Handout:)“Prospect)Theory:)An)Analysis)of)Decision)under ... ·...

Handout: “Prospect Theory: An Analysis of Decision under Risk” Ye Chen, Manuel Ludwig-‐Dehm, Yin Xiao, Zulma Barrail

2011

1

Handout: Prospect Theory: An Analysis of Decision under Risk Daniel Kahneman and Amos Tversky

1. Introduction

This paper presents a critique of expected utility theory as a descriptive model of decision making under risk and introduces prospect theory as an alternative model.

Expected utility theory is widely accepted as a descriptive model of decision making under risk and has been generally accepted as a normative model of rational choice. Hence, it is assumed that all rational people would like to follow the predictions made by this theory.

2. Critique

Short Recap of Expected Utility Theory (EUT)

Decision making under risk can be interpreted as choice between prospects. Kahnemann and Tversky, KT in the following, describe a prospect (!!, !!;… ; !!, !!) as a contract that yields outcome !! with probability !!. The prospect (!,!; 0, 1 − !) is for simplicity denoted as (!,!). EUT is based on three theorems:

(i) Expectation: Expected utility is the sum of the individual utilities of the different outcomes weighted by each probability:

! !!, !!;… ; !!, !! = !!! !! +⋯+ !!! !!

(ii) Asset integration: !!, !!;… ; !!, !! is acceptable at asset position w iff ! ! + !!, !!;… ; ! + !!, !! > ! ! .

That is, the final assets matter, as they are the carrier of value, not the loss or gain (as later will be proposed by prospect theory).

(iii) Risk Aversion: u is concave ( !. !. !! > 0 , !!! < 0), and an individual prefers the certain

outcome x over a gamble with the expected value x.

Empirical Violations of the Predictions of Expected Utility Theory

Then, KT demonstrate how the results from their experiments violate the theorems. The experiments are hypothetical choice problems1 and were conducted with students and university faculty members.

1 For a critique of the validity and use of hypothetical experiments in slightly different contexts and strategies to overcome the possible bias involved see e.g. Blumenschein et al. (2008), Eliciting Willingness to Pay Without Bias: Evidence from A Field Experiment, The Economic Journal, 118 (January), pp. 114–137.


2011

2

Certainty, Probability and Possibility

KT then move on to present the results from experiments that illustrate how people tend to overweight outcomes that are considered certain (p=1) relative to outcomes which are merely probable (p<1). The first one to introduce this critique of expected utility theory was Maurice Allais, who however used extremely large gains. KT replicate his results by their hypothetical choice experiment using moderate gains. In the following choice problems that were given to the participants of the experiments, N denotes the total number of respondents and the number in brackets the percentage of people that chose each option.

According to expected utility theory, the above problems should have led to the result that people on average prefer A to B and C to B, or vice versa, as Problem 2 is obtained from Problem 1 by deducting a 0.66 chance of winning 2,400 from both sides, thus not changing the inequality.

Nevertheless, while the first preferences imply

the second one implies the reverse, which clearly is a violation of expected utility theory (inconsistent preferences). The authors stress the impact of the above elimination of .66 x 2,400 on Choice B in Problem 1, which is turned from a sure gain into a merely probable one. Hence, they conclude that this change reduces the desirability of B more than that of A, and people as a result prefer C over D in Problem 2.

KT demonstrate the same phenomenon with another experiment involving only two outcomes:


2011

3

Again, Problem 4 is obtained from Problem three without changing the inequality indicated by the choices in Problem 3, i.e. B preferred to A, which should lead to the outcome of D preferred to C in Problem 4. Nevertheless, a division of the probabilities of both sides of the inequality in Problem 3 by 4 which according to expected utility theory should not change preferences, leads to preferences that are inconsistent according to expected utility theory as they are reversed by an operation that should not have an impact. This is as the substitution axiom of EUT states that if B is preferred to A, any (probability) mixture (B, p) must be preferred to (A, p). The experiments indicate that people do not follow this axiom, as reducing the probability of the sure gain (choice B in Problem 3)by ¾ has a larger effect than reducing the probability of the probable gain (choice A in Problem 3) by ¾.

This is what the authors, following Allais, call the certainty effect.

The following example illustrates this effect with a non-‐monetary example, in which Problem 6 is obtained from Problem 5 by dividing the probabilities at each side of the inequality by 10:

However, the substitution axiom is not only violated when sure gains are involved. The following example shows that even when substantial gains and not substantial gains are reduced in a way that should not change the preferences of people, respondents in the experiments exhibit attitudes towards risk that are not captured by EUT.


2011

4

Note that Problem 8 is obtained from Problem 7 by dividing the probabilities by 450, while choice B involves no sure gain but only a substantial probability (in contrast to the preceding experiments.

Thus, the authors conclude that EUT is not capturing risk attitudes of people correctly and suggest the following generalization that can explain the violation of the substitution axiom: If (y, pq) is equivalent to (x, p), then (y,pqr) is preferred to (x, pr), if 0<p,q and r<1.

The Reflection Effect

While the certainty effect is observed when positive prospects are involved, the authors examine the effect of changing probabilities (again in a way that preferences should not change according to EUT) in the negative domain. The following table depicts not only the results from the previously introduced experiments, but replicated them by using reversed outcomes, i.e. losses of –x and -‐y (right side of the table) instead of gains of y and y (left side).

The table contrasts the certainty effect which occurs when positive prospects are involved, with the effect that occurs when negative prospects are involved. The table shows, that when the same prospects as in Problems 3, 4, 7, and 8 are taken and multiplied by -‐1, turning them into losses of the same absolute value, the preference order indicated by the inequality signs is reversed.


2011

5

Problem 3’ for instance shows that when losses are involved people prefer the gamble of (-‐4000, .80) to a sure loss of -‐3000, even though the expected value of of the latter choice is larger than the one of the former. Thus, both Problem 3 and 3’ violate the expectation theorem in the same way. Hence, people exhibit risk adversity with positive prospects but risk seeking behavior in the negative domain, indicating a convex value function. This behavior can be explained by overweighting of certain outcomes relative to uncertain outcome both in the negative and positive domain. It should be noted that the existence of the reflection effect shows that aversion for uncertainty cannot be the explanation of the certainty effect, as then the same behavior should be exhibited in the negative domain as well. The authors conclude that certainty increases the aversiveness of losses as well as the desirability of gains.

Probabilistic Insurance

The authors then show that even the widely used argument in favor of EUT, insurance purchases, i.e. the payment of a premium for a reduction of risk, does not necessarily imply that the utility function is concave everywhere and that people are risk averse. This is as contrary to risk aversion people often prefer insurances that offer limited coverage with low or zero deductible to similar ones that offer maximal higher coverage with higher deductibles. To illustrate this they cite the results of an experiment in which people were confronted with the following choice:


2011

6

According to EUT, if indifferent between buying a full insurance or not, people should definitely be willing to buy the corresponding probabilistic insurance. Formally,

!" ! − ! + 1 − ! ! ! = !(! − !) implies

1 − ! !" ! − ! + !"# ! − ! + 1 − ! ! ! − !" > !(! − !) KT then set u(w-‐x)=0 and u(w)=1, to obtain u(w-‐y)=1-‐p. The goal however was to show that u(w-‐ry)>1-‐rp, which would only hold if the utility function is concave. Thus, the aversion for probabilistic insurance in the experiment (similar results are reported by other authors as well) violates the prediction of EUT and shows that the utility function of individuals is not necessarily concave everywhere.

The Isolation Effect

To show that not only the certainty and reflection effect may lead to inconsistent preferences KT introduce the isolation effect, that states that people often disregard components that the two alternatives in a choice problem share, which can lead to different preferences for the same choice problem, as there are often several ways to decompose common and distinctive components of two alternatives. Participants of another experiment were asked to consider the following two-‐stage game: In the first stage, there is a probability of .75 that the game ends, without anything, and a probability of .25 that the game continues and you have to choose between the prospects (4000, .80) and (3000). The choice has to be made before the game starts.

This framing can be visualized with the following decision tree, in which squares denote decision nodes and circles chance nodes.

Note, however, that this problem corresponds to Problem 4, just that the framing is different, as in Problem 10 (tree above), the participants had the choice between a sure and a risky gain, while in Problem 4 (game tree below) participants faced two risky gains.


2011

7

The results however indicate that even though the expected gains are the same, the change in framing (the event `not winning 3,000´is included in the event `not winning 4,000´ in the upper game tree (Problem 10), leads to contrary results that indicate inconsistent preferences according to EUT.

While in Problem 10 78% of the subjects chose the sure gain of 3,000, only 35% chose the prospect that involved the gain of 3,000 in Problem 4. Hence, the dependency of events can lead to a reversal in preferences, i.e. different representations of probabilities can alter preferences.

The next example shows that varying the representations of outcomes may change preferences as well, and that hence changes, i.e. gains and losses, are carrier of wealth, and not final asset positions as advocated by EUT.

Note that in Problem 11 and 12 the options A and C are identical (2,000, .50; 1000, .50) and B and D are identical as well (1,500).

Hence, the bonus did not enter the comparison and moving from Problem 11 to Problem 12 by adding 1,000 to the bonus and deducting 1,000 from all outcomes changed the preferences of the subjects.


2011

8

3. Prospect Theory

Prospect theory modifies expected utility theory by relaxing expected principle. Instead, it takes psychological factors into account, and merges them into the definition of overall value of an edited prospect.

There are two processes in prospect theory:

a. Editing Process Editing is a process that involves the way how prospect is presented to people. Although it is beyond discussion in this paper, it is noteworthy that proper usage of editing can lead people to answer expected results while facing choice problems. On the grounds that what people are sensitive with is gain or loss referred to some reference point rather than final wealth they get, editing benefits showing or hiding common factors in a prospect. Operations (1) to (5) are applied on single prospect. (1) Coding

Coding is strategy that changes location of reference point, thereby changing outcomes as gains or losses as well. e.g. Problem 11 & Problem 12

(2) Combination Combination eliminates repeated outcomes. It is a bit like merging similar terms in mathematics. e.g. (200, 0.25; 200, 0.25) ó (200, 0.5)

(3) Segregation Riskless component can be segregated from risky one if exists. e.g. (300, 0.6; 500, 0.4) ó (200, 0.4) with sure gain 300

(4) Simplification (Rounding) This operation refers rounding probability or outcomes. As a result, extremely impossible outcomes may be discarded. e.g. (300, 0.6; 501, 0.4) ó (300, 0.6; 500, 0.4) (300, 0.6; 501, 0.04) ó (300, 0.6)

(5) Detection of dominance By quick scan of all prospects, the dominated choice is discarded without further consideration. e.g. (300, 0.5; 500, 0.3) and (30, 0.5; 50, 0.3) ó (300, 0.5; 500, 0.3)

Operation (6) is applied on two or more prospects simultaneously.

(6) Cancellation


2011

9

Discarding shared components in prospects is one of the reasons that cause isolation effects discussed in previous section. Cancellation can be implicitly implemented by decision maker so that it is a little trickily different from discussion in this paper. e.g. Problem 11 & Problem 12

b. Evaluation Process

Note: In following discussion, all evaluation is assumed to occur when further editing is impossible, which indicates disambiguation in the description for prospects.

The Model

Prospect is defined as the form of ( )x, p; y, q .Three parameters are designed to represent

psychological impact on expected theory. -‐ ( )pπ is a decision weight assigned for each probability p -‐ ( )v x is the subjective value for each outcome x -‐ V is the overall value of edited prospects Note: 1. Strictly positive prospect: , 0x y > and 1p q+ =

2. Strictly negative prospect: , 0x y < and 1p q+ =

3. Regular prospect: any prospects other than those in 1 and 2 4. Probability for null outcome is 1 p q− − , where 1p q+ ≤

5. Typically ( ) ( ) 1p qπ π+ <

6. v is defined on outcomes while V is defined on prospects 7. ( ,1.0) ( ) ( )V x V x v x= =

Prospect Theory

If ( )x, p; y, q is regular prospect,

( , ; , ) ( ) ( ) ( ) ( )V x p y q p v x q v yπ π= + (1)

If ( )x, p; y, q is either strictly positive or strictly negative prospect,

( , ; , ) ( ) ( )[ ( ) ( )]V x p y q v y p v x v yπ= + − (2)

where | | | | 0x y> > .

Note:

1. Equations (1) and (2) are subjective values interpreted by decision maker 2. These equations relax expected principle 3. Equation (2) separates riskless component from risky component, and assigns a subjective

weight to value-‐difference between these two components


2011

10

The Value Function

Note: 1. Derivation of shape of value function is based on psychological and empirical analysis 2. Perceptual apparatus is more sensitive for evaluating differences rather than absolute

magnitudes 3. Value is a function of two variables: xΔ , change of monetary outcome, and 0x , the initial

monetary outcome. Therefore 0( , )v f x x= Δ

4. Due to psychology, value function in positive domain is a concave function 5. Due to Reflection Effect and 3, value function in negative domain is a convex function 6. 3 and 4 indicates decreasing marginal value of both gains and losses with magnitude 7. The level of sensitivity towards gains and losses, namely slope of value function, tends to be

steeper if it is closer to reference point 8. Due to the fact that people favor certain gains and risky losses, value function defined in

negative domain is steeper than that in positive domain 9. There might be other special factors influencing the trend of value function

Figure 3 is a sample of value function in prospect theory, without consideration for assumption of special factors and risk-‐preference.


2011

11

The Weighting Function

In prospect theory, the value of each outcome is multiplied by a decision weight.

• What is a decision weight? o It is an inference from choices between prospects o It is not a probability.

• What is a weighting function?

It is a function that relates decision weights to stated probabilities.

• Properties of the weighting function ! ! 1. Increasing function of p. 2. Outcomes contingent on an impossible event are ignored ! 0 = 0 3. Outcomes contingent on a certain event are given a decision weight =1. ! 1 = 1 4. The scale is normalized so that ! ! is the ratio of the weight associated with the probability p

to the weight associated with the certain event. 5. For small values of p:

a. ! is a SUBADDITIVE function of p, i.e: ! !" > !"(!)

0 < ! < 1. Recall : “ Small probabilities at both prospects makes prospect with larger gain more attractive” Prospect (6000, .001) ≫ (3000, .002) Hence:

! . 001 ∗ ! 6000 > ! . 002 ∗ !(3000) ! . 001! . 002

>! 3000! 6000

>12

By concavity of v.

b. Very low probabilities are generally OVERWEIGHTED: ! ! > ! for small p.

Consider the following choice problems:

Problem 14 (5000, .001) or (5) N=72 [72]* [28]

Result: People prefer a lottery ticket over the expected value of that ticket.

! . 001 ! 5000 > !(5)

! . 001 >! 5

! 5000> .001

Assuming value function for gains is concave.

Problem 14’ Result:


2011

12

(-‐5000, .001) or (-‐5) N=72 [17] [83]*

People prefer a small certain loss over a small probability of a large loss.

! . 001 ! −5000 < !(−5)

. 001 < ! . 001 <! −5

! −5000

Assuming the value function for losses is convex.

6. For all 0 < ! < 1, ! ! + ! 1 − ! < 1. This property is called “SUBCERTAINTY”. “The sum of the weights associated with complementary events is typically less than the weight associated with the certain event”.

Example:

Recall equation (1) Value ! of prospect !, !; !, ! , where ! ! is value of outcome:

! !, !; !, ! = ! ! ! ! + ! ! !(!)

Problem 1 (2500, .33;2400,.66;0,.01)<(2400)

! 2400 > ! . 66 ! 2400 + ! . 33 ! 2500 + ! . 01 ! 0= ! . 66 ! 2400 + ! . 33 ! 2500

1 − ! . 66 ! 2400 > ! . 33 ! 2500

Problem 2 (2500,.33;0,.67)> (2400,.34; 0,.66)

! . 33 ! 2500 + ! 0 ! 0 > ! . 34 ! 2400 + ! . 66 ! 0

! . 33 ! 2500 > ! . 34 ! 2400

Combining results from Problem 1 and Problem 2:

1 − ! . 66 > ! . 34 !" ! . 66 + ! . 34 < 1

7. ! is regressive with respect to p.

The preferences are less sensitive to variations of probability than the expectation principle would dictate. The slope of ! in the interval (0,1) can be viewed as a measure of sensitivity.

This property generates the important “four-‐fold pattern of risk attitudes” (illustrated in TABLE 1 from paper), which is risk-‐seeking for small probability gains and large probability losses, and risk aversion for small probability losses and large probability gains.

8. SUBPROPORTIONALITY

For a fixed ratio of probabilities, the ratio of the corresponding decision weights is closer to unity when the probabilities are low than when they are high


2011

13

Let’s recall the experimental results reported by Kahneman and Tversky in problem 3 and 4 :

A: (4000,.80)< B: (3000) A < B ⇐ !"#!"#$%& !" !"#!$%$"$%&' !"#$% !" !"#$#"% !ℎ!"#$

“If B is preferred to A, then any (probability) mixture (B,p) must be preferred to the mixture (A,p).”

C: (4000,.20)> D: (3000,.25) C=(A,.25)> D=(B,.25)

In a more general way:

If (x,p) is equivalent to (y,pq) then (x,pr) is not preferred to (y,pqr), 0<p,q,r≤1.

One violation of the substitution axiom is the general case:

! ! ! ! = ! !" ! ! !"#$!%& ! !" !(!) ≤ ! !"# !(!)

ℎ!"#!: ! !"! !

=! !! !

!"# !"#$% ! !! !

≤! !"#! !"

!" ℎ!"#…

! !"! !

≤! !"#! !"

⇐ !"#$%&$&%'(&)*+(', !"#!$"%&

This property holds if and only if !"#$ is a convex function of log !.

Example of a subproportional function

! ! = !!(! !" ! )^! where 0 < ! < 1

We see that !"#$ is a convex function of log !.

! log !! ln !

= ! −!"# !!!

!! log !! ln ! ! = −!(! − 1) −!"# !!! > 0

As → 1 , probability weighting approximates the linear, expected utility case.

As ! → 0, probability weighting approximates a step function (piecewise constant function having only finitely many pieces) , flat everywhere, except at the endpoints


2011

14

Example of a weighting function which satisfies:

• Overweighting and subadditive for small values of p. • Subcertainty • Subproportionality.

We can see that ! changes abruptly near the endpoints, where ! 0 = 0 !"# ! 1 = 1.

The apparent discontinuities of ! at the endpoints are consistent with the notion that individuals are limited in their ability to comprehend and evaluate extreme probabilities, highly unlikely events

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

probability

deci

sion

wei

ght

EXPECTATION PRINCIPLE

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


2011

15

are either ignored or overweighted, and the difference between high probability and certainty is either neglected or exaggerated. Therefore, ! is not well behaved in the endpoints.

Example of Zeckhauser that illustrates non linearity of !

Suppose you are about to play Roussian roulette:

For which option would you offer more money?

a) Remove one bullet from a gun loaded with 4 bullets. b) Remove one bullet from a gun loaded with 1 bullet.

Economic rationality:

Choose a), where the value of money is presumably reduced by the considerable probability that one will not live to enjoy it

Most people:

Choose b). They are willing to pay much more for a reduction of the probability of death from 1/6 to zero than a reduction from 4/6 to 3/6.

Objections to the assumption of nonlinearity in !

1)

Compare the following prospects: (!, !; !, !) and (!, !!; !, !!), where ! + ! = !! + !! < 1.

Since any individual would be indifferent between both prospects, it could be argued that:

! ! + ! ! = ! !! + !(!!). This implies that ! is the identity function.

This argument is INVALID in the present theory, which assumes that the probabilities of identical outcomes are combined in the editing of prospects.

2)

Suppose ! > ! > 0, ! > !!, !"# ! + ! = !! + !! < 1. Hence !, !; !, ! dominates (!, !!; !, !!).

If preference obeys dominance:

! ! ! ! + ! ! ! ! > ! !! ! ! + ! !! ! ! !"…

! ! − ! !!

! !! − !(!)>! !! !

As ! approaches !, ! ! − ! !! approaches ! !! − !(!).


2011

16

Since ! − !! = !! − !,! must be essentially linear, or else dominance must be violated.

Direct violations of dominance are prevented, in the present theory, by the assumption that dominated alternatives are detected and eliminated prior to the evaluation of prospects.

However, the theory permits indirect violations of dominance.

Finally, it should be noted that measurement of values and decision weights should be based on choices between specified prospects rather than on bids. There is some empirical evidence that people might prefer A over B, but bid more for B than for A.

4. Discussion

Risk Attitudes

• From Allais’ example, via the modified utility theory above, we can get

π(.33)v(2500) > π(.34)v(2400)π(.33)v(2500)+π(.66)v(2400) > v(2400)

Therefore,

π(.33)π(.34)

>v(2400)v(2500)

>π(.33)1−π(.66)

• Similarly, in problems 7 and 8, we still have

π(.001)π(.002)

>v(3000)v(6000)

>π(.45)1−π(.90)

• Hence, the violation of the independence axiom in problems 1 and 2 is attributed in this case to the

inequality

π(pq)π(p)

≤π(pqr)π(pr)

(subproportionality). Even more, this analysis shows the bound of v-‐ratio

when the violation occurs.


2011

17

• The proof of the preference for regular insurance over probabilistic insurance, as can been observed in Problem 9, is presented below. If

(−x, p) is indifferent to

(−y), then

(−y) is preferred to

(−x, p /2;−y, p /2;−y /2,1− p) .

Proof: Let

f (x) = −v(−x). Since the value function

v(x) is convex,

f is a concave function of

x . What we need to show is:

f (y) ≤ f (y /2)+π(p /2)[ f (y) − f (y /2)]+π(p /2)[ f (x) − f (y /2)]= π(p /2) f (x)+π(p /2) f (y)+[1−2π(p /2)] f (y /2)

Since

2 f (y /2) ≥ f (y)by the concavity and

π(p) f (x) = f (y) by the indifference, it suffices to prove that

f (y) ≤ π(p /2)π(p)

f (y)+π(p /2) f (y)+ [1−2π(p /2)] f (y) /2

⇔π(p) /2 ≤ π(p /2)

which follows from the subadditivity of

π .

• Attitudes toward risk are determined jointly v and

π . Consider the gamble

(x, p) and

(px) , risk seeking is implied if and only if

π(p) > v(px) /v(x) when x>0. Hence, overweighting is necessary but not sufficient for risk seeking in the domain of gains.


2011

18

Shifts of Reference

• An expectation or aspiration level will affect the preference. A change of reference point alters the preference order for prospects. In particular, the present theory implies that a negative translation of a choice problem, such as arises from incomplete adaptation to recent losses, increases risk seeking in some situations.

• If a risky prospect

(x, p;−y,1− p) is just acceptable, then

(x − z, p;−y − z,1− p) is preferred over

(−z) for

x,y,z > 0,x > z .

Proof: First, notice that

V (x, p;−y,1− p) = 0 means that

π(p)v(x) = −π(1− p)v(−y).

Next,

V (x − z, p;−y − z,1− p)= π(p)v(x − z)+π(1− p)v(−y − z)> π(p)v(x) −π(p)v(z)+π(1− p)v(−y)+π(1− p)v(−z)

(by the properties of v)

= −π(1− p)v(−y) −π(p)v(z)+π(1− p)v(−y)+π(1− p)v(−z)

(by substitution)

= −π(p)v(z)+π(1− p)v(−z)> v(−z)[π(p)+π(1− p)]

(since

v(−z) < −v(z))

> v(−z)

(by subcertainty)


2011

19

• This analysis suggests that a person who has not made peace with his losses is likely to accept gambles that would be unacceptable to him otherwise.

• Another important case of a shift of reference point arises when a person formulates his decision problem in terms of final assets, as advocate in decision analysis, rather than in terms of gains and losses, as people usually do.

• Current decision theories assume that the decision whether to pay 10 for the gamble

(1000,.01) is treated as a choice between

(990,.01;−10,.99) and

(0). Instead, we suggest that people usually evaluate the gamble and its cost separately. Thus, the gamble should be treated as a decision between

(1000,.01) and

(−10).

• Through the discussion before, if one is indifferent between

(990,.01;−10,.99) and

(0), then one will not pay 10 to purchase the prospect

(1000,.01). Thus, people are expected to exhibit more risk seeking in deciding whether to accept a fair gamble than in deciding whether to purchase a gamble for a fair price.

Extensions

• Prospect theory should be extended in several directions:

1. All the equations to prospects could be extended to the case of any number of outcomes.

2. The theory is applicable to choices involving other attributes as quality of life or the number of lives that could be lost or saved as a consequence of a policy decision.

3. Theory can also be extended to the typical situation of choice, where the probabilities of

outcomes are not explicitly given.

The present analysis of preference has developed two themes , one concerns editing operations that determine how prospects are perceived, and the other involves the judgmental principles that govern the evaluation of gains and losses and the weighting of uncertain outcomes. They provide a useful framework for the descriptive analysis of choice

Handout:)“Prospect)Theory:)An)Analysis)of)Decision)under ... ·...

Documents

Transcript of Handout:)“Prospect)Theory:)An)Analysis)of)Decision)under ... ·...