ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
TOWARD A BEHAVIORAL THEORY OF INFORMATION VALUE
by
Michael
WP 1191-81
E.
Treacy
February,
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
1981
TOWARD A BEHAVIORAL THEORY OF INFORMATION VALUE
by
Michael
WP 1191-81
E.
Treacy
February,
1981
INTRODUCTION
There does not presently exist
though
even
direction,
this
in
model of the value of information in
there
Surprisingly,
setting.
realistic managerial
effort
a
successful
a
little
very
could
model
systems,
support
information
of
profoundly affect our understanding
is
a
organizational design, and managerial accounting.
Such a model would delineate the important variables that affect value.
It
would enable
information
sources of
providing
by
designs and configurations.
sources
information
design
prescriptive theory of
a
to
meaningful
allow
and
apply
organization
of
for valuing potential
basis
a
would
It
and
a
broad
class
of
between
comparisons
computer-based information support systems and groups of staff analysts
working to supply information to busy line executives.
decision theory
areas
important
integrate
have to
produce
to
a
of
economics,
The model would
and
psychology,
realistic description of the managerial
use of information.
In
this paper, we set directions for the development of such
with
We start
create
a
a
a
model.
review of the efforts made in information economics to
model of the value of information.
The single source,
single
decision model is reviewed to illustrate the assumptions and techniques
of this approach.
Five major modifications of the models, suggested by
descriptive theories
study, are
reviewed
discussed
in
a
of
in
managerial
turn.
concluding
behavior found in other fields of
Finally,
section
that
this
entire
indicates
-^J^^ooo
approach
some
is
general
requirements of any plausible model of information value.
ECONOMICS MODELS OF INFORMATION VALUE
concerned with
the
information
of
value
theory
statistical
One branch of economics and another in
have
been
more than twenty-five
for
years. [Hirshleifer 1973] Operating as two distinct schools, information
economics and statistical decision analysis have produced
similar models
that
value
information
context
the
in
a
information.
It
the
a
very restricted setting.
fundamental
axioms
which
upon
L.J.
the
wrote
decision analysis models are based,
idealized theory of the behavior of
of
several
of
theory which describes information
is
value only in the context of an economically rational,
operating in
of
knowledge
restrictive assumptions about the behavior, ability, and
actors using
series
actor,
Savage, the originator of
information
his
that
economics
was,
"a
and
highly
person with respect to
'rational'
a
perfect
decisions ."[Savage 1954, p. ?]
Our concern is with the value of information to
all his
flaws
and
complex environment.
imperfections,
a
realistic
than upon
a
a
a
with
more realistic, more
valid descriptive model of the value of
realistic manager.
description
the
in
manager,
We are attempting to prescribe the variables that
must be considered to produce
information to
acting
real
a
sterile,
of
Such a model must be founded
upon
the managerial use of information, rather
prescriptive
assumptions
economics and statistical decision analysis.
of
information
Next, we shall review one of the models of information economics as
the techniques and assumptions of that approach.
illustration of
we shall
turn to a
economics models
discussion
that
would
of
of
modifications
the
an
Then
information
make them more descriptive of managerial
behavior and of the obtainable benefits of information.
The economics models of information value vary
the complexity
of
along
two
dimensions:
the information source and the number of decisions.
The information source can be a single
signal,
a
single
information
system, or multiple information systems and the decisions can be single
or multiple.
Figure
1
illustrates this diversity and indicates some
references for each type of model
SINGLE
SIGNAL
SINGLE
DECISION
MULTIPLE
DECISIONS
.
SINGLE
INFORMATION
SOURCE
MULTIPLE
INFORMATION
SOURCES
source or multiple decision models,
Let us assume that we have a decision problem for which we
A finite set of possible actions, A
from which the decision maker must
complete the decision problem.
A finite
=
{a
a
,
choose
are
....
a
given
},
one action to
of future states of nature, S =
{s^,
which are numerable, exhaustive with respect
to the outcomes of actions, and mutually exclusive.
s
.
,
.
,
set
s
},
A set of prior probabilities, {p(s, ),
p(s ),
of each state of nature obtaining.
They sum to
.
.
.
p(s
)}
1.
A stationary utility function, the value of which
depends
only upon the chosen action, a
and the state of nature that
J
occurs, s
U = u(s.,a.).
,
.
1
J
An information source,
from Y
=
{y
,
y
,
.
.
.
which will produce one signal
the set of possible signals.
N,
y^}
,
A matrix of probabilities of each signal
each state of nature.
{p(yi,ls.)}
The sequence of steps is
produces one
calculate
a
signal,
then
y'.
as
follows.
decision
The
revised probability, p(s.ly')
which may obtain.
An action,
a',
is
occuring,
information
The
maker
given
uses
source
signal to
the
for each state of nature, s.,
then
chosen
maximize
to
the
J
expected value
of the outcomes.
Finally,
a
and the decision maker receives value u(s!,a'.
The valuation of the information source
signals are
received,
as
the
s!
difference
occurs
ex
The value of an
between
the
obtains,
).
ante
,
before
actions are chosen, or states obtain.
must deal in expected quantities.
is defined
certain state,
information
expected
information source and the expected value without.
any
Thus, it
source
value with the
V
EV(N) - EV(0)
=
If no source of information is used, the decision maker will choose
action based
probabilitites of states of nature occuring.
prior
upon
an
Specifically, he will choose
which maximizes the expected
a.'
value
of
choose
an
the outcome.
EV(a
=
)
J
SUM {p(s )u(s
)}
,a
i
i
s
J
i
EV(0)
=
EV(a')
=
J
MAX {EV(a.)}
J
3
i
=
MAX SUM {p(s^)u(s^,a
as
J
.)}
i
If a source of information is used, the decision maker will
action based upon his revised probabilities of states occuring.
for a
moment
that
signal
computes p(s.ly,') for all
1
k
is
y'
Assume
Then the decision maker
produced.
using the Bayesian revision formula:
si
1
P(yi^ls^)p(s^)
P(s.ly')
=
SUM {p(y^|s.)p(s.))
Each quantity on the right hand side is
is again the choice of an action a'
a
known primitive.
to maximize the expected
J
the outcome.
EV(a.ly')
=
SUM {p(s ly;)u(s
1
,a
)}
The problem
value
of
Thus, after the signal
obtains, the problem is to choose
yj^
EV(a<|y')
J
=
MAX {EV(a
k
•
as
,
where
)
k
MAX SUM {p(3. ly')u(3.
^j
y'
y
J
=
Signal
I
aj
1
K
,a ,)}
1
J
i
will occur with probability p(y').
source
information
The
evaluator can calculate p(y') using the formula:
k
SUM {p(y|^l3^)p(s^)}
=
p(y|^)
Again, each quantity on the right
Thus, before
hand
side
is
known
a
any signal is received, the probability of receiving each
signal and the expected value of the outcomes for each
computed.
primitive.
the
Then,
information source,
EV(N)
=
N,
expected
outcomes
of
for
can
using
be
the
is:
SUM {p(yj^)[MAX EV(a ly^^)]}
a
y,
k
=
value
signal
J
SUM {p(y )[MAX SUM
K
k
{p( s.
I
1
y
)
K
u( s. ,a
1
.
) } ]
J
1
j
readily
The value of the information source is now
deducible
as
the
difference of two computed quantities.
V
=
Notice that this model concerns
the problem
of
EV(N) - EV(0)
a
problem within
a
problem.
There
is
choosing an action and there is the problem of valuing
the information system.
and the information
We can call these the decision maker's problem
system
evaluator's
problem,
respectively.
The
evaluator is
assuming
that
is acting perfectly
maker
decision
the
Under this assumption this is a valid model of
rationally.
value
the
obtainable by the decision maker from the information source.
For an economically irrational decision maker, the obtainable value
source
the information
model.
may
be
This is because the
difference between
more
us represent the expected value of the
maker
EV.
decision maker by
information
the
by
EV
outcomes
of
and
a
of
economically
the
Then we have:
EV(N)
>
EV'(N)
EV(0)
>
EV'(0)
always
maker
decision
option of behaving exactly like the irrational decision maker.
But note,
EV'(N) - EV'(0).
information source
may
decision maker than to
to
the
probabilities of
nothing
say
can
we
EV(N) - EV(0) and
To move
is
economically irrational
the
This is true because the economically rational
has the
source
To demonstrate this, let
expected quantities.
two
rational decision
less than predicted by this
or
of
value
of
have
a
about
more value to an economically irrational
source
Is
k
state
possible combination of signals.
accomplish this
only
model,
the
states of nature must be changed.
each
is
of
rational decision maker.
multiple
of
magnitude
relative
Thus, it is interesting to note, an
needs the matrix of probabilities {p(y
the probability
the
)}
of
The decision maker
for each source,
so
that
i
obtaining
The
revision
can
Bayesian
be
revised for every
revision
formula
to
significantly more complicated than for the single
source model, but conceptually the same.
The multiple decision problem further complicates the model, because
potentially
signal at
any
decision.
The formulation of this model over
where every
point
decision
time
in
problem
can
known
is
every future
impact
fixed
a
a
time
horizon,
in advance, becomes a rather
messy dynamic programming problem.
AREAS OF MODIFICATION
These economics models of information value poorly describe
of information
in
inadequacies
managerial
models, as suggested by
We
a
settings.
these models have been organized for
of
discussion into five sections.
indicated.
roles
managerial decision making and hence poorly reflect
the obtainable value of information in realistic
The descriptive
the
In
each, possible modifications of
the
reading of other related fields of study, are
conclude
with
some
remarks
on
the
difficulty
of
implementing such modifications and the efficacy of this approach.
1
.
The Decision Process
According to economics
effect upon
fault if
the
decision
models,
decision
making
managerial activities
which
information
process.
is
derives
54] Simon writes:
from
its
This orientation is difficult to
interpreted
broadly,
for
almost
all
use information can be classified as some
phase of the intelligence-design-choice-review decision
1965, p.
value
process .[Simon
finding
Decision making comprises four principle phases:
occasions for making a decision, finding possible courses of
action, choosing among courses of action, and evaluating past,
account for most
These four activities
choices.
40]
of what executives do. [Simon 1977, p.
....
Mintzberg's study of the work of five chief executives reinforces
finding. [Mintzberg 1973,
activities (12 percent)
p.
and
in
but
All
250]
giving
in ceremonial
spent
time
information
this
(8
percent)
is
phases
in
attributable to one or more phases of decision making.
Witte[1972] formally tested for the existence of
the decision process using
equipment.
He
divided
a
each
different
sample of 233 decisions to aquire computer
decision
process
into
periods and characterized each activity in each period
gathering,
choice.
development,
alternatives
alternatives
hypothesis
The evidence supported the
that
equal time
ten
information
as
evaluation,
or
phases
multiple
exist within the decision process.
The difficulty with the economics models is that they concentrate
upon
only one phase of decision making, the choice among alternative courses
of action.
assume that an occasion for decision making has been
They
found and that all possible courses
every conceivable
of
consequences
and
managers
have
for
But, by the
of events have been determined.
course
time these assumptions are satisfied,
great deal
action
already
used
a
of information and expended the majority of their effort on
the problem. [Simon
information at
making process,
the
1977,
p.
40] Decisions are profoundly
intelligence
because
without
and
design
information
phases
to
affected
by
of the decision
identify
problems.
10
structure alternatives,
consequences, no choice is ever
estimate
and
made
It
is
evidently necessary that
value be
expanded
the
models
information
of
consideration of these earlier phases,
include
to
economics
intelligence and design, if they are to accurately reflect the benefits
of information.
modelled since
it
phase,
final
The
review,
need
not
explicitly
be
usually part of the intelligence phase of other
is
decisions, and could be captured as such in
multiple decision
a
model.
The phase theory of decision making implies not only that decisions are
activities,
comprised of different
follow
a
pattern,
set
implementation of
support the
a
progression
chosen
the
hypothesis
but
also
from
the phases followed
that
evidence
a
Even when each decision was divided into subdecisions
the hypothesis was found
Mintzberg, Raisinghani
cycling through
,
phases
that
and
Theoret
[
1
976
also
]
not
clear progression.
,
no
support
for
found
evidence
of
during the decision process, in their study of
cycling
is
used
as
in
a
different
decisions
seem
to
organizations.
means of comprehending and
clarifying complex decision processes and that "the
novel strategic
does
to
.
twenty-five strategic decision processes
They suggest
recognition
initial
Witte's
actions.
activities
these
that
most
complex
and
involve the greatest incidence of
comprehension cycles". [p. 265] Evidence was also found that interrupts,
created by internal and external pressures and by the appearance of new
options, caused cycling.
11
The authors build their findings into
model
intelligence-design-choice
comprised of
posit
and
that
recognition
decision
routines:
two
elaboration
an
of
simple
the
intelligence
is
diagnosis.
and
Diagnosis is an optional routine used to clarify and define the issues.
Decision recognition
either
crisis,
a
occurs
there
are sufficient signals about
problem, or an opportunity.
a
of six strategic decisions within one company.
March
Cyert and
suggested
response to problems
p.
This catagorization
of
was first suggested by Carter[1971] in his study
stimulus
problems by
when
decision
that
rather
than
to
recognition
perceived
of
theory
The earlier
always
was
opportunities
.[
1
a
963.
116]
Pounds[1969] has
presented
problem identification,
theoretical
a
structure
analysing
for
one type of decision recognition, as
a
process
of comparing information about real events against the predictions of
The models managers use are
chosen 'model' of normality.
explicit derivations
from
historical
and
planning
implicit
data
or
a
or
models
imposed by others or derived from outside the organization.
There exists no design for design;
this phase of
not well
March[1963]
largely
actions.
understood.
a
Cyert
and
decision
posit
that
matter of problem-directed search for acceptable
How
than clear.
this
search
is
making
is
design is
alternative
accomplished, though, is somewhat less
12
Mintzberg, Raisinghani
and Theoret suggest
,
depending
very different
ready-made or
custom-made
a
ready-made
appropriate for
are necessary
ReitmanE 1964]
solutions.
solutions,
has
They
activity
jesign
decision
the
solution.
note
is
maker sought
search
that
a
is
but that more elaborate models
of
description
the
for
whether
upon
that
design
the
of
custom-made
detail on the various forms of
further
design activity.
In
there
summary,
intelligence and
of
All
information.
in
exist
literature
the
This
from
decision implementation is somewhat less than
to
work
the
that
as important phases of the
The exact nature of each phase and their order
decision recognition
clear.
activities
design
decision process.
agreement
general
is
implicitly
information
has
suggests
value
several
roles
for
equivalent to the expected
improvement (which may be zero) from knowledge of the information.
Tne
addition of some consideration of the intelligence and design processes
to the
model
should
provide
a
more
evaluation
accurate
of
the
managerial uses of information.
2.
Human Judgement Under Uncertainty
There are two competing paradigms of the utilization of information
judgement and
thought.
choice,
the
Bayesian
and
the
regression
in
schools of
The essential difference between the two is in the manner
of
assessment of the relationship between information and the states about
which one
is
drawing
inference.
The
Bayesians
propose the use of
conditional probabilities and Bayes' theorem to assess
the
impact
of
13
information
obtaining.
judgements
prior
upon
regression
The
of
formalized
school,
probability
states'
the
the
in
of
model
lens
1956], uses correlations of states
proposed by Brunswik [Brunswik 1952,
with information cues to weight the importance of each cue in the final
After
judgement.
between
rivalry
judgement, che
hundred
several
the
psychology
studies
intense.
remains
schools
two
human
of
conceptual overlap, attempts at unifying the two views
Despite obvious
have met with limited success [Slovic and Lichtenstein
1971,
.
van
Breda
1973]
Savage
ever since
probability into
1954] This
a
first joined the concepts of utility and subjective
why the economics information value models require that
is
K
p(s.)
IK
1
formulation of
revised
the
information source
upon
decision
receipt
maker's
of signal
problem
y'
evaluator's problem), for it is
than
to
estimate
both
p(s.)
and
i
revision formula.
a
simpler matter to
the
presence
of
p(y!|s.) and apply the Bayesian
k
1
a
valid description of human behavior only under
the assumptions that the intelligence and design phases
and
the
from
The economics model of how we arrive at the function
p(s.ly') appears to be
that p(s.)
is a curious
K
1
K
It
.
apart
(as
produce directly subjective estimates of p(s.ly') in
,
functions
probability
p(y'|s.), for the derivation of p(s.|y'), the probabilities of each
state obtaining
y|
making .[Savage
formal, axiomatic theory of decision
the decision maker have knowledge of the
and
utilization
information
Economics has adhered to the Bayesian view of
p(y'|s.)
are
already
given.
As
are
complete,
discussed
previous section, we must remove such assumptions from the model.
in the
T4
Reformulation of the model to indicate direct estimation of p(s
1
y
the decision maker simplifies the decision maker's problem, but
the information valuation problem almost unchanged.
information source
value
)
by
k
i
leaves
The calculation of
requires knowledge of p(yJ, which is
still
not directly estimatable, but can be most easily derived from p(s
)
and
i
p(y.|s.).
Notice that the economics model of information value had the
decision maker's and the information source evaluator's primitive
type requirements
coincide.
When the model is descriptively enhanced,
the data required by the decision
evaluation of
an
data
information
maker
source
and
required
data
the
disconnected.
become
for
This has
interesting implications for the ability of decision makers to evaluate
their own sources of information.
We shall not pursue them here.
Further complications must
be
considered
maker's direct
of
p(s |y').
estimation
i
modelling
in
There is
the
large and growing
a
k
body of psychology literature that documents and theorizes on
of systematic
bias
estimation of probabilities.
the
in
Kahneman have identified three important
estimate
probabilities
and
have
heuristics
demonstrated
systematic biasing of estimates .[Kahneman and
and Kahneman
1971,
1974]
The
decison
'prospect
by
Tversky and
which
how
these
Tversky
1973;
theory'
evidence
people
lead
to
Tversky
they have developed
sheds considerable light on how outcomes are framed as gains and losses
in evaluating utilities and on the transient nature
[Kahneman and
Tversky
1979;
Tversky
and
Kahneman
information value needs to include consideration
biases, for they induce
a
of
of
these
values.
1981] A model of
these
systematic
systematic subutilization of information, and
decrease the obtainable value of information.
15
3.
The Choice of Actions
Economics information value models
set
A,
in every state of nature in S.
expected
maximizes the
formula for EV(N) in
There is
decision
the
maker
evidence
actions
that
which
action
the
This is apparent from the
economics
information
the
chooses
He
of outcomes.
value
considerable
that
of every action, from their potential action
consequences
explore the
require
we
reviewed.
chosen
on a much
model
are
simpler basis.
Simon was one of the first to question the maximum expected value model
of choice.
He developed
submitted it
as
normative model
the
well
known
of
idea
satisf icing,
and
better description of individual behavior and as
a
rational
of
information gathering
behavior
under
and processing .[Simon
of
costly
1957,
1959] He
conditions
1955,
1956,
a
suggested that an action choice rule more descriptive of human behavior
would be to determine
a
minimum aspiration level,
outcome and
sequentially
an action a'
is found
L,
for
decision
a
search and test potential actions,
,
until
need not be accurately determined;
one
a
such that:
MIN u(s.
s
^
,a'
)
J
>
-
L
1
In
this formulation, u(s
,
a')
i
only needs
to
aspiration.
action choice
know
L and
J
whether u(s.,
u(s.,
a'.)
could
a'.)
be
is greater than
L,
multidimensional.
the level of
Then,
rule need not be modified, but the chosen action
satisfy the rule along every dimension.
This obviates the need
tradeoff among dimensions of the objective.
a',
the
must
for
a
16
Cyert and March extended this idea to the theory of the firm [Cyert and
March 1962] and considerable work has continued
1978] Stigler has explored the economics of the
rational theory, [March
ideas
search activity .[Stigler 1961] Many of these
model of
bounded
area,
this
in
serve
and
value
information
as
a
simplify
could
a
description of
better
decision making behavior.
Soelberg[ 1966,
studied
1967]
the
job decisions.
students making
He
behavior
graduate
fifty-two
of
found evidence that individuals had
more than one acceptable choice alternative before ending their search,
Soelberg developed
in contradiction to strict satisficing behavior.
a
theory of decision making that combines the notions of maximizing along
the most
important
one
or
two dimensions of outcome and satisficing
along all others, to explain his findings.
The conflict between Simon's and Soelberg' s theories of choice behavior
Raisinghani
Mintzberg,
using
resolved
can be
and
,
Theoret's
solutions.
They
write, "The hypothesis with the strongest support in our study is
that
ready-made
differentiation between
the
organization
solution.
.
solutions
.
contrast,
typically
alternatives"
seeking and
In
designs
.[
fully-developed
one
them
256] Soelberg'
from
custom-made
organizations
selected
1976, p.
choosing
only
and
among
from
s
that
among
chose
a
custom-made
ready-made
sample was of decision
ready-made
of
number
makers
solutions (job offers),
whereas many of Simon's conclusions appear to have germinated from
observations of
problems
his
involving custom-made solutions, such as the
widely referenced description of
a
computer aquisition decision made in
17
the early
1950 's .[Cyert
,
Simon, and Trow,
1956]
Different simplified choice rules could also be modelled.
For example,
one could model the practice of developing plans based upon assumptions
about most likely future scenarios.
the most
This is equivalent to
identifying
likely state of nature and choosing an action to maximize the
value of the outcome if that state obtains.
The
decision
rule
would
be, choose a', such that:
J
u(s'.,a'.)
MAX u(s'.,a
=
.)
J
where
p(s'.ly')
=MAXp(s.|y')
s
Several variations of this simplification are possible.
M.
Multiple Signal Resolution
There is little evidence that individuals resolve multiple and possibly
conflicting signals through
'Bayesian'
psychologists
a
have
complex Bayesian revision process.
developed
Even
about individuals'
theories
misaggregation of multiple signals to explain the apparent conservative
revision of prior probability
Gettys and
Manley 1963;
estimates .[Beach
Wheeler and Beach 1968;
Edwards
1968;
Tversky and Kahneman
1974] The regression paradigm offers no better description of
signal resolution.
Contrary- to
its
predictions,
lower
test-retest
reliability
probabilities. [Hoffman and Blanchard 1961;
of
multiple
experiments
indicated that increased numbers of signals lead to decreased
and
1968;
accuracy
judgements
Hayes 1964;
have
Einhorn
of
1971]
18
heuristic
Possibly, the
used
modelled more closely as
a
signals
may
be
Sufficient conflict among signals could
confidence
decreased
multiple
voting process, with each signal weighted by
the reliability of its source.
lead to
resolve
to
an increased propensity to collect
and
more information.
As with
modelling
the
design
phase
of
decision
the
process,
the
direction to take in modelling multiple signal resolution is not clear.
should
Nevertheless, it
be
possible
to improve upon the descriptive
ability of the complex Bayesian revision process adopted by information
economics.
Multiple Decisions Over Time
5.
How do managers deal with information over time?
assume that
of
a
models
design all future decision problems at the beginning
they
finite time horizon [Feltham
.
information source
stream of
Tne economics
outcome
information signals
is
valued
improvements
optimally.
as
1968,
1972]
the
present
gained
by
a
In
this
context,
an
value of the expected
decision
maker
using
The solution to this problem can only
be derived using dynamic programming, for one considers the
impact
of
each signal in the present decision as well as in all future decisions.
It
is
not
the
reuse of the information source, but of the particular
information signals that makes the decision maker's problem so absurdly
counter to intuitive notions of managerial behavior.
19
appear
to
historical information
in
The economists
have
In
separate
to
model
the
of
use
This might be accomplished
decision making.
much more simply if we do not
historical information.
trying
been
the
information
source
from
this way, the new information signals may
embody historical information and the
complexity
overwrought
of
the
problem
has
problem disappears.
The other major modification
of
the
multiple
already been suggested in an earlier section.
decision
Decision problems cannot
be defined and enumerated at the beginning of any period of time.
must be
They
discovered, selected, or assigned with little forewarning.
have suggested that this
problem
identification
issue
We
best
can
be
described by adding an intelligence phase to the model.
CONCLUSIONS
We have reviewed
a
the
value
of
information
from
and criticized it from the perspective of descriptive
economics theory
validity.
standard model of
Five major areas of revision have been discussed.
in these areas would bring the model
into
closer
alignment
Revisions
with
our
knowledge of the behavior of managerial decision making.
This paper has set
a
direction, but made little movement in the
direction.
To
direction;
we need a conception
guide
our
future
path
of
the
we
need
final
a
chosen
goal as well as
product,
requirements for the final model that we wish to create.
a
qualitative
20
Our requirements are two.
The model should be simple and complete.
simple, we mean that it should
be
free
decisions
from
may
unnecessarily
Individual
'decision areas'
in
be simplified.
By complete, we mean that the model
major uses of information which
suggestions for
in this regard.
expanding
detailed
have to be aggregated into
considerations.
the final model.
Preference functions may have
derive
By
benefit
for
to
should capture the
the
firm.
Our
the decision process should help us greatly
21
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Witte,
,
,
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