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08*,A/Prospect Theory, Framingand Behavioral Traps 20 . Yuval Shahar M.D., Ph.D. /Prospect Theory (Kahneman and Tversky, 1979) 400H Normative decision-analysis theory assumes that outcomes of decisions (prospects) are described in terms of total wealth
In reality, however, prospects are considered in terms of gains, losses, or neutral outcomes relative to some reference point (the current state)
In Prospect Theory a decision maker considers prospects using a function that values all prospects relative to a reference point.
Phase I is framing the decision problem
Phase II is evaluating the prospects4 ZM Z >
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0Properties of Value Functions in Prospect Theory0 The Value function V(X), where X is a prospect:
Is defined by gains and losses from a reference point
Is concave for gains, and convex for losses
The value function is steepest near the point of reference: Sensitivity to losses or gains is maximal in the very first unit of gain or loss
Is steeper in the losses domain than in the gains domain
Suggests a basic human mechanism (it is easier to make people unhappy than happy)
Thus, the negative effect of a loss is larger than the positive effect of a gain
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$A Value Function in Prospect Theory$
#Decision Weights in Prospect Theory# In Prospect Theory, a probability p is not used as is, but has a decision weight (p)
Thus, the expected value of a prospect is
V(X, p; Y, q) = V(X) (p) + V(Y) (q)
A simple prospect has one positive and one negative value, such that p+q 1
If p+q <1 we assume the other values or probabilities are 0; for example, ($100, 0.1; $0, 0.7; $-20, 0.2)
The weight of middle to high probabilities is relatively reduced as opposed to the two endpoints; thus, going from p=0 to p=0.05 or from p=0.95 to p=1 is more significant than going from p=0.30 to p=0.35 (the certainty effect )J Z,! Z Z"&
&&D ' I 0A Decision-Weighting Functionin Prospect Theory0
Pseudo-Certainty Effects (I) e(N = 85) Consider a 2-stage game: In the 1st stage there is a 75% chance of ending the game without winning anything and a 25% chance of moving into the 2nd stage. If you reach the 2nd stage you have a choice:
A sure win of $30 (preferred by 74%)
An 80% chance of winning $45 (preferred by 26%)
You need to make your choice before the start of the game
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Pseudo-Certainty Effects (II) $(N=81) Which option do you prefer:
A 25% chance to win $30 (preferred by 42%)
A 20% chance to win $45 (preferred by 58%)
In fact, prospect A offers a 25% chance of winning $30 (like C); prospect B offers a 25% x 80% = 20% chance of winning $45 (like D)
The failure of invariance is due to the fact that in options A,B people consider the second stage in isolation (framing) and then give a higher decision weight to the sure gain (a pseudo-certainty effect) in option B, as opposed to the lower weight of the increase from 20% to 25% in options C,D# ZV Z Z]$ *Certainty Effects: Probabilistic Insurance++$* Imagine the following insurance options:
Pay a premium for full coverage
Pay half the premium for full coverage during half the time, to be decided at random (e.g., only on odd dates of the month)
Most people reject option (2), contrary to normative theory (which predicts preference towards it, due to a concave utility function)
The reason is that reducing the risk probability from p to p/2 has a smaller decision weight than reducing the risk from p/2 to 0 (the certainty effect)
This suggests (and has been verified) that framing an insurance as giving full protection against specific risks makes it more attractive (e.g. only fire vs. flood and fire)) Z Z ZG Z)$& ( Prospect Theory and Framing Risky prospects can be framed in different ways- as gains or as losses
Changing the description of a prospect should not change decisions, but it does, in a way predicted by Prospect Theory
Framing a prospect as a loss rather than a gain, by changing the reference point, changes the decision, due to the properties of the value function (which is steeper in the losses domain, i.e., tends to show loss aversion) Z4.(
Framing: Loss Aversion (I) SImagine the US is preparing for the outbreak of an Asian disease, expected to kill 600 people (N = 152 subjects):
If program A is adopted, 200 people will be saved (72% preference)
If program B is adopted, there is one third probability that 600 people will be saved and two thirds probability that no people will be saved (28% preference)r Z Z_$3:S Framing: Loss Aversion (II) AImagine the US is preparing for the outbreak of an Asian disease, expected to kill 600 people (N = 155 subjects):
If program C is adopted, 400 people will die (22% preference)
If program D is adopted, there is one third probability that nobody will die and two thirds probability that 600 people will die (78% preference)r Z Z_$*6A Mental Accounts Imagine the following situations:
you are about to purchase a jacket for $125 and a calculator for $15. The salesman mentions that the calculator is on sale for $10 at another branch of the store 20 minutes away by car.
you are about to purchase a jacket for $15 and a calculator for $125. The salesman mentions that the calculator is on sale for $120 at another branch of the store 20 minutes away by car.
68% (N=88) of subjects were willing to drive to the other store in A, but only 29% (N=93) in B" Zu Z_ Z"uK
Framing and Mental Accounts Three potential framing options, or accounts:
Minimal (considers only differences between local options, such as gaining $5, disregarding common features)
Topical (considers the context in which the decision arises, such as reducing the price of the calculator from $15 to $10)
Comprehensive (includes both jacket and calculator in relation to total monthly expenses)
People usually frame decisions in terms of topical accounts; thus the savings on the calculators are considered relative to their prices in each option. ZC Z Z$$Bt
N+] 3Loss Aversion : The Endowment Effect(Thaler, 1980)(4$$.& [It is more painful to give up an asset than it is pleasurable to buy it, an endowment effect
Thus, selling prices are higher than buying prices, contrary to economic theory
There is a status quo bias (Samuelson and Zeckhauser 1988) since disadvantages of leaving the current state seem larger than advantages, for multi-attribute utility functions] P $%. y CEndowments Effects and Fairness(Kahneman, Knetch and Thaler, 1986)D $b! :Evaluate the two situations for fairness:
A shortage had developed for a car model and the dealer now prices it $200 above list price (29% acceptability)
A shortage had developed for a car model and the dealer, who had been giving $200 discounts, now sells the model for list price (58% acceptability)
Perception of fairness depends on whether the question is framed as a reduction in gain or as an actual loss
Imposing a surcharge is considered less fair than eliminating a discount; thus, cash prices are presented as a discount, rather than credit prices a surcharge * Z Z Z ]m
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: Framing: Losses Versus Costs Consider the following two propositions:
A gamble that offers a 10% chance of winning $95 and a 90% chance of losing $5
A payment of $5 to participate in a lottery with a 10% chance of winning $100 and a 90% chance of winning nothing
55 of 132 subjects reversed their preferences, 42 of them rejecting A and accepting B
Thinking of $5 as payment (cost) rather than a loss makes the venture more acceptable
Similarly in experiments in which insurance is presented as the cost of protection vs. a sure loss) Z Z Z)hk
%Framing: Sunk-Cost (Dead Loss) Effect&&$% Framing negative outcomes as costs rather than as a loss improves subjective feelings, as in:
Playing with a tennis elbow in a tennis club, in spite of pain, maintains evaluation of the membership fee as a cost rather than a dead loss
Continuing a project that has already cost a lot without any results, rather than starting a new one, although the previous costs are sunk costs
Eating bad-tasting food you have already paid forz^ ZP Z^p
2 Summary Understanding human behavior requires
separation of prospects into positive and negative, relative to a status quo, rather than considering absolute values, and
consideration of decision weights rather than probabilities
Loss aversion, endowment effects, and status quo bias predict (correctly) less symmetry and reversibility in the world than do normative theories
Framing changes the way decision makers treat the same problem, as can be predicted when the nature of these anomalies is taken into account' Z Z! Z' \
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Times New RomanTimes New Roman (Hebrew)Symbol 0Prospect Theory, Framing and Behavioral Traps 0Prospect Theory (Kahneman and Tversky, 1979) 1Properties of Value Functions in Prospect Theory%A Value Function in Prospect Theory$Decision Weights in Prospect Theory1A Decision-Weighting Function in Prospect TheoryPseudo-Certainty Effects (I)Pseudo-Certainty Effects (II)+Certainty Effects: Probabilistic InsuranceProspect Theory and Framing Framing: Loss Aversion (I)Framing: Loss Aversion (II)Mental AccountsFraming and Mental Accounts4Loss Aversion : The Endowment Effect (Thaler, 1980)DEndowments Effects and Fairness (Kahneman, Knetch and Thaler, 1986)Framing: Losses Versus Costs&Framing: Sunk-Cost (Dead Loss) EffectSummary _ۇyovalyoval
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