Utility Theory & Prospect Theory
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Transcript of Utility Theory & Prospect Theory
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7/30/2019 Utility Theory & Prospect Theory
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Chapter 6Prospect Theory
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Theory for decision making under risk
Normative Theory
Expected Utility Theory(von Neumann and Morgenstern, 1944)
Objective probability judgment
A set of intuitive axioms
Roots to be found in Bernoulli
(1738)
Descriptive Theory
Prospect Theory(Kahneman and Tversky, 1979)
Explicitly not normative
Positive application (summarizes
what people actually do)
Probably the most widely cited
(influential) social science paper
ever published
Advice how you should decide Prediction of what you will decide
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Prospect Theory
Editing Phase
Choice problem
Evaluation Phase
Probability
weighting Value Function
Decision
Prospect theory is strictly defined for choice
situations involving risk, although it has found its
way into other disciplines as well (e.g. marketing)
This is the preparation before options are evaluated.
Based on perception and psychological processes,
the presented information is organized.
This the link between observing information and
performing a choice. In contrast to expected utility
theory, risk is evaluated on two different dimensions.
(1) Probabilities and (2) payoffs
In contrast to normative choice theories, the goal of
prospect theory is to provide good prediction of
choices
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Editing Phase: Coding
In contrast to expected utility theory, decision makers do not consider their final
wealth. They consider gains and losses compared to a reference point.
During the editing phase, decision makers will decide what reference point to use
(e.g. opportunity cost, minimum wage requirement, etc.)
The payoffs of the lottery will then be coded as a gain or a loss
Choice Problem Modification
Option L
200.50
Option S
10
Expected
earnings in an
experiment
10
Option L
100.5-10
Option S
0
or
Reference Point
orEvaluation
Phase
Coding
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Editing Phase: Combination
In the evaluation phase, as in expected utility theory, only payoffs and
probabilities are considered
Therefore, probabilities of events with identical outcomes are combined
to one event.
Choice Problem
Option L
20E1(0.1)20E2(0.5)0
Option S
10
Option L
200.60
Option S
10
or
Reduction to Payoffs and Probabilities
orEvaluation
Phase
Combination
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Editing Phase: Simplification
People have difficulties to pick up small numerical differences in
probabilities and payoffs
For both, probabilities and payoffs, are modified to simpler numbers
Choice Problem
Option L
210.490
Option S
10
Option L
200.50
Option S
10
or
Rounding up/down to simpler numbers
orEvaluation
Phase
Simplification
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Editing Phase: Segregation
People perceive situations involving risk different than situations involving
sure outcomes (i.e. sure payoffs are not risky payoffs with probability 1)
Sure gains are segregated from the lottery, the same is true for sure losses
Choice Problem
Option L
300.2510
Option S
15
Option L
10 + 200.250
Option S
15
or
Disentangle safe from risky payoffs
orEvaluation
Phase
Segregation
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Editing Phase: Cancellation (Type I)
People focus on differences rather than similarities when evaluating
prospects
Equal payoffs of two options are therefore not considered when
performing a choice (are considered not to have an influence on wealth)
Choice Problem
Option L
200.250.5-5
Option S
200.2150.5-10
Option L
00.250.5-5
Option S
00.2150.5-10
or
Identical payoffs are not considered
orEvaluation
Phase
Cancellation
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Editing Phase: Cancellation (Type II)
In expected utility theory we have the Reduction of Compound Lotteries
axiom
In prospect theory: two-stage lotteries are reduced to the reduced form
If in the first stage one payoff is zero, the first stage is neglected all
together
Two-stage Lottery Neglecting of the first stage
Evaluation
Phase
Cancellation
0
20
000.25
0.75
0.8
0.2
20
00
0.8
0.2
h l
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Editing Phase
Note:
The sequence of editing
procedures may differ between
decision makers and choice
problems
The sequence of editingprocedures probably depends on
the task and framing of the
choice problem
The application of some editing
procedures may prevent othersfrom being applied
Coding
Combination
Simplification
Segregation
Cancellation
B h i l Fi
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Note down your decisions for the following scenario
Story: 600 people are attacked by a fatal disease
Choice: Which program would you prefer
Program A: Saving 200 lives for sure
Program B: Saving 600 lives with 1/3 probability
S1
B h i l Fi
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Note down your decisions for the following scenario
Story: 600 people are attacked by a fatal disease
Choice: Which program would you prefer
Program A: Losing 400 lives for sure
Program B: Losing 600 lives with 2/3 probability
S2
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Note down your decisions for the following scenario
Story: Imagine that you have just been given 1000 Euro
Choice: Which option would you prefer
Option A: You receive 500 Euro for sure
Option B: You receive 1000 Euro with 50% chance
and nothing otherwise
S3
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Note down your decisions for the following scenario
Story: Imagine that you have just been given 2000 Euro
Choice: Which option would you prefer
Option A: You have to pay back 500 Euro for sure
Option B: You have to pay back 1000 Euro with 50% chance
and nothing otherwise
S4
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Framing effect
Story: 600 people are attacked by a fatal disease
Choice: Which program would you prefer
Live-saving frame:
Program A: Saving 200 lives for sure Program B: Saving 600 lives with 1/3 probability
Live-losing frame:
Program A: Losing 400 lives for sure
Program B: Losing 600 lives with 2/3 probability
Program A and B are identical in both scenarios.
Only the Frame of choice tasks changes
S1
S2
Blacked Out
To be revealed in the lecture
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Framing Effect
Story: Imagine that you have just been given 1000 Euro
Choice: Which option would you prefer
Option A: You receive 500 Euro for sure
Option B: You receive 1000 Euro with 50% chanceand nothing otherwise
Story: Imagine that you have just been given 2000 Euro
Choice: Which option would you prefer
Option A: You have to pay back 500 Euro for sure
Option B: You have to pay back 1000 Euro with 50% chance
and nothing otherwise
Option A and B are identical in both scenarios.
Only the Frame of choice tasks changes
S3
S4
Blacked Out
To be revealed in the lecture
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Evaluation Phase: Value Function
Three characteristics
Decreasing marginal utility for
gains (risk-aversion), identical
to expected utility theory ()
Risk-seeking for losses ()
Loss-aversion, i.e. people
generally reject lotteries of the
form +X0.5-X ()
Does loss aversion exist in expected utility theory?
Can you think of an experimental method to measure loss aversion?
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Evaluation Phase: Probability Weighting
Kahneman and Tversky, 1979 Kahneman and Tversky 1992
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e a o a a ce
Fourfold pattern of risk attitude
Payoff
Probability
low high
risk-seeking
risk-averse risk-seeking
risk-averse
but not a new idea
(Friedman and Savage, 1948 )
and (Markowitz, 1952)
Implicit in Prospect Theory
(Kahneman and Tversky, 1979)
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What are the lessons learned in Chapter 6?
Please take some time to compile a list of a few bullet points about
the most important facts you took from this chapter.
Check and discuss your list with that of your neighbor
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Lessons learned: Chapter 6
There are two approaches in modeling decision making under risk
Normative (i.e. expected utility theory)
Descriptive (i.e. prospect theory)
Prospect theory consists of two processes
Editing phase (psychological biases concerning the numerical information) Evaluation Phase
Value function (similar to expected utility theory)
Probability function
Implication of evaluation phase: fourfold pattern of risk preferences
Blacked Out
To be revealed in the lecture
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References: Chapter 6
Friedman, Milton and L. J. Savage (1948). The utility analysis of choices involving risk.
Journal of Political Economy, 56 (4), 297-304.
Kahneman, Daniel and Amos Tversky (1979). Prospect theory: An analysis of decision
under risk. Econometrica, 47 (2), 263-292.
Markowitz, Harry (1952). The utility of wealth. Journal of Political Economy, 60 (2),
151-158.
Neumann, John von and Oskar Morgenstern (1944). Theory of Games and Economic
Behavior. Princeton University Press: Princeton.
Tversky, Amos and Daniel Kahneman (1992). Advances in prospect theory: Cumulative
representation of uncertainty. Journal of Risk and Uncertainty, 5 (4), 297-323.