Preferences In Ambiguity
Aversion
Our discussion so far has centered on understanding
how people act when the outcomes of gambles have
known objective probabilities.
In reality, probabilities are rarely objectively known.
To handle these situations, Savage (1964) develops a
counterpart to expected utility known as subjective
expected utility (SEU).
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10:13 AM
Preferences In Ambiguity
Aversion
Under certain axioms, preferences can be
represented by the expectation of a utility
function. This time weighted by the individual’s
subjective probability assessment.
Experimental work in the last few decades has
been as unkind to SEU as it was to EU. The
violations this time are of a different nature, but
they may be just as relevant for financial
experts.
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Preferences In Ambiguity
Aversion
The classic experiment was described by Ellsberg
(1961).
Suppose that there are two urns, 1 and 2.
Urn 1 also contains 100 balls, a mix of red and blue,
but the subject does not know the proportion of
each.
Urn 2 contains a total of 100 balls, 50 red and 50
blue.
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Preferences In Ambiguity
Aversion
Subjects are asked to choose one of the following two
gambles, each of which involves a possible payment of
$100, depending on the colour of a ball drawn at
random from the relevant urn.
a1: a ball is drawn from Urn 1, $100 if red, $0 if blue,
a2: a ball is drawn from Urn 2, $100 if red, $0 if blue.
Note your choice (Urn 1 mixed, Urn 2 50/50).
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Preferences In Ambiguity
Aversion
Subjects are then also asked to choose between the
following two gambles:
b1: a ball is drawn from Urn 1, $100 if blue, $0 if red,
b2: a ball is drawn from Urn 2, $100 if blue, $0 if red.
Note your choice (Urn 1 mixed, Urn 2 50/50).
a2 is typically preferred to a1, while b2 is chosen over b1.
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Preferences In Ambiguity
Aversion
These choices are inconsistent with SEU: the choice
of a2 implies a subjective probability that fewer than
50% of the balls in Urn 1 are red, while the choice of
b2 implies the opposite. (You could choose a1 and b2
or a2 and b1.)
The experiment suggests that people do not like
situations where they are uncertain about the
probability distribution of a gamble.
Such situations are known as situations of ambiguity,
and the general dislike for them, as ambiguity
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aversion.
Preferences In Ambiguity
Aversion
An early discussion of this aversion can be found in
Knight (1921), who defines risk as a gamble with
known distribution and uncertainty as a gamble with
unknown distribution, and suggests that people
dislike uncertainty more than risk.
SEU does not allow agents to express their degree
of confidence about a probability distribution and
therefore cannot capture such aversion.
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Preferences In Ambiguity
Aversion
Were you to accept the various forms of utility then
Edwards and Fasolo (2001) tabulate nineteen steps
to reaching a decision.
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Step
1
2
3
4
5
6
7
8
9
10
11
12
13
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15
16
17
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Preferences In Ambiguity
Aversion
Task
Identify options
Identify possible outcomes of each option
Identify attributes with which to evaluate outcomes
Score each outcome on each attribute
Weight attributes
Aggregate scores and weights into utilities (multi-attribute utility)
record
Identify events that determine which outcome will follow choice of an option
For each event, specify a prior distribution
revision step
Identify information that might modify the probabilities specified in step 8
If information is free or cheap, buy it (maximum subjectively expected utility)
If information costs, find out how much
cycle step
Determine the conditional gain from information purchase
Aggregate cost of information and gain from having it (maximum subjectively expected
utility)
Decide whether to buy the information (maximum subjectively expected utility and
Bayes’ theorem of probability theory)
If information is bought, update prior probabilities (Bayes’ theorem of probability
theory)
record
Back to Step 11. Iterate till no new information is bought (maximum subjectively
expected utility)
Assemble the numbers output at steps 6 and 15.
Calculate expected utilities (maximum subjectively expected utility)
Choose the option with the highest expected utility (maximum subjectively expected
utility)
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Step
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
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Preferences In Ambiguity
Aversion
Task
Identify options
Identify possible outcomes of each option
Identify attributes with which to evaluate outcomes
Score each outcome on each attribute
Weight attributes
Aggregate scores and weights into utilities (multi-attribute utility)
record
Identify events that determine which outcome will follow choice of an option
For each event, specify a prior distribution
revision step
Identify information that might modify the probabilities specified in step 8
If information is free or cheap, buy it (maximum subjectively expected utility)
If information costs, find out how much
cycle step
Determine the conditional gain from information purchase
Aggregate cost of information and gain from having it (maximum subjectively expected
utility)
Decide whether to buy the information (maximum subjectively expected utility and
Bayes’ theorem of probability theory)
If information is bought, update prior probabilities (Bayes’ theorem of probability
theory)
record
Back to Step 11. Iterate till no new information is bought (maximum subjectively
expected utility)
Assemble the numbers output at steps 6 and 15.
Calculate expected utilities (maximum subjectively expected utility)
Choose the option with the highest expected utility (maximum subjectively expected
utility)
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Preferences In Ambiguity
Aversion
Ambiguity aversion appears in a wide variety of contexts.
For example, a researcher might ask a subject for his
estimate of the probability that a certain team will win
its upcoming football match, to which the subject might
respond 0.4.
The researcher then asks the subject to imagine a
chance machine, which will display 1 with probability 0.4
and 0 otherwise, and asks whether the subject would
prefer to bet on the football game – an ambiguous bet –
or on the machine, which offers no ambiguity.
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Preferences In Ambiguity
Aversion
In general, people prefer to bet on the machine,
illustrating aversion to ambiguity.
Heath and Tversky (1991) argue that in the real world,
ambiguity aversion has much to do with how competent
an individual feels he is at assessing the relevant
distribution.
Ambiguity aversion over a bet can be strengthened by
highlighting subjects’ feelings of incompetence, either by
showing them other bets in which they have more
expertise, or by mentioning other people who are more
qualified to evaluate the bet (Fox and Tversky 1995).8.12
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Preferences In Ambiguity
Aversion
Further evidence that supports the competence
hypothesis is that in situations where people feel
especially competent in evaluating a gamble, the
opposite of ambiguity aversion, namely a “preference
for the familiar”, has been observed.
In the example above, people chosen to be especially
knowledgeable about football often prefer to bet on
the outcome of the game than on the chance
machine. Just as with ambiguity aversion, such
behaviour cannot be captured by SEU.
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Preferences In Ambiguity
Aversion - Choices and Reasons
Other research establishes even more dramatically
the role of reasons in decision-making.
For instance, Tversky and Shafir (1992b)
demonstrate that when people are searching, they do
not merely search to find a high-value option — as
assumed in conventional search theory — but also
seem to search for a “reason” to end their search
and make one particular choice. (See “heuristics” in
the first lecture.)
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Preferences In Ambiguity
Aversion - Choices and Reasons
Tversky and Shafir (1992b) conducted experiments
where subjects were asked either to choose among
existing options, or to engage in a costly further
search.
In addition to a parallel experiment where subjects
were asked to choose among gambles for real
monetary stakes, a hypothetical apartment-search
problem was posed.
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Preferences In Ambiguity
Aversion - Choices and Reasons
Shafir, Simonson, and Tversky (1993, pp. 19-20)
summarise it as follows: Subjects were presented
choices between hypothetical student apartments.
Some subjects received the following problem:
Conflict:
Imagine that you face a choice between two
apartments with the following characteristics:
x) $290 a month, 25 minutes from campus
y) $350 a month, 7 minutes from campus
Both have one bedroom and a kitchenette.
Note your choice.
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Preferences In Ambiguity
Aversion - Choices and Reasons
You can choose now between the two apartments or
you can continue to search for apartments (to be
selected at random from the list you received).
In that case, there is some risk of losing one or both
of the apartments you have found. (Refer back to
the heuristics in lecture 1.)
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Preferences In Ambiguity
Aversion - Choices and Reasons
Other subjects received a similar problem except
that option y was replaced by option x’, to yield a
Choice between:
Dominance:
x) $290 a month, 25 minutes from campus
x′) $330 a month, 25 minutes from campus
Both have one bedroom and a kitchenette.
Note your choice.
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Preferences In Ambiguity
Aversion - Choices and Reasons
In both pairs of problems the choice between x and y
- the conflict condition - is nontrivial because the x
is better on one dimension and the y is better on the
other.
In contrast, the choice between x and x′ - the
dominance condition – involves no conflict because
the former strictly dominates the latter.
Thus, while there is no obvious reason to choose one
option over the other in the conflict condition, there
is a decisive argument for preferring one of the two
alternatives in the dominance condition.
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Preferences In Ambiguity
Aversion - Choices and Reasons
On average, subjects requested an additional
alternative 64% of the time in the conflict condition
(x,y), and only 40% of the time in the dominance
condition (x,x’).
Subjects’ tendency to search for additional options,
in other words, was greater when the choice among
alternatives was harder to rationalize, than when
there was a compelling reason and the decision was
easy.
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Preferences In Ambiguity
Aversion - Choices and Reasons
Why is the greater propensity to search further
under the conflict condition (x,y) than under the
dominance condition (x,x’) inconsistent with the
utility-maximization model?
Clearly U(x) > U(x′) for all subjects; it is
indeterminate whether subjects would asses
U(x) > U(y) or U(y) > U(x).
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Preferences In Ambiguity
Aversion - Choices and Reasons
But if the decision to keep searching were based
simply on some perceived continuation utility, V.
Then any subject who would choose to stop under the
dominance condition (x,x’), indicating that U(x) = V,
would also choose to stop under the conflict
condition (x,x’).
Since they could always choose x where U(x) = V, or
choose y, if U(y) > U(x), and do even better.
The aggregate data, on seeking alternatives, reject
the value-maximization hypothesis.
What explains the pattern?
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Preferences In Ambiguity
Aversion - Choices and Reasons
Tversky and Shafir (1992b) argue that the choice in the
conflict condition (x,y) is difficult, and lacks a clear
reason to choose x versus y - one is cheaper, the other
is closer to campus, and it is hard to weigh these two
attractive features.
The dominance condition (x,x’), on the other hand, yields
an obvious choice - x is just as close as x′ and is
cheaper. This is a simple, obvious “reason” to choose x.
The experiment suggests that search behaviour may be
explained in part by the search for “reasons” rather
than solely by the search for “value.”
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Preferences In Ambiguity
Aversion - Choices and Reasons
Tversky and Shafir (1992a) show that, even if the
information will not affect their decision, people are
likely to delay decisions until they learn information that
may affect their reason for making the decision.
Students were asked, under different hypothetical
scenarios, whether they would like to buy a bargain
package for a Hawaii vacation during winter break.
Prior to the vacation, they would find out whether they
had passed or failed an important exam; if they failed,
they would have to re-take the exam after winter break.
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Preferences In Ambiguity
Aversion - Choices and Reasons
Students were given the choice to buy the vacation
package, not buy the package, or pay a non-refundable
$50 fee to delay the decision. Three conditions were run:
The students were told either
a)
They would not know whether they passed the exam
when they had to choose - but if they bought the
“delay option," they would then know whether they
passed before they ultimately had to decide.
b)
They failed the exam, and would have to re-take
after winter break.
c)
They passed the exam.
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Preferences In Ambiguity
Aversion - Choices and Reasons
Of those asked in condition a (don’t know), 32% chose
to buy the package, 7% chose not to buy the package,
and 61% chose to pay $50 to delay the decision.
The delay option makes perfect sense: If your
decision whether to take the vacation depends on
whether or not you passed the exam, you may pay to
wait to find out first.
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Preferences In Ambiguity
Aversion - Choices and Reasons
However, the results in conditions b (fail) and c (pass)
rule out this explanation - only 31% in each group chose
the delay option, and between 54% and 57% chose to
buy the vacation (and, respectively, 16% and 12% chose
not to take the package).
That is, a majority of both passers and failers would
choose to buy the vacation, yet without knowing, far
fewer would choose to buy the vacation.
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Preferences In Ambiguity
Aversion - Choices and Reasons
Tversky and Shafir (1992a) argue that the key is
that the reason for going on the vacation is very
different depending on whether or not you pass either you are going as a reward for a job well done,
or to refresh yourself before retaking the exam.
Like the apartment-search example, this example
illustrates that people choose to defer decisions in
part because they seek a clear-cut reason for their
choice, not just to get the highest value out of their
choice.
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Preferences In Ambiguity
Aversion - Choices and Reasons
In a similar vein, Redelmeier and Shafir (1995) report
related results. Groups of physicians were randomly
picked to respond to each of two hypothetical
scenarios:
A)
Whether to prescribe one treatment in one
category of treatments (e.g., medication) or one
treatment in a second category (e.g., surgery), or
B)
Whether to prescribe one of two treatments in
the first category, or one treatment in the
second category.
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Preferences In Ambiguity
Aversion - Choices and Reasons
They found that more physicians chose the second
category in Scenario B — apparently because the
decision felt less arbitrary than choosing one of two,
hard-to distinguish choices (medication or surgery).
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Is This Area “Important”
Who said, when describing Kahneman and Smith?
Daniel Kahneman of Princeton University, USA
“for having integrated insights from psychological
research into economic science, especially concerning
human judgment and decision-making under uncertainty”
and
Vernon L. Smith of George Mason University, USA
“for having established laboratory experiments as a tool
in empirical economic analysis, especially in the study of
alternative market mechanisms”.
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Is This Area “Important”
The Royal Swedish Academy of Sciences on deciding
that the Bank of Sweden Prize in Economic Sciences in
Memory of Alfred Nobel, 2002 be awarded to Kahneman
and Smith.
Advanced Information
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Psychological and Experimental
Economics
Traditionally, much of economic research has relied
on the assumption of a “homo œconomicus” motivated
by self-interest and capable of rational decision
making. Economics has also been widely considered a
non-experimental science, relying on observation of
real-world economies rather than controlled
laboratory experiments.
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Psychological and Experimental
Economics
Nowadays, however, a growing body of research is
devoted to modifying and testing basic economic
assumptions; moreover, economic research relies
increasingly on data collected in the lab rather than
in the field. This research has its roots in two
distinct, but currently converging, areas: the analysis
of human judgment and decision-making by cognitive
psychologists, and the empirical testing of
predictions from economic theory by experimental
economists.
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Daniel Kahneman
Has integrated insights from psychology into
economics, thereby laying the foundation for a new
field of research.
Kahneman’s main findings concern decision-making
under uncertainty, where he has demonstrated how
human decisions may systematically depart from
those predicted by standard economic theory.
Together with Amos Tversky (deceased in 1996), he
has formulated prospect theory as an alternative,
that better accounts for observed behaviour.
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Daniel Kahneman
Kahneman has also discovered how human judgment
may take heuristic shortcuts that systematically
depart from basic principles of probability.
His work has inspired a new generation of
researchers in economics and finance to enrich
economic theory using insights from cognitive
psychology into intrinsic human motivation.
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Vernon Smith
Has laid the foundation for the field of experimental
economics.
He has developed an array of experimental methods,
setting standards for what constitutes a reliable
laboratory experiment in economics.
In his own experimental work, he has demonstrated
the importance of alternative market institutions,
e.g., how the revenue expected by a seller depends on
the choice of auction method (see later).
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Vernon Smith
Smith has also spearheaded “wind-tunnel tests”, where
trials of new, alternative market designs – e.g., when
deregulating electricity markets – are carried out in
the lab before being implemented in practice.
His work has been instrumental in establishing
experiments as an essential tool in empirical economic
analysis.
Not much psychology here!
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By The Way
The four auction types are:
1. the English auction, where buyers announce their
bids in an increasing order until no higher bid is
submitted;
2. the Dutch auction, where a high initial bid is
gradually lowered until a buyer melds his acceptance;
3. the first-price auction, with sealed bids, where the
highest bidder pays his own bid to the seller;
4. the sealed-bid second-price auction, where the
highest bidder pays the second highest bid.
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Next Week
Overconfidence
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