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Prospect theory: an analysis of decision under risk

01 Mar 1979-Econometrica (Cambridge University Press)-Vol. 47, Iss: 2, pp 263-291

Abstract: This paper presents a critique of expected utility theory as a descriptive model of decision making under risk, and develops an alternative model, called prospect theory. Choices among risky prospects exhibit several pervasive effects that are inconsistent with the basic tenets of utility theory. In particular, people underweight outcomes that are merely probable in comparison with outcomes that are obtained with certainty. This tendency, called the certainty effect, contributes to risk aversion in choices involving sure gains and to risk seeking in choices involving sure losses. In addition, people generally discard components that are shared by all prospects under consideration. This tendency, called the isolation effect, leads to inconsistent preferences when the same choice is presented in different forms. An alternative theory of choice is developed, in which value is assigned to gains and losses rather than to final assets and in which probabilities are replaced by decision weights. The value function is normally concave for gains, commonly convex for losses, and is generally steeper for losses than for gains. Decision weights are generally lower than the corresponding probabilities, except in the range of low prob- abilities. Overweighting of low probabilities may contribute to the attractiveness of both insurance and gambling. EXPECTED UTILITY THEORY has dominated the analysis of decision making under risk. It has been generally accepted as a normative model of rational choice (24), and widely applied as a descriptive model of economic behavior, e.g. (15, 4). Thus, it is assumed that all reasonable people would wish to obey the axioms of the theory (47, 36), and that most people actually do, most of the time. The present paper describes several classes of choice problems in which preferences systematically violate the axioms of expected utility theory. In the light of these observations we argue that utility theory, as it is commonly interpreted and applied, is not an adequate descriptive model and we propose an alternative account of choice under risk. 2. CRITIQUE

Summary (6 min read)

Jump to: [1. INTRODUCTION][50% chance to win nothing;][Certainty, Probability, and Possibility][N = 66 [73]* [27]][The Reflection Effect][Probabilistic Insurance][N=95 [20] [80]*][pu (w-x) + (1-p) u (w) = u (w-y) implies][Without loss of generality, we can set u(w -x) = 0 and u(w) = 1. Hence, u(wy) = 1-p, and we wish to show that rp(1-p)+(1-p)u(w-ry)> 1-p or u(w-ry)> 1-rp which holds if and only if u is concave. This is a rather puzzling consequence of the risk aversion hypothesis of utility theory, because probabilistic insurance appears intuitively riskier than regular insurance, which entirely eliminates the element of risk. Evidently, the intuitive notion of risk is not adequately captured by the assumed concavity of the utility function for wealth.][The Isolation Effect][The preceding problem illustrated how preferences may be altered by different representations of probabilities. We now show how choices may be altered by varying the representation of outcomes.][3. THEORY][) equals r(p)v(x) +[1 -r(p)]v(y). Hence, equation (2) reduces to equation (1) if wr(p) + r(lp) = 1. As will be shown later, this condition is not generally satisfied. Many elements of the evaluation model have appeared in previous attempts to modify expected utility theory. Markowitz][[3, 42]). Similar models were developed by Fellner [12], who introduced the concept of decision weight to explain aversion for ambiguity, and by van Dam [46] who attempted to scale decision weights. For other critical analyses of expected utility theory and alternative choice models, see Allais [2], Coombs [6], Fishburn][The Value Function][v(y)+v(-y)>v(x)+v(-x) and v(-y)-v(-x)>v(x)-v(y).][The Weighting Function][N=72 [17]][4. DISCUSSION][Risk][Shifts of Reference] and [Extensions]

1. INTRODUCTION

  • The present paper describes several classes of choice problems in which preferences systematically violate the axioms of expected utility theory.

50% chance to win nothing;

  • To appreciate the significance of the amounts involved, note that the median net monthly income for a family is about 3,000 Israeli pounds.
  • Several forms of each questionnaire were constructed so that subjects were exposed to the problems in different orders.
  • The problems described in this paper are selected illustrations of a series of effects.
  • The pattern of results was essentially identical to the results obtained from Israeli subjects.
  • The reliance on hypothetical choices raises obvious questions regarding the validity of the method and the generalizability of the results.

Certainty, Probability, and Possibility

  • In expected utility theory, the utilities of outcomes are weighted by their probabilities.
  • The best known counter-example to expected utility theory which e*ploits the certainty effect was introduced by the French economist Maurice Allais in 1953 [2] .
  • The following pair of choice problems is a variation of Allais' example, which differs from the original in that it refers to moderate rather than to extremely large gains.
  • The number of respondents who answered each problem is denoted by N, and the percentage who choose each option is given in brackets.
  • The certainty effect is not the only type of violation of the substitution axiom.

N = 66 [73]* [27]

  • Note that in Problem 7 the probabilities of winning are substantial (.90 and .45), and most people choose the prospect where winning is more probable.
  • Most people choose the prospect that offers the larger gain.
  • Similar results have been reported by MacCrimmon and Larsson [28] .
  • The above problems illustrate common attitudes toward risk or chance that cannot be captured by the expected utility model.
  • The results suggest the following empirical generalization concerning the manner in which the substitution axiom is violated.

The Reflection Effect

  • The previous section discussed preferences between positive prospects, i.e., prospects that involve no losses.
  • His subjects were indifferent between (100, .65; -100, .35) and (0), indicating risk aversion.
  • Second, recall that the preferences between the positive prospects in Table I are inconsistent with expected utility theory.
  • In the positive domain, the certainty effect contributes to a risk averse preference for a sure gain over a larger gain that is merely probable.
  • Third, the reflection effect eliminates aversion for uncertainty or variability as an explanation of the certainty effect.

Probabilistic Insurance

  • The prevalence of the purchase of insurance against both large and small losses has been regarded by many as strong evidence for the concavity of the utility function for money.
  • To illustrate this concept, consider the following problem, which was presented to 95 Stanford University students.
  • In this program you pay half of the regular premium.
  • In case of damage, there is a 50 per cent chance that you pay the other half of the premium and the insurance company covers all the losses; and there is a 50 per cent chance that you get back your insurance payment and suffer all the losses.
  • Under these circumstances, would you purchase probabilistic insurance: Yes, No.

N=95 [20] [80]*

  • It is worth noting that probabilistic insurance represents many forms of protective action where one pays a certain cost to reduce the probability of an undesirable event-without eliminating it altogether.
  • The installation of a burglar alarm, the replacement of old tires, and the decision to stop smoking can all be viewed as probabilistic insurance.
  • The responses to Problem 9 and to several other variants of the same question indicate that probabilistic insurance is generally unattractive.
  • In contrast to these data, expected utility theory (with a concave u) implies that probabilistic insurance is superior to regular insurance.

pu (w-x) + (1-p) u (w) = u (w-y) implies

  • (1r)pu(w -x) + rpu(wy) + (-p)u(w ry)> u(wy).

Without loss of generality, we can set u(w -x) = 0 and u(w) = 1. Hence, u(wy) = 1-p, and we wish to show that rp(1-p)+(1-p)u(w-ry)> 1-p or u(w-ry)> 1-rp which holds if and only if u is concave. This is a rather puzzling consequence of the risk aversion hypothesis of utility theory, because probabilistic insurance appears intuitively riskier than regular insurance, which entirely eliminates the element of risk. Evidently, the intuitive notion of risk is not adequately captured by the assumed concavity of the utility function for wealth.

  • The aversion for probabilistic insurance is particularly intriguing because all insurance is, in a sense, probabilistic.
  • The most avid buyer of insurance remains vulnerable to many financial and other risks which his policies do not cover.
  • There appears to be a significant difference between probabilistic insurance and what may be called contingent insurance, which provides the certainty of coverage for a specified type of risk.
  • Thus, two prospects that are equivalent in probabilities and outcomes could have different values depending on their formulation.
  • Several demonstrations of this general phenomenon are described in the next section.

The Isolation Effect

  • In order to simplify the choice between alternatives, people often disregard components that the alternatives share, and focus on the components that distinguish them (Tversky [44] ).
  • This approach to choice problems may produce inconsistent preferences, because a pair of prospects can be decomposed into common and distinctive components in more than one way, and different decompositions sometimes lead to different preferences.
  • The essential difference between the two representations is in the location of the decision node.
  • Thus, the outcome of winning 3,000 has a certainty advantage in the sequential formulation, which it does not have in the standard formulation.
  • The isolation effect implies that the contingent certainty of the fixed return enhances the attractiveness of this option, relative to a risky venture with the same probabilities and outcomes.

The preceding problem illustrated how preferences may be altered by different representations of probabilities. We now show how choices may be altered by varying the representation of outcomes.

  • Consider the following problems, which were presented to two different groups of subjects.
  • In fact, Problem 12 is obtained from Problem 11 by adding 1,000 to the initial bonus, and subtracting 1,000 from all outcomes.
  • Evidently, the subjects did not integrate the bonus with the prospects.
  • The choice between a total wealth of $100,000 and even chances to own $95,000 or $105,000 should be independent of whether one currently owns the smaller or the larger of these two amounts.
  • The responses to Problem 12 and to several of the previous questions suggest that this pattern will be obtained if the individual owns the smaller amount, but not if he owns the larger amount.

3. THEORY

  • The two scales coincide for sure prospects, where V(x, 1.0) = V(x) = v(x).

) equals r(p)v(x) +[1 -r(p)]v(y). Hence, equation (2) reduces to equation (1) if wr(p) + r(lp) = 1. As will be shown later, this condition is not generally satisfied. Many elements of the evaluation model have appeared in previous attempts to modify expected utility theory. Markowitz

  • The replacement of probabilities by more general weights was proposed by Edwards [9] , and this model was investigated in several empirical studies (e.g.,.

[3, 42]). Similar models were developed by Fellner [12], who introduced the concept of decision weight to explain aversion for ambiguity, and by van Dam [46] who attempted to scale decision weights. For other critical analyses of expected utility theory and alternative choice models, see Allais [2], Coombs [6], Fishburn

  • The equations of prospect theory retain the general bilinear form that underlies expected utility theory.
  • In order to accomodate the effects described in the first part of the paper, the authors are compelled to assume that values are attached to changes rather than to final states, and that decision weights do not coincide with stated probabilities.
  • These departures from expected utility theory must lead to normatively unacceptable consequences, such as inconsistencies, intransitivities, and violations of dominance.
  • Such anomalies of preference are normally corrected by the decision maker when he realizes that his preferences are inconsistent, intransitive, or inadmissible.
  • In these circumstances the anomalies implied by prospect theory are expected to occur.

The Value Function

  • An essential feature of the present theory is that the carriers of value are changes in wealth or welfare, rather than final states.
  • An individual's attitude to money, say, could be described by a book, where each page presents the value function for changes at a particular asset position.
  • Many sensory and perceptual dimensions share the property that the psychological response is a concave function of the magnitude of physical change.
  • These preferences are in accord with the hypothesis that the value function is concave for gains and convex for losses.
  • Hence, the derived value function of an individual does not always reflect "pure" attitudes to money, since it could be affected by additional consequences associated with specific amounts.

v(y)+v(-y)>v(x)+v(-x) and v(-y)-v(-x)>v(x)-v(y).

  • Thus, the value function for losses is steeper than the value function for gains.
  • Decision weights could produce risk aversion and risk seeking even with a linear value function.
  • Nevertheless, it is of interest that the main properties ascribed to the value function have been observed in a detailed analysis of von Neumann-Morgenstern utility functions for changes wealth (Fishburn and Kochenberger [14] ).
  • The functions had been obtained from thirty decision makers in various fields of business, in five independent studies [5, 18, 19, 21, 40] .
  • With a single exception, utility functions were considerably steeper for losses than for gains.

The Weighting Function

  • Decision weights are inferred from choices between prospects much as subjective probabilities are inferred from preferences in the Ramsey-Savage approach.
  • For any reasonable person, the probability of winning is .50 in this situation.
  • The two scales coincide (i.e., 77(p) = p) if the expectation principle holds, but not otherwise.
  • The authors turn now to discuss the salient properties of the weighting function 7r, which relates decision weights to stated probabilities.
  • The pattern of preferences in Problems 7 and 7', however, suggests that subadditivity need not hold for large values of p.

N=72 [17]

  • Note that in Problem 14, people prefer what is in effect a lottery ticket over the expected value of that ticket.
  • A similar quantum of doubt could impose an upper limit on any decision weight that is less than unity.
  • The following example, due to Zeckhauser, illustrates the hypothesized nonlinearity of ir.
  • Most people feel that they would be willing to pay much more for a reduction of the probability of death from 1/6 to zero than for a reduction from 4/6 to 3/6.
  • Because prospect theory has been proposed as a model of choice, the inconsistency of bids and choices implies that the measurement of values and decision weights should be based on choices between specified prospects rather than on bids or other production tasks.

4. DISCUSSION

  • In the final section the authors show how prospect theory accounts for observed attitudes toward risk, discuss alternative representations of choice problems induced by shifts of reference point, and sketch several extensions of the present treatment.
  • Expected utility theory is violated in the above manner, therefore, whenever the v-ratio of the two outcomes is bounded by the respective 7r-ratios.
  • The same analysis applies to other violations of the substitution axiom, both in the positive and in the negative domain.

Risk

  • The authors next prove that the preference for regular insurance over probabilistic insurance, observed in Problem 9, follows from prospect theory-provided the probability of loss is overweighted.
  • This analysis restricts risk seeking in the domain of gains and risk aversion in the domain of losses to small probabilities, where overweighting is expected to hold.
  • In prospect theory, the overweighting of small probabilities favors both gambling and insurance, while the S-shaped value function tends to inhibit both behaviors.
  • A comprehensive theory of insurance behavior should consider, in addition to pure attitudes toward uncertainty and money, such factors as the value of security, social norms of prudence, the aversiveness of a large number of small payments spread over time, information and misinformation regarding probabilities and outcomes, and many others.
  • Some effects of these variables could be described within the present framework, e.g., as changes of reference point, transformations of the value function, or manipulations of probabilities or decision weights.

Shifts of Reference

  • So far in this paper, gains and losses were defined by the amounts of money that are obtained or paid when a prospect is played, and the reference point was taken to be the status quo, or one's current assets.
  • The well known observation [31] that the tendency to bet on long shots increases in the course of the betting day provides some support for the hypothesis that a failure to adapt to losses or to attain an expected gain induces risk seeking.
  • The preceding argument entails that insurance is likely to be more attractive in the former representation than in the latter.
  • Another important case of a shift of reference point arises when a person formulates his decision problem in terms of final assets, as advocated in decision analysis, rather than in terms of gains and losses, as people usually do.
  • If this hypothesis is correct, the decision to pay 10 for (1,000, .0 1), for example, is no longer equivalent to the decision to accept the gamble (990, .01; -10, .99).

Extensions

  • Some generalizations are immediate; others require further development.
  • When the number of outcomes is large, however, additional editing operations may be invoked to simplify evaluation.
  • The manner in which complex options, e.g., compound prospects, are reduced to simpler ones is yet to be investigated.
  • The theory is readily applicable to choices involving other attributes, e.g., quality of life or the number of lives that could be lost or saved as a consequence of a policy decision.
  • In such situations, decision weights must be attached to particular events rather than to stated probabilities, but they are expected to exhibit the essential properties that were ascribed to the weighting function.

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Prospect Theory: An Analysis of Decision under Risk
Author(s): Daniel Kahneman and Amos Tversky
Source:
Econometrica,
Vol. 47, No. 2 (Mar., 1979), pp. 263-292
Published by: The Econometric Society
Stable URL: http://www.jstor.org/stable/1914185
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E
C
O
N
OMETRICA
I
C
I
VOLUME 47
MARCH,
1979
NUMBER 2
PROSPECT
THEORY:
AN
ANALYSIS
OF
DECISION
UNDER
RISK
BY
DANIEL KAHNEMAN
AND
AMOS
TVERSKY'
This
paper
presents a
critique
of
expected
utility
theory as a
descriptive
model of
decision
making
under
risk,
and
develops
an
alternative
model, called
prospect
theory.
Choices
among
risky prospects
exhibit several
pervasive effects
that
are
inconsistent with
the
basic tenets of
utility
theory.
In
particular,
people
underweight
outcomes that
are
merely probable in
comparison
with outcomes
that are
obtained with
certainty.
This
tendency,
called the
certainty
effect,
contributes
to
risk aversion in
choices
involving sure
gains and
to
risk
seeking in
choices
involving sure
losses.
In
addition,
people
generally
discard
components that are
shared
by
all
prospects
under
consideration.
This
tendency,
called the isolation
effect,
leads
to
inconsistent
preferences when
the
same
choice is
presented
in
different
forms. An
alternative theory
of
choice is
developed,
in which
value
is
assigned
to
gains
and
losses rather
than
to final
assets
and in
which
probabilities are
replaced
by
decision
weights. The value
function is
normally
concave for
gains,
commonly
convex
for
losses, and is
generally
steeper
for
losses than for
gains.
Decision weights
are
generally lower than
the
corresponding
probabilities,
except
in
the range
of low
prob-
abilities.
Overweighting
of
low
probabilities may
contribute to the
attractiveness
of both
insurance
and
gambling.
1.
INTRODUCTION
EXPECTED
UTILITY THEORY
has
dominated the
analysis
of
decision
making
under
risk. It
has
been
generally
accepted
as a
normative model
of
rational choice
[24],
and
widely
applied
as a
descriptive model of
economic
behavior,
e.g. [15,
4].
Thus,
it is
assumed that
all
reasonable
people
would wish to
obey
the
axioms
of
the
theory
[47,
36],
and
that most
people
actually do,
most
of
the
time.
The
present
paper
describes
several
classes
of
choice
problems
in
which
preferences
systematically
violate
the axioms
of
expected
utility
theory.
In
the
light
of these
observations
we
argue
that
utility
theory,
as it
is
commonly
interpreted
and
applied,
is not
an
adequate
descriptive
model and we
propose
an
alternative
account
of
choice under risk.
2.
CRITIQUE
Decision
making
under
risk
can
be viewed as
a
choice
between
prospects
or
gambles.
A
prospect
(x1,
Pi;
...
;
xn,
pn)
is
a
contract that
yields
outcome
xi
with
probability
Pi,
where
Pl
+
P2
+
...
+
pn
=
1.
To
simplify
notation,
we
omit
null
outcomes
and
use
(x, p)
to
denote the
prospect
(x,
p; 0,
1-
p)
that
yields x
with
probability p
and
0
with
probability
1-p.
The
(riskless)
prospect
that
yields
x
with
certainty
is
denoted
by (x).
The
present
discussion is
restricted
to
prospects
with
so-called
objective
or
standard
probabilities.
The
application
of
expected
utility
theory
to
choices
between
prospects
is
based
on
the
following
three
tenets.
(i)
Expectation:
U(X1,
Pi;
...
;
Xn,
Pn)
=
pi
u
(x1)
+...
+PnU
(Xn)
1
This work was
supported
in
part by
grants
from the
Harry
F.
Guggenheim
Foundation and from
the
Advanced
Research
Projects
Agency
of the
Department
of
Defense
and was monitored
by
Office
of
Naval Research under
Contract
N00014-78-C-0100
(ARPA
Order No.
3469)
under
Subcontract
78-072-0722 from
Decisions
and
Designs,
Inc.
to
Perceptronics,
Inc. We
also thank the
Center
for
Advanced
Study in the
Behavioral
Sciences
at
Stanford
for
its
support.
263

264
D.
KAHNEMAN
AND
A.
TVERSKY
That is,
the overall
utility
of
a
prospect,
denoted
by U,
is
the
expected
utility
of
its
outcomes.
(ii)
Asset
Integration:
(xi, Pi;
...
;
Xn,
P)
is
acceptable
at
asset
position
w
iff
U(w +x1,
pl;
...
;
w
+Xn,
Pn)
>
u(w).
That
is,
a
prospect
is
acceptable
if
the
utility
resulting
from
integrating
the
prospect with
one's assets exceeds the
utility
of
those assets
alone.
Thus,
the
domain
of
the
utility
function is
final
states
(which
include
one's asset
position)
rather
than gains or
losses.
Although the
domain
of
the
utility
function is
not
limited
to
any particular
class
of
consequences,
most
applications
of
the
theory
have been
concerned
with
monetary
outcomes.
Furthermore,
most
economic
applications
introduce
the
following additional
assumption.
(iii) Risk
Aversion:
u
is
concave
(u"
<
0).
A
person is risk
averse
if
he
prefers
the
certain
prospect (x)
to
any
risky
prospect
with
expected value
x.
In
expected
utility
theory,
risk
aversion is
equivalent
to
the
concavity
of
the
utility
function.
The
prevalence
of
risk
aversion
is
perhaps
the
best
known
generalization
regarding
risky
choices. It led
the
early
decision
theorists
of
the
eighteenth
century
to
propose
that
utility
is a
concave
function
of
money,
and
this
idea
has
been retained
in
modern treatments
(Pratt
[33],
Arrow
[4]).
In
the
following
sections
we demonstrate
several
phenomena which violate
these
tenets
of
expected
utility
theory.
The
demonstrations
are based
on
the
responses
of
students
and
university
faculty
to
hypothetical
choice
problems. The
respondents
were
presented
with
problems
of
the
type
illustrated
below.
Which
of
the
following
would
you prefer?
A:
50% chance to
win
1,000,
B: 450
for
sure.
50% chance to
win
nothing;
The
outcomes
refer to
Israeli
currency. To
appreciate
the
significance
of the
amounts
involved, note that
the
median
net
monthly
income
for a
family is
about
3,000
Israeli
pounds.
The
respondents were
asked to
imagine
that they
were
actually
faced
with the
choice
described in
the
problem,
and to
indicate the
decision
they
would
have
made
in
such
a
case. The
responses were
anonymous,
and
the
instructions
specified
that
there
was
no
'correct'
answer to
such
problems,
and that
the
aim
of
the
study
was to
find
out
how
people
choose
among
risky
prospects.
The
problems
were
presented in
questionnaire
form,
with at
most a
dozen
problems
per
booklet.
Several
forms
of
each
questionnaire were
con-
structed
so that
subjects
were
exposed to
the
problems in
different
orders. In
addition,
two
versions of
each
problem
were
used
in
which
the
left-right
position
of
the
prospects was
reversed.
The
problems
described
in
this
paper are
selected
illustrations
of
a
series
of
effects.
Every effect has been
observed
in
several
problems
with
different
outcomes and
probabilities.
Some
of
the
problems
have
also been
presented to
groups
of
students
and
faculty at
the
University
of
Stockholm
and
at the

PROSPECT THEORY 265
University
of
Michigan. The pattern
of results was
essentially
identical to
the
results obtained from Israeli subjects.
The reliance on hypothetical choices raises obvious questions regarding the
validity
of
the method and the generalizability
of
the
results.
We are keenly
aware
of these problems. However, all other methods that have been used
to
test utility
theory also suffer from severe drawbacks. Real
choices can be
investigated
either
in the field, by naturalistic or statistical observations
of
economic behavior,
or in
the laboratory.
Field studies can
only provide
for rather crude tests of
qualitative
predictions, because probabilities
and
utilities
cannot
be adequately
measured
in
such
contexts. Laboratory experiments
have been
designed
to obtain
precise
measures
of
utility
and
probability from actual choices, but these experimental
studies typically involve contrived gambles
for
small stakes,
and a
large number
of
repetitions of very similar problems. These features
of
laboratory gambling
complicate the interpretation
of
the results and restrict their generality.
By default,
the method
of
hypothetical
choices
emerges
as
the
simplest pro-
cedure by
which a
large
number
of
theoretical questions
can
be
investigated.
The
use
of
the method relies
on
the assumption
that
people
often
know
how
they
would behave in actual situations
of
choice, and
on
the further assumption that the
subjects have
no
special reason
to
disguise their true preferences.
If
people
are
reasonably accurate
in
predicting their choices, the presence
of
common
and
systematic
violations of
expected utility theory
in
hypothetical problems provides
presumptive evidence against that theory.
Certainty, Probability,
and
Possibility
In
expected utility theory, the utilities of outcomes are weighted by their
probabilities. The present
section
describes
a
series
of
choice problems
in
which
people's preferences systematically violate this principle. We first show that
people overweight
outcomes that are
considered certain, relative
to
outcomes
which are
merely probable-a phenomenon which we label the certainty effect.
The best
known
counter-example
to
expected utility theory which e*ploits the
certainty effect
was
introduced by the French economist Maurice Allais
in
1953
[2].
Allais'
example
has
been discussed
from
both normative
and
descriptive
standpoints by many
authors
[28, 38]. The following pair
of
choice problems is
a
variation
of Allais'
example,
which
differs from the original
in that it
refers
to
moderate
rather
than
to
extremely large gains. The number
of
respondents who
answered each
problem
is
denoted by N,
and
the
percentage
who
choose
each
option
is
given
in
brackets.
PROBLEM 1: Choose between
A:
2,500
with
probability .33, B: 2,400
with
certainty.
2,400
with
probability .66,
0 with
probability .01;
N=72
[18]
[82]*

266
D.
KAHNEMAN
AND
A.
TVERSKY
PROBLEM 2: Choose between
C: 2,500 with probability
.33, D: 2,400 with probability .34,
0
with probability
.67; 0 with probability .66.
N
=72
[83]*
[17]
The data show that 82 per cent of
the subjects chose B in Problem 1, and 83 per
cent
of
the subjects chose C
in
Problem 2. Each of these preferences is significant
at the .01 level, as denoted by the
asterisk. Moreover, the analysis of individual
patterns
of
choice indicates that
a
majority
of
respondents (61 per cent) made the
modal choice
in
both problems. This
pattern of preferences violates expected
utility theory
in
the manner
originally described by Allais. According to that
theory, with u (0)
=
0, the first
preference implies
u(2,400)> .33u(2,500)
+
.66u(2,400)
or
.34u(2,400)> .33u(2,500)
while
the second
preference implies
the reverse
inequality.
Note that Problem
2
is
obtained
from Problem
1
by
eliminating
a .66
chance
of
winning
2400 from both
prospects. under consideration.
Evidently,
this
change produces
a
greater
reduc-
tion in
desirability when
it alters
the character
of the
prospect
from
a sure
gain
to a
probable one,
than when
both
the
original
and the reduced
prospects
are
uncertain.
A
simpler
demonstration
of
the same
phenomenon, involving only
two-
outcome
gambles
is
given
below.
This
example
is also based
on Allais
[2].
PROBLEM
3:
A:
(4,000,.80),
or
B:
(3,000).
N
=
95
[20]
[80]*
PROBLEM 4:
C:
(4,000,.20),
or
D:
(3,000,.25).
N=
95
[65]*
[35]
In
this
pair
of
problems
as well as
in
all
other
problem-pairs
in
this
section,
over
half
the
respondents
violated
expected
utility theory.
To
show that the modal
pattern
of
preferences
in
Problems 3
and 4
is
not
compatible
with the
theory,
set
u(0)
=
0,
and
recall that the choice
of
B
implies u(3,000)/u(4,000) >4/5,
whereas the choice
of
C
implies
the reverse
inequality.
Note that the
prospect
C
=
(4,000, .20)
can be
expressed
as
(A, .25),
while the
prospect
D
=
(3,000, .25)
can
be rewritten
as
(B,.25).
The substitution
axiom
of
utility theory
asserts that
if
B is
preferred
to
A,
then
any
(probability)
mixture
(B, p)
must be
preferred
to
the
mixture
(A, p).
Our
subjects
did
not
obey
this axiom.
Apparently, reducing
the
probability
of
winning
from 1.0
to
.25 has
a
greater
effect than the reduction from

Citations
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Journal ArticleDOI
James G. March1Institutions (1)
Abstract: This paper considers the relation between the exploration of new possibilities and the exploitation of old certainties in organizational learning. It examines some complications in allocating resources between the two, particularly those introduced by the distribution of costs and benefits across time and space, and the effects of ecological interaction. Two general situations involving the development and use of knowledge in organizations are modeled. The first is the case of mutual learning between members of an organization and an organizational code. The second is the case of learning and competitive advantage in competition for primacy. The paper develops an argument that adaptive processes, by refining exploitation more rapidly than exploration, are likely to become effective in the short run but self-destructive in the long run. The possibility that certain common organizational practices ameliorate that tendency is assessed.

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Journal ArticleDOI
Amos Tversky1, Daniel Kahneman2Institutions (2)
30 Jan 1981-Science
TL;DR: The psychological principles that govern the perception of decision problems and the evaluation of probabilities and outcomes produce predictable shifts of preference when the same problem is framed in different ways.
Abstract: The psychological principles that govern the perception of decision problems and the evaluation of probabilities and outcomes produce predictable shifts of preference when the same problem is framed in different ways. Reversals of preference are demonstrated in choices regarding monetary outcomes, both hypothetical and real, and in questions pertaining to the loss of human lives. The effects of frames on preferences are compared to the effects of perspectives on perceptual appearance. The dependence of preferences on the formulation of decision problems is a significant concern for the theory of rational choice.

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Amos Tversky1, Daniel Kahneman2Institutions (2)
Abstract: We develop a new version of prospect theory that employs cumulative rather than separable decision weights and extends the theory in several respects. This version, called cumulative prospect theory, applies to uncertain as well as to risky prospects with any number of outcomes, and it allows different weighting functions for gains and for losses. Two principles, diminishing sensitivity and loss aversion, are invoked to explain the characteristic curvature of the value function and the weighting functions. A review of the experimental evidence and the results of a new experiment confirm a distinctive fourfold pattern of risk attitudes: risk aversion for gains and risk seeking for losses of high probability; risk seeking for gains and risk aversion for losses of low probability. Expected utility theory reigned for several decades as the dominant normative and descriptive model of decision making under uncertainty, but it has come under serious question in recent years. There is now general agreement that the theory does not provide an adequate description of individual choice: a substantial body of evidence shows that decision makers systematically violate its basic tenets. Many alternative models have been proposed in response to this empirical challenge (for reviews, see Camerer, 1989; Fishburn, 1988; Machina, 1987). Some time ago we presented a model of choice, called prospect theory, which explained the major violations of expected utility theory in choices between risky prospects with a small number of outcomes (Kahneman and Tversky, 1979; Tversky and Kahneman, 1986). The key elements of this theory are 1) a value function that is concave for gains, convex for losses, and steeper for losses than for gains,

12,066 citations


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Abstract: Agency theory is an important, yet controversial, theory. This paper reviews agency theory, its contributions to organization theory, and the extant empirical work and develops testable propositions. The conclusions are that agency theory (a) offers unique insight into information systems, outcome uncertainty, incentives, and risk and (b) is an empirically valid perspective, particularly when coupled with complementary perspectives. The principal recommendation is to incorporate an agency perspective in studies of the many problems having a cooperative structure.

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Cites methods from "Prospect theory: an analysis of dec..."

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References
More filters

Book
Amos Tversky1, Daniel Kahneman1Institutions (1)
01 Jan 1974-
Abstract: This article described three heuristics that are employed in making judgements under uncertainty: (i) representativeness, which is usually employed when people are asked to judge the probability that an object or event A belongs to class or process B; (ii) availability of instances or scenarios, which is often employed when people are asked to assess the frequency of a class or the plausibility of a particular development; and (iii) adjustment from an anchor, which is usually employed in numerical prediction when a relevant value is available. These heuristics are highly economical and usually effective, but they lead to systematic and predictable errors. A better understanding of these heuristics and of the biases to which they lead could improve judgements and decisions in situations of uncertainty.

30,770 citations


Book
01 Jan 1944-
Abstract: This is the classic work upon which modern-day game theory is based. What began more than sixty years ago as a modest proposal that a mathematician and an economist write a short paper together blossomed, in 1944, when Princeton University Press published "Theory of Games and Economic Behavior." In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences.

19,323 citations


Book
01 Jan 1976-
Abstract: Many of the complex problems faced by decision makers involve multiple conflicting objectives. This book describes how a confused decision maker, who wishes to make a reasonable and responsible choice among alternatives, can systematically probe his true feelings in order to make those critically important, vexing trade-offs between incommensurable objectives. The theory is illustrated by many real concrete examples taken from a host of disciplinary settings. The standard approach in decision theory or decision analysis specifies a simplified single objective like monetary return to maximise. By generalising from the single objective case to the multiple objective case, this book considerably widens the range of applicability of decision analysis.

8,891 citations


Book
Leonard J. Savage1Institutions (1)
01 Jan 1954-

7,540 citations


"Prospect theory: an analysis of dec..." refers methods in this paper

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Journal ArticleDOI
Daniel Ellsberg1Institutions (1)
Abstract: Are there uncertainties that are not risks? There has always been a good deal of skepticism about the behavioral significance of Frank Knight's distinction between “measurable uncertainty” or “risk”, which may be represented by numerical probabilities, and “unmeasurable uncertainty” which cannot. Knight maintained that the latter “uncertainty” prevailed – and hence that numerical probabilities were inapplicable – in situations when the decision-maker was ignorant of the statistical frequencies of events relevant to his decision; or when a priori calculations were impossible; or when the relevant events were in some sense unique; or when an important, once-and-for-all decision was concerned. Yet the feeling has persisted that, even in these situations, people tend to behave “as though” they assigned numerical probabilities, or “degrees of belief,” to the events impinging on their actions. However, it is hard either to confirm or to deny such a proposition in the absence of precisely-defined procedures for measuring these alleged “degrees of belief.” What might it mean operationally, in terms of refutable predictions about observable phenomena, to say that someone behaves “as if” he assigned quantitative likelihoods to events: or to say that he does not? An intuitive answer may emerge if we consider an example proposed by Shackle, who takes an extreme form of the Knightian position that statistical information on frequencies within a large, repetitive class of events is strictly irrelevant to a decision whose outcome depends on a single trial.

6,526 citations


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