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Tversky and Kahnemann: Framing of Decisions

• Agenda:– Expected Utility Theory– Violations of EU’s axioms of choice: Framing

Effects• Nontransparent Dominance• Certainty and Pseudocertainty Effects• Tradeoff Contrast• Extremeness Aversion

– Conflict between descriptive and normative theories and conclusion

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Expected Utility Theory

• Normative model of the modern theory of decision making under risk (Neumann & Morgenstern)

• Four substantive assumptions:– 1. Cancellation

• elimination of any state of the world that yields the same outcome regardless of one’s choice

• necessary for the representation of preference between prospects as the maximization of expected utility - (highly challenged and questioned)

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Expected Utility Theory– 2. Transitivity of preference

• necessary for the representation of preference by an ordinal utility scale u such that A is preferred to B whenever u(A) > u(B); (independent on other available options - (questioned)

– 3. Dominance• if one option is better than another in one state and at least as

good in all other states, the dominant option should be chosen - (simple, compelling and accepted)

– 4. Invariance• different representations of the same choice problem should

yield the same preference, independent of their description - (basic principle, tacitly assumed, accepted)

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Problem: Violations of axioms of choice

• Several experiments have proven that the “deviations of actual behavior from the normative model are too widespread to be ignored, too systematic to be dismissed as random error, and too fundamental to be accommodated by relaxing the normative system” (Tversky & Kahnemann), e.g. Allais Paradox (1953); Ellsberg Paradox (1961)...

• Theory of rational decision cannot provide adequate description of choice behavior

• Kahnemann & Tversky (1979) developed an alternative outcome-based approach called “PROSPECT THEORY” in order to explain many of the EU anomalies

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Framing• Expected utility theory assumes description

invariance: different formulations of the same choice problem should give rise to the same preference order

• Evidence that variations in the framing of options (in the description) yield systematically different preferences

• Framing effects lead to violation of the invariance and the dominance axioms of expected utility theory

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Nontransparent Dominance• Lottery Example: Choose from a box with differently coloured marbles

Problem 1 (N=88)

Option A: 90% white 6% red 1% green 1% blue 2% yellow

$0 win $45 win $30 lose $15 lose $15

Option B: 90% white 6% red 1% green 1% blue 2% yellow

$0 win $45 win $45 lose $10 lose $15

Problem 2 (N=124)

Option C: 90% white 6% red 1% green 3% yellow

$0 win $45 win $30 lose $15

Option D: 90% white 7% red 1% green 2% yellow

$0 win $45 lose $10 lose $15

[0%]

[100%]

[58%]

[42%]

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Nontransparent Dominance• Results of Lottery Example:

– Two formulations of the same problem elicit different preferences (violation of invariance)

• finer partition used in problem 1• the number of positive and negative outcomes alone can enhance the

attractiveness of an option (option C)

– Dominance rule is obeyed only when its application is transparent

– Dominance can be masked by a frame

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Nontransparent Dominance• Transparency in a Perceptual Example:

Müller-Lyer-Illusion

• whether relation of dominance is detected depends on– Framing (transparency)– Details of partitioning– Sophistication and experience of decision maker

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Certainty and Pseudocertainty Effects

Problem 1 (N=77): Which of the following options do you prefer?

A. sure gain of $30

B. 80% chance to win $45, 20% chance to win nothing

Problem 2 (N=81): Which of the following options do you prefer?

C. 25% chance to win $30, 75% chance to win nothing

D. 20% chance to win $45, 80% chance to win nothing

[78% ]

[22%]

[42% ]

[58%]

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Certainty Effect

• Problem 1 and 2 : In problem 2, the probabilities of winning are reduced by a factor of four

• Preference switched due to certainty effect: Reduction of probability of winning from certainty to 0.25 has greater effect than the reduction from 0.8 to 0.2(45) (0.8) (30) (1)(45) (0.2) (30) (0.25)v vv v

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Certainty and Pseudocertainty Effects

Problem 1 (N=77): Which of the following options do you prefer?

A. sure gain of $30

B. 80% chance to win $45, 20% chance to win nothing

Problem 2 (N=81): Which of the following options do you prefer?

C. 25% chance to win $30, 75% chance to win nothing

D. 20% chance to win $45, 80% chance to win nothing

Problem 3 (N=85): Two-stage game

Stage 1: 75% chance to end the game without winning anything, 25% chance to move to stage 2

Stage 2:

E. sure win of $30

F. 80% chance to win $45, 20% chance to win nothing

[78% ]

[22%]

[42% ]

[58%] [74% ]

[26%]

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Pseudocertainty Effect

• Problem 2 and 3 : Identical in terms of probabilities and outcomes

• Framing as two-stage game encourages the application of cancellation: Failing to reach second step is discarded

• Pseudocertainty Effect: Risk-averse choice in problem 3 but not in 2, outcome that is actually uncertain (3) is weighted as if it were certain

(45) (0.8 0.25) (30) (1 0.25)v v

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Certainty and Pseudocertainty EffectsProblem 1:

Overweighing of the outcome that is obtained with certainty due to loss aversion

Problem 2:

Reduces probability of winning by factor of 4

Problem 3:

Introduces ex ante stage that gives 25% chance for second stage

Different choice due to certainty effect; violation

of cancellation

Application of cancellation - same choice as in problem 1; risk-averse

choice due to pseudocertainty

Same problem, differently framed

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Framing - Findings

• Axioms of rational choice are– generally satisfied in transparent situations– often violated in nontransparent situations

• Framing enriches and complicates analysis of choice

• Framing of decisions depends on– Language of presentation– Nature of display– Context of choice

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Simonson and Tversky (1992): Value Maximization

• Basic assumption of classical economic theory: Consumer selects alternative with highest value, preference is independent of the context

• BUT: consumer preferences are influenced by context of choice

• Effects of Context on Choice:– 1. TRADEOFF CONTRAST– 2. EXTREMENESS AVERSION

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1. Tradeoff Contrast• People tend to compare an available option to

– other choices that are currently available (Local Effect) – options that have been encountered in the past (Background

Effect)• e.g. a circle appears large when surrounded by small circles

and small when surrounded by large ones

• Applies to single attributes (e.g. size) as well as to tradeoffs between attributes (e.g. price and quality)

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Local Effect

• If y is clearly superior to z but x is not:

Attribute 1

Attr

i but

e 2 x

y

z

• Tradeoff Contrast Hypothesis implies:

• Addition of z can increase y’s market share, yielding:

• Violates value maximization principle: popularity of an option cannot be increased by enlarging the offered set

( ; ) ( ; )zP y x P y x

( ; , ) ( ; )P y x z P y x

Asymmetric Dominance Effect

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Enhancement & Detraction

• Enhances the attractiveness of y; y fares better in triple than in pairs (explained by extremeness aversion)

Attribute 1

Attr

i but

e 2

xy

zw

• Assumption: no strong preference between x and z; z is dominated by y but not by x

• Tradeoff Contrast Hypothesis: offered set will affect choice even when no option has a decisive advantage over another

( ; ) ( ; )( ; ) ( ; )x

z

P y z P y zP y x P y x

• Detracts from the attractiveness of w; w fares worse in triple than in pairs

( ; ) ( ; )( ; ) ( ; )x

z

P w z P w zP w x P w x

Once a third option is introduced, the decision maker can compare three tradeoffs, which...

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2. Extremeness Aversion (1/3)• Implications of value maximization:

– If y is between x and z on all relevant attributes, then

– Middle option (y) is expected to lose relatively more than the other extreme option x from the introduction of z

• At variance with extremeness aversion: y will lose relatively less than x from the introduction of z

( ; ) ( ; )( ; ) ( ; )

x

z

P y z P y zP y x P y x

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Extremeness Aversion (2/3)• Main features:

– An option is more attractive to the respondent if it is an intermediate option in a choice set

– Attractiveness is lower for extreme options• Based on Principle of Loss Aversion: losses loom

larger than gains• Alternatives are evaluated in terms of their advantages

and disadvantages relative to other options; disadvantages are weighted more heavily than advantages

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Extremeness Aversion (3/3)•

•

Attribute 1

Attr

i but

e 2 x

y

z

1 1 1x y z

2 2 2x y z

• Each extreme option (x and z) has a large advantage and a large disadvantage relative to the other extreme; small advantage and small disadvantage relative to the middle option (y)

• Middle option (y) has small advantages and small disadvantages relative to both extremes

• If (pairwise) disadvantages loom larger than the corresponding advantages, the middle option should fare better in the triple than in the pairs.

•

•

( ; ) ( ; )xP y z P y z

( ; ) ( ; )zP y x P y x

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Example for Extremeness Aversion

• In group 1 & 2, the cameras varied across three dimensions: – two qualitative dimensions (optics, resolution)– one price dimension

• Group 3: introduction of a forth dimension (recording of video sequences) for camera 3 in order to emphasize its quality and innovativeness

cam. 1 cam. 2 cam. 1 cam. 2 cam. 3 cam. 1 cam. 2 cam. 3people

interviewedabsolute number

10 16 2 19 5 3 12 9

relative number

0,385 0,615 0,077 0,731 0,192 0,125 0,5 0,375

group 1 group 2 group 3

26 26 24

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Theory• Framing effects and

associated failures of invariance are ubiquitous - can’t be ignored by adequate descriptive theory

• Invariance is normatively indispensable - no adequate prescriptive theory should permit its violation

• Seems unrealizable to construct a theory that is both descriptively and normatively acceptable

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Prospect Theory

• Several models of risky choice tried to explain the observed violations of expected utility

• PROSPECT THEORY differs by being descriptive, without normative claims

• Explains preferences, whether or not they can be rationalized

• Accommodates violation of dominance and invariance, especially in nontransparent situations

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Conclusion• To retain rational model in its descriptive role, relevant

bolstering assumptions must be validated• Defence of rationality: The substantial violations of the

standard model are– restricted to insignificant choice problems– attributable to the cost of thinking and will thus be eliminated by

proper incentives– quickly eliminated by learning (accurate and immediate feedback)– inconsequential because of corrective effects of the market

• Where they fail, implications of the descriptive analysis must be traced

Questions?Thanks for your attention.

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Nontransparent Dominance• Transparency in a Perceptual Example:

Müller-Lyer-Illusion

• whether relation of dominance is detected depends on– Framing (transparency)– Details of partitioning– Sophistication and experience of decision maker

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Compromise and Polarization• Both inequalities hold

– –

• Addition of an extreme option increases share of the middle option relative to the other extreme

• Expected if disadvantages loom larger than advantages on both attributes

• Only one inequality holds (disadvantages loom larger than advantages only on one dimension but not on the other)

• e.g. extremeness aversion for quality, little or no extremeness aversion for price – Consumers find lowest quality

more aversive than highest price

– Asymmetry between price and quality

( ; ) ( ; )xP y z P y z( ; ) ( ; )zP y x P y x