Lecture 2

Transcript

Lecture 2

Ce.R.D. - Center for Research on Risk and Decision
DPSS - University of Padova
http://decision.psy.unipd.it/
Prospect theory
Behavioral Economics class
Faculty of Economics - University of Padova
Academic year 2010/2011
Ce.R.D.
Centro di Ricerca sul
Rischio e la Decisione
Prospect theory:
A descriptive model of decisions
Starting with their studies on the violation of rationality principles, Kahneman
and Tversky (1979; 1992) proposed a model aimed at describing decisions in a
more accurate (and realistic) way:
Such model has been labeled Prospect Theory.
Prospect theory is not in contradiction with the Expected Utility theory,
but rather aims at completing and integrating it.
Expected Utility theory provides a model about how individuals
should behave when they are striving to maximize the outcome of
their decisions.
Prospect theory provides a model about the cognitive processes
that induce individuals to make sub-optimal decisions in their
everyday life.
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Prospect theory:
A descriptive model of decisions
By a matter of fact, Kahneman and Tversky’s model considers the Expected
Utility model as the benchmark to measure the quality of choices made by
individuals in many different domains (economics, healthcare, law, policy making,
etc.).
When making choices under uncertainty, individuals have a tendency to
simplify the decision process as much as possible in order to save their
cognitive resources.
In other words, cognitive limitations (e.g., memory and attention
limitations) make difficult to perform the complex computations
required to extract the expected utility of each alternative.
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What is a prospect?
The term «prospect» substitutes the economic term lottery, and aims at making
clearer the subjective status that alternatives have for decision makers.
A prospect is a combination of all possibile outcomes of an alternative
and the probabilities associated with each of these outcomes.
Prospect X: (x1, p1; ... ; xn, pn) where p1 + ... + pn = 1
For seek of simplicity it is possible to omit null outcomes and use
the (x, p) notation to indicate the prospect (x, p; 0, 1-p) which offers
the outcome x with probability p and 0 with probability 1 - p.
Sure prospects that offer the certainty of obtaining x can be
identified with the form (x).
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Two stages of the decision process
In the Prospect theory, we distinguish between two stages of the decision
process:
«Editing» phase
At this stage, decision makers perform a preliminary analysis of the
alternatives that leads to a simplified version of the available
prospects.
«Evaluation» phase
At this stage, the simplified prospects created in the editing phase
are evaluated and the prospect with the highest value is chosen.
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The «editing» phase
The preliminary analysis of prospects is carried out mostly at the unconscious
level (we are unaware of doing it) and makes use of wide number of mental
operations:
The most common editing procedures are:
Coding.
Combination.
Segregation.
Cancellation.
Simplification.
Detection of dominance.
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operations:
Coding.
Combination.
Segregation.
Cancellation.
Simplification.
Ce.R.D.
operations:
Coding.
Combination.
Segregation.
Cancellation.
Simplification.
Ce.R.D.
operations:
Coding.
Combination.
Segregation.
Cancellation.
Simplification.
Ce.R.D.
operations:
Coding.
Combination.
Segregation.
Cancellation.
Simplification.
Ce.R.D.
operations:
Coding.
Combination.
Segregation.
Cancellation.
Simplification.
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«Coding»
Results offered by a prospect are coded on the basis of a reference point («are
they above the reference point? then this is good...!»; «are they below the
reference point? then this is bad...!»).
People represent the outcomes of a prospect in terms of gains or
losses compared to their situation at the time of the decision
(alternatively they may use as a reference point a goal that they wish
to achieve).
From an economical point of view, an investor should always judge
a €3000 gain as positive.
However, a €3000 gain could be considered as a loss if the goal
(reference point) was a €4000 gain.
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«Combination»
Using this procedure the decision maker can combine outcomes that have
identical amount but different probabilities of happening.
Example:
Prospect Y: (€100, 0.25; - €200, 0.3; €100, 0.45)
this prospect could be simplified as follows:
Prospect Y’: (€100, 0.7; - €200, 0.3)
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«Segregation»
On some occasions, the decision maker could be faced with the evaluation of
prospects that offer both riskless and risky outcomes. On these occasions, it is
possible to separate sure and uncertain outcomes:
Example:
Prospect Z: (€400, 0.8; €150, 0.2)
could be simplified as follows:
Prospect Z’: (€150; €250, 0.8)
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«Cancellation»
To simplify the choice among different prospects a decision maker can cancel,
or eliminate, the components that are common to all prospects:
Example, if he has to choose between the following prospects:
Prospect A: (€1000, 0.25; - €100, 0.75)
Prospect B: (€1000, 0.1; €500, 0.4; - €200, 0.5)
then the two prospects could be simplified as follows:
Prospetto A’: (€1000, 0.15; - €100, 0.75)
Prospetto B’: (€500, 0.4; - €200, 0.5)
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«Simplification»
Often, the decision maker can simplify the elements of a prospect that make it
less easy to evaluate.
For instance, one type of simplification is to round the value of
outcomes and probabilities:
Prospect X: (€199, 0.49; - €201, 0.49; - €100, 0.02)
this prospect can be simplified as follows:
Prospect X’: (€200, 0.5; - €200, 0.5)
In this way, however, a prospect that was initially slightly
disadvantageous will now be perceived as perfectly neutral.
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«Detection of dominance»
Usually, decision makers attempt to identify the relationships of dominance
among different alternatives and discard those prospects that are dominated by
others.
However, as we have seen while dealing with the violation of
dominance, real decision makers are often deceived by the way
alternatives are described.
They are able to detect a relationship of dominance when it is
easy to spot simply by comparing two prospect but not when it
this requires complex mental computations.
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A very important aspect of the editing phase is that the different simplification
procedures can be applied without a precise order. Their use depends on which
information attracts the attention of a decision maker.
This is a problem when we are trying to predict the evaluations (and
consequently the choices) people make, because:
the use of a particular simplification procedure may prevent the use
of another procedure.
therefore the order used to apply these procedures to a prospect
has a huge impact on the final look of prospects at the time of the
decision.
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Many intuitive reasoning strategies that we will see in future lectures (heuristics
and economic behaviors) arise from these simplification procedures.
From this point of view, the editing phase is a fundamental stage in
the decision process.
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The «evaluation» phase
In the evaluation phase, the decision maker compares the simplified forms of
each available prospect.
The evaluation phase is based on two different functions that a
decision maker uses to evaluate, subjectively, the outcomes and the
probabilities associated with those outcomes.
The «weighing» function.
The «value» function.
The «evaluation» phase:
Weighing function
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Subjective
probabilities
Objective evaluation of probabilities
Weighing function
0
100
Objective probabilities
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Weighing function
Subjective
probabilities
The weighing function casts light on two
important issues regarding the
subjective evaluation of probabilities:
Objective evaluation of probabilities
Low probabilities are usually
overestimated.
Weighing function
Medium and high probabilities
are usually underestimated.
0
100
Objective probabilities
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Weighing function
This means that unlikely outcomes are overestimated compared with the
certainty of not getting them.
At the same time, likely outcomes are underestimated compared with the
certainty of getting them.
This point explains the certainty effect and the example we made
while analyzing the violation of independence.
Going from a sure win to a highly probable one (es., 98%)
significantly reduces the level of attractiveness of an alternative
(high probabilities are underestimated).
Going from a sure loss to a highly probable one makes an
alternative less negative (the small chance to avoid a loss is
overestimated).
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The «evaluation» phase:
Value function
Subjective result
Gain frame
Status quo
- 500
+ 500
Loss frame
Objective result
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Value function
The value function proposed by Kahneman
and Tversky (1979; 1992) has three main
characteristics:
Outcomes are evaluated on the
basis of a reference point and are
categorized as gains or losses.
Subjective result
Gain frame
In both frames (gains and losses)
the function is characterized by a
diminishing sensitivity at the
extremes.
Right out of the reference point,
the function is steeper in the loss
frame than in the gain frame.
Status quo
- 500
+ 500
Loss frame
Objective result
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Value function
These characteristics of the value function are at the basis of a series of
behaviors that are considered irrational by an economic point of view:
Loss aversion.
Reference point.
Framing effect.
Status quo bias.
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Value function
Loss aversion.
Reference point.
Framing effect.
Status quo bias.
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Value function
Loss aversion.
Reference point.
Framing effect.
Status quo bias.
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Value function
Loss aversion.
Reference point.
Framing effect.
Status quo bias.
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«Loss aversion»
Since the value function is steeper in the loss frame than in the gain frame,
people have an asymmetric perception of the outcomes that fall below and
above the reference point.
The pain induced by a loss is about double the happiness induced by
a gain of the same absolute value.
From a psychological point of view, a gain and a loss of equal
amount do not cancel each other. An individual would perceive their
combined results as a loss.
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«Loss aversion»
For this reason, people are often not willing to accept the following gamble:
A 50% chance of gaining €100 and a 50% chance of losing €100.
The psychological weight of the potential loss overcomes that of the
potential gain and the gamble is perceived as «unfair».
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«Loss aversion»
Loss aversion can be tested presenting questions like the following:
Imagine you have to decide whether to accept or not a gamble which
consist in throwing a fair coin. If you lose you will have to pay €100 to
another person.
In order to accept this gamble, which is the minimum amount of
money that you wish to receive if you win?
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«Reference point»
Imagine you can choose in which society to live:
Would you prefer to live in Society A or in Society B?
Society A: Your salary is €50.000; other people salary is €25.000.
Society B: Your salary is €100.000; other people salary is €200.000.
Now, what would you prefer in this second situation:
Imagine that we know how to measure IQ with high precision. Would you
prefer to live in Society C or in Society D?
Society A: Your IQ is 110; the average IQ is 90.
Society B: Your IQ is 130; the average IQ is 150.
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«Reference point»
Imagine you can choose in which society to live:
Would you prefer to live in Society A or in Society B?
Society A: Your salary is €50.000; other people salary is €25.000.
Society B: Your salary is €100.000; other people salary is €200.000.
Now, what would you prefer in this second situation:
Imagine that we know how to measure IQ with high precision. Would you
prefer to live in Society C or in Society D?
Society A: Your IQ is 110; the average IQ is 90.
Society B: Your IQ is 130; the average IQ is 150.
Most people choose Society A in both cases, because they prefer to get a
lower salary or to be less intelligent as long as they are better than others.
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«Reference point»
Because of loss aversion, as well as the tendency to code outcomes in terms of
gains and losses, people are more able to make comparative evaluations rather
than absolute ones:
When choosing between two outcomes individuals may prefer the less
positive one if it grants the possibility of being above average (i.e.,
better than other people).
This behavior is clearly irrational, since from an objective point of view
a rational actor should always aim at the best alternative in absolute
terms (rational actors are not influenced by other people but simply
seek to maximize their wealth).
However, on many occasions, the feeling of being above average is
more important than the actual result obtained, therefore helps
increasing, subjectively, the value of an objectively inferior alternative.
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«Framing» effect
The framing effect arises when preferences are modified by the way
alternatives are described (e.g., as gains or as losses).
We saw a case of framing effect while dealing with the violation of
independence.
Problems that are described in different, but logically equivalent
ways induce people to modify their choices.
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«Framing» effect
Example (Tversky & Kahneman, 1981):
Imagine that Italy is preparing for the outbreak of an unusual Asian
disease, which is expected to kill 600 people. Two alternative
programs to combat this disease have been proposed. Assume that
the exact scientific estimate of the consequences of the programs are
as follows:
If program A is adopted, 200 people will be saved.
If program B is adopted, there is a 1/3 probability that 600
people will be saved, and a 2/3 probability that no people will
be saved.
Which of the two programs would you favor?
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«Framing» effect
Example (Tversky & Kahneman, 1981):
Imagine that Italy is preparing for the outbreak of an unusual Asian
disease, which is expected to kill 600 people. Two alternative
programs to combat this disease have been proposed. Assume that
the exact scientific estimate of the consequences of the programs are
as follows:
If program C is adopted, 400 people will die.
If program D is adopted, there is a 1/3 probability that nobody
will die, and a 2/3 probability that 600 people will die.
Which of the two programs would you favor?
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«Framing» effect
Usually, the majority of respondents presented with programs A and B (gains)
prefer the safest alternative (A; risk aversion), whereas the majority of
respondents presented with programs C and D prefer the uncertain alternative
(D; risk seeking).
However, the two pairs of programs are identical since they are complementary
to each other:
Program A will save 200 people out of 600 for sure (400 will die
exactly as it is stated in program C).
The same reasoning holds for the two uncertain programs (D’s
outcomes are complementary to B’s outcomes).
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«Framing» effect
A consumer behavior experiment showed the framing effect in the use of food
labels (Levin & Gaeth, 1988).
Participants were presented with some meat and were asked to judge
it. There were two different conditions:
Cond1 «only label»: Half of the participants were told that the meat
was «75% lean», whereas the other participants were told that the
meat was «25% fat».
Cond2 «label and tasting»: Participants were provided with either
one or the other label (75% lean or 25% fat) but were also allowed
to taste the meat before judging it.
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«Framing»
All participants judged the meat on the following four rating scales ranging from
0 to 7:
Good taste vs. bad taste.
Oily vs. not oily.
High quality vs. low quality.
Fat vs. lean.
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«Framing»
6
*
*
*
5.69
25% Fat
75% Lean
*
5.33
5.15
*
4.49
4.43
4
*
*
4.71
4.67
4.71
4.13
3.95
3.66
5.00
3.57
3.43
2.96
2.83
2
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Condizione 1: only label
Fa
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Condizione 2: label + tasting
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«Status quo bias»
When a decision is made under uncertainty decision makers can choose to
«not decide» and maintain things as they already are.
This may happen for several different reasons:
Inertia and procrastination (to modify things a person may have
to engage in actions that require effort, time or money).
Uncertainty (modifying things may oblige the decision maker to
face an uncertain condition that can led to both positive or negative
results, but the negative ones weigh more than the positive).
Inexperience (non-expert individuals are often against changes,
especially if a situation looks already satisfying because they are
unable to judge the chance that a change would produce an
improvement).
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«Status quo bias»
Example: Car insurances in New Jersey and Philadelphia (Johnson & Hershey,
1993).
In the early ‘90s car insurance laws were modified in both states. To
reduce costs of the policies it was decided the introduction of a new policy
which excluded the theft and fire accidents and covered only third party
damages. However:
In New Jersey, new drivers were insured by default with the lowcost solution (opt-in solution) and could upgrade it to full coverage.
In Pennsylvania, new drivers were obliged to buy the full coverage
solution (opt-out solution) and could downgrade it to the low-cost
policy.
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«Status quo bias»
Johnson and Hershey analyzed drivers’ choices in the two states and found that
the default solution (the one drivers had to make upon buying a car) had a
significant effect on their decisions about car insurance policies:
Only 20% of drivers from New Jersey decided to upgrade their
insurance to the full coverage policy (they had the low-cost policy as
the default solution).
In contrast, almost 75% of drivers from Pennsylvania decided to keep
the full coverage policy (that was the default solution in their state).
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«Status quo bias»
The decision process behind the status quo bias is so strong that is now very
popular in policy making:
In the United States it has been used to increase the amount of
employees participation to integrative pension plans (SMaRTTM,
Benartzi & Thaler, 2004).
In the past an employee had to actively decide whether to
participate in a pension plan or not (opt-in), whereas now they had
to decide whether to exit from the plan or not (opt-out) as they are
made part of the plan by default upon signing a contract with their
employer
Countries whose citizens are organ donors by default (opt-out) have a
rate of organ donation much higher than countries whose citizens are
not organ donors by default (opt-in).
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«Status quo bias»
Mean = 97.56%
Opt-in
99.9
98.0
99.9
99.9
99.5
99.6
85.9
Mean = 15.23%
(Fonte: Johnson & Goldstein (2003). Do defaults save lives? Science, 302, 1338-1339).
Sweden
Portugal
Poland
Hungary
France
Belgium
United Kingdom
Holland
4.3
12.0
Austria
17.2
Germany
27.5
Denmark
100%
86%
71%
57%
43%
29%
14%
0%
Opt-out

Lecture 2

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