B) 1:3 chance of getting $ 4 000 ornothing • Whichlotterywouldyouchoose • X) sureloss of $ 3 000 • Y) 3:1 chance of losing $ 4 000 ornothing

  4. Conclusion 1 • Whatmattersis not finalposition, but changesrelative to somereference point (status quo) • Depending on thereference point a givenconsequencemay be interpreted as gainorloss (framing) • Peopleare • Riskproneinthedomain of losses • Riskaverseinthedomain of gains

  5. 20.1 i 20.2(orhow we perceiveprobabilities) 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) • Blue • 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) • Blue and Red • Yellow and Red Ellsbergparadox(1962?) [uncertainty aversion] Many peoplechoose: • Bluein 20.1 • Yellow and Redin 20.2

  6. Whyisitstrange…

  7. 17.1 i17.2(orhow we perceiveobjectiveprobabilities) 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) [commonconsequenceeffectviolation of independence] Many peoplechoose P over Q and Q’ over P’ • P betterthan Q • U(1)>0.1*U(5)+0.89*U(1)+0.01*U(0) • Substitute for U(0)=0and rearrange: • 0.11*U(1)>0.1*U(5) • Hence P’ betterthan Q’

  8. 18.1 i18.2(orhow we perceiveobjectiveprobabilities) 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 peoplechoose P over Q and Q’ over P’ • P betterthan 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’ betterthan Q’

  9. Common consequence violatesindependence 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

  10. Common ratio violatesindependence P=(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)

  11. Commonconsequenceeffectinthe Machina triangle 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) p2 1mln 1 5mln 0 1 p1

  12. Fanning out p2 1mln 1 5mln 0 1 p1

  13. Conclusion 2 • We oftenperceiveprobabilities as iftheydidn’tconform to thelaws of probability • We preferriskthanuncertaintyuncertaintyaversion(Ellsbergparadox) • Certaintyeffect - we attach to high a value to certainty(Allaisparadox) • Maximizingutilitymay not describe many ourchoices

  14. 11 (orendowmenteffect) 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

  15. Conclusion 3 • We arereluctant to departfromthe status quo • We dont’t want to part withwhat’soursorwhat we boughtoracquired

  16. Peopleusuallypaymoreifn=1 Expectedutilityimpliestheopposite: 1/3 versus 1/6

  17. FamousZeckhauser’sparadox

  18. Conclusion 4 • People do not weighprobabilitiesevenly • Theyoverweighlowprobabilities • Theyunderweigh high probabilities

  19. Recap • Behavior • Thecontext of decisionisimportant (reference point, whatisgain, whatisloss) • We perceiveprobabilitiesinthewrongway (e.g. attachtoo much priority to a givenevent) • We areattractedtoo much to what we have (status quo bias) • We likesuregains, we dislikesurelosses • We dislikelossesmorethat we likegains (lossesloomlargerthangains) • Theory • ExpectedUtilityTheorydoes not acommodatethesefeatures

  20. Probabilityweighting

  21. Exercise

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