CHAPTER 3-4
ASSESSING CONSEQUENCES AND LIKELIHOODS
How much would it cost to construct a building like that one
over there? How many baseball gloves should your store plan to
sell this spring if you price and advertise them as you did last
year? What is the probability that a vaccine against AIDS will
be discovered in the next five years at the current rate of
government support of AIDS research? What are the chances that
you will be a good enough violinist to make a living playing
professionally?
Estimating the likelihoods of the good and bad consequences
that may follow a given course of action, and attaching values to
them, are crucial activities in determining the overall "present
value" of the option being considered. There usually are many
possible ways of making estimates, based on some blend of
abstract theoretical ideas, information already available,
information you will develop from scratch, experience and ideas
of other people, and other modes of operation of human brains in
your and others' heads.
Sometimes you can do most or even all of the job with
systematic scientific procedures of the sort described in the
previous chapter. For example, if you wish to know the
probabilities of various quantities of baseball gloves being sold
in your store in April, a systematic study of the April sales in
the past four or five years, combined with the forecasting
techniques described in Chapter 4-4, will probably provide a very
reliable "probability distribution", as the result is called.
But if this is the first year your store is open, you have no
history to analyse scientifically, and hence you must use other
methods of the sort described in this chapter.
Or, how good a chance is there that a space launch will blow
up before getting into orbit? Or that a vaccine against AIDS
will be discovered before the year 2005? Or that the Roman
Catholic Church will allow women to serve as priests as of the
year 2020? These questions are of a different sort than are
usually tackled with standard methods of empirical research.
This chapter discusses a few selected issues in the practice of
guesstimating answers to such questions. The estimation task is
closely related to the discussions in Chapters 3-2 and 3-3 of
experts, libraries, and scientific inquiry, and to the assessment
of your basic values discussed in Chapter 2-1. It also overlaps
the discussion of forecasting in Chapter 4-4.
Sometimes an estimate is expressed as a single physical
quantity, as for example the response to "How many people do you
think will show up for the concert tonight?" And sometimes the
estimate is expressed as the probability of a given "simple"
event such as the discovery of an AIDS vaccine. (Calculating the
probability of complex events from simple events is discussed in
Chapter 1-4.) This chapter concentrates on the special problem
of phrasing the estimate in the form of the probabilities
associated with the event.
The main modes of thought that enter into estimation may be
characterized as theoretical (or engineering) and experiential
(or scientific). The estimation may be any possible combination
of the two modes. If the process is mainly experiential and if
the experience is systematically gathered, the process is that
described in Chapter 3-3. The remarks in this chapter refer to
the theoretical mode, and its combination with unsystematically-
gathered experience using various heuristics.
It is common for theory and experience to contend for
dominance, either within your own thinking or between two people
working on the same estimate. In my experience, people tend to
give too much weight to abstract thinking and too little to the
available data. When a body of experience is available, I
recommend that you lean on it to the greatest extent possible,
and almost never push it aside in favor of theorizing. Of course
there are situations when it is prudent to ignore the data
completely, and rely wholly on the theory, but such situations
are rare.
SOME PRINCIPLES FOR ESTIMATING COSTS AND BENEFITS
1. Ensure that all the relevant costs and benefits are
included and none are forgotten. It is amazingly easy to
overlook a crucial factor -- for example, the raw materials
needed, or the cost of taxes -- when estimating the cost of a
building, or the benefit of the learning you will acquire in the
course of a job. With respect to costs, the best technique for
ensuring that all crucial factors are included is to refer to
past experience, because it necessarily embodies all the relevant
factors.
Let's consider the issue in the context of estimating costs
in a business situation.
More specifically, imagine estimating the expenditures
connected with a task with which the firm already has a great
deal of experience - say a construction firm concerned with a bid
on a small parking lot of the sort that the firm has done many
times before. Another example might be a firm that has
manufactured only one product - say, men's shirts - and wishes to
estimate the cost of a batch. A third example is estimation of
the cost of another hamburger shop to a chain franchising
operation.
A firm with considerable relevant experience may estimate
cost directly from its own records. In the case of another
hamburger shop, the estimate may simply be the average total cost
of shops recently built by the chain, as already computed by
them. In the case of the parking lot or excavation, the
construction firm may be able to estimate with good accuracy the
amounts required of the main components, labor and machine time,
and their current prices. The shirt manufacturer may have to do
a more detailed analysis to estimate the cost of a batch of
shirts, if the garments have design specifications. That firm
may consult its past purchase records for quantities and prices
of yarn, buttons, wrapping, labor, and so on.
Even if your firm has a great deal of experience with a
process, however, cost estimation may run into many snags. For
example, the firm may want information about costs at output
levels different from those it has produced at before, and it may
not have sufficient records about the inputs necessary to operate
at those output levels. One must also check that there was no
stockpiling and no depletion of stockpiles during past
observation periods. And, of course, machines with long lives
are a big problem; because of the change of technology over time,
records alone may not show what the relevant expenditures on
machinery will be during the period for which the decision will
be made (which must almost always be a long time period if there
are long-lived machines). Perhaps the only case in which all the
necessary information on equipment costs could come from records
would be where the firm does construction or other jobs on an ad
hoc contractual basis -- rents all its equipment, and hires
workers for the one job only.
If the firm does not have direct experience with the process
being costed, then it must make (or have made) an analysis of the
process, together with estimates of the requirements for each
aspect of the job. For example, after it has built 100 identical
McDonald's hamburger franchises, the firm can refer directly to
its records to learn the necessary inputs of wood, tile, paint,
plumbing labor, carpentry labor, and so on; but before it has
built the first such shop, the firm must get, from architects,
engineers, and contractors, estimates of how much of each input
the planned building would require. These construction experts
analyze the various operations required, and measure the extent
of each operation (such as the number of electrical outlets
needed). Then they estimate the material and labor required for
each aspect of the work on the basis of their general knowledge
and experience with similar projects.
Big construction projects such as dams or spacecraft for
moon shots exemplify jobs whose cost estimation draws little from
past records and requires careful analysis by engineers and
designers. But even in already-operating assembly-line
operations, one must often use engineering analysis to estimate
the relevant expenditures, especially when dealing with new or
altered items. For example, an auto manufacturer needs to know
the outlays on material and labor, and the amount of assembly-
line time, that will be required for various proposed new models
of cars. The aspects of the car that continue the same as in the
past years can be costed from past years' records; but the new
aspects must be costed by analysis done by designers, engineers,
and skilled craftsmen. Analysis is also necessary when a firm
considers producing a quantity of output at a level of capacity
different from the one it has been working at. For example, if
the highest previous level of operation has been 10,000 units per
week, and the firm wants to know the expenditures relevant to
producing 15,000 units a week, the judgments of supervisors,
plant engineers, maintenance men, and so on must be sought and
used.
Movie-making is an industry in which cost estimation is
notoriously treacherous. Films that started out with budgets of
$30 million have ended up costing $300 million (and then
flopped!). Perhaps careful estimation can be done for such items
as travel, set construction, and so on. But how can one predict
in advance that the female star will get furious at the male star
and walk off the set halfway through the filming?
In costing new operations, experimentation is particularly
useful. Consider the example of an engineer who wants to
estimate the cost of digging a foundation for a building in half-
frozen ground for the new pipeline, in an area where no building
has been done before. They may put a man on a bulldozer to work
for a day to see how fast the work goes. Or, if a shoe
manufacturer wants to determine the cost of a new style, she
often may have the people at the benches try out some of the
necessary operations to see how long they take, and to find out
how much material is required. Experimentation is also used as
an adjunct to other estimation methods to fill gaps in records or
knowledge.
The two ways of estimating cost -- engineering and
experiential -- are mirrored in the two modes of estimation in
many other circumstances. In medicine, for example, a physician
may attempt to estimate the likelihood that a patient who has had
a stroke will have another stroke on the basis of the patients
"risk factors" of weight, smoking behavior, blood pressure, race,
and cholesterol, perhaps adding in the physician's specific
knowledge of this patient's physical and mental condition. This
is called the clinical approach. Or the physician may focus on
the statistics that a person who has had one stroke will have
another, an experiential approach. If there are no such
statistics, the physician would have to rely on the clinical
approach, but in the presence of such data, it would be poor
thinking to ignore them. But raw statistics on the entire
population that do not present separately the information by the
categories of risk categories, are too broad, and the physician
would be wise to adjust such aggregate data in light of the
patient's particular risk factors. That is, it would be wise to
make engineering-type adjustments to the experiential information
in such a situation. An even better prediction for a given
patient could be developed using formal methods of statistical
analysis, but not even the best physicians have gone this far
yet. And too many of them simply ignore the experiential data
and proceed on clinical judgment alone -- whatever that means --
often because they are not comfortable with statistical data.
Another example of the tension between theory and experience
is found in estimating the availability of raw materials in the
future based on geological and Malthusian theory, versus the
history of raw-material scarcity based upon prices throughout
human history; the two approaches give diametrically opposed
predictions, with the latter being the approach that is validated
by history, of course.
The issue is not simply theory versus empirical knowledge in
the abstract, but rather how good the particular theory and data
are. A good theory will fit the known facts reasonably well, and
is soundly constructed; a bad theory does not do so, and is worse
than no theory. Yet abstractions have an amazing power to
bewitch us, and perhaps the more so if we have more education.
An example is the theory of economies of scale in manufacturing,
the cornerstone of government monopoly operation under of the
banner of greater efficiency. But this theory leaves out the
stimulating forces of competition, and the deadening effect of
their absence, which account for government monopoly doing worse
than private enterprise in almost every case -- even the extreme
(and amazing) case of competing electric utilities up and down
the same streets; more details are in Chapter 00.
Typically, bad theories leave out a crucial factor -- as,
for example, the importance of energizing competition in the
electrical-utility example above -- or include a wrong assumption
-- such as the Marxian theory that people will work just as hard
for the community when they do not feel exploited by the
capitalist class as they do when they own the enterprise (such as
the farm). This assumption is now (1990) in the process of being
massively discredited by the happenings in Eastern Europe.
2. It is important to ensure that all the important impacts,
upon all the people and groups that are affected, are brought
into the estimation. The failure to do so is one of the great
errors in thinking, discussed at length in Chapter 4-6(?).
Sometimes the effect is merely offensive to one's tastes or
values, as when people in (for example) the United States
quantify the loss of life in the Vietnam War only with respect to
American lives, omitting the loss of Vietnamese and others.
Sometimes the effect is socially destructive, as when a chemical
plant takes into account only its own direct costs and ignores
the costs to the community of the pollutants that it dumps into
the river. Other examples of focusing only on the "seen" and
neglecting the "unseen" effects may be found in Chapter 4-6.
Sometimes even obvious elements are neglected because the
estimation seems difficult. A university is likely to ignore the
value of a piece of land in its building plans simply because the
accountants find it difficult to assign a value to the land.
These are some of the factors often neglected when
estimating the overall value of a course of conduct: a)
Knowledge gained. A wise person or business will often take on a
job that does not seem obviously profitable in order to learn
skills that can be valuable later on. This includes information
about the environment as well as individual knowhow. b) Credit
and reputation. An activity that enhances those crucial elements
leaves you better prepared for the future; a detrimental activity
does the opposite. c) Attention. The number of activities that
you can keep your eye on is limited. When you hire someone to
paint your house, you must count as a cost the attention you will
have to pay to make sure the job is getting done right. You may
decide that a more expensive painter, whom you will not need to
check on at all, would be a better buy, or you may even decide to
forego having the job done because you cannot afford to divert
attention to it. 3. Subjective benefits and costs are very
slippery. What is the money cost to you of sitting and reading
this hour? Costs other than money? How do you learn my costs of
sitting here? How do I learn what my costs will be five years
from now? One of the greatest difficulties in thinking about
costs and benefits is that your assessment of them right now may
be importantly different than your assessment of them later on,
after the event is over. The shock of jumping into cold water
seems insignificant after you jump, but beforehand it looms so
large that you may shilly-shally about jumping for many minutes.
And the value of making a trip to the deathbed of a dying friend
may come to loom larger in your mind years after the friend dies.
It often helps to assess these costs and benefits if you
tryto imagine that now it is five years later. Ask yourself how
you would assess the cost or benefit from that perspective.
These later-on assessments tie into the subject of making
binding commitments. A method of integrating this present-
standpoint distortion into your decision-making apparatus is
described in Chapter 00.
4. The tougher and more important the issue, the less
information there is to go on, usually. It is in the nature of
important issues that they come along infrequently and each one
is different than others. Hence there is little information to
draw on when a very important issue arises. If the situation
becomes repetitive, information accumulates. Before the first
prototype aircraft is built, there are great "unk-unks" --
industry slang for unknown unknowns. Afterwards, learning
reduces the uncertainty greatly.
ESTIMATING PROBABILITIES
Every estimate is a matter of estimating probabilities. If
you estimate that a building is 500 feet high, you may not
actually add, "give or take 75 feet", but some such assessment of
the possible error in your estimate is implicit. And even that
sort of statement is a vague substitute for the "probability
distribution" -- the probability of the building being between
400 and 425 feet high, the probability of being between 425 and
450 feet high, and so on. In that fashion, every estimate is
implicitly a distribution of probabilities.
Probabilities can be known with considerable reliability if
a great deal of data exists. For example, probabilities of death
by age and sex for randomly-selected individuals may be estimated
on the basis of large amounts of experience, as may the
probability of outcomes on a roulette wheel. In other cases one
feels as if the probability is being picked out of the air almost
without foundation. For example, our family once was in Chaco
Canyon when drops of rain began to fall. The road was a dirt
track. Would we be unable to leave because of mud if we did not
leave immediately? Would we be trapped in mud if we did leave?
We had nothing to go on, no knowledge of the likelihood of heavy
rain in that desert area, no knowledge of the effect of rain on
the road, and so on. Nor did we have any way of obtaining
information. Yet we had to make some estimates in order to
decide what to do.
Mortality estimates are considered to be "objective", in
contrast to our "subjective" estimates about being trapped in
Chaco Canyon mud. There is much philosophical discussion
relevant to these matters, but from an operational point of view
we treat these probabilities in identical fashion. Some
statisticians worry that people inevitably estimate subjective
probabilities in a fashion that will fool themselves. Maybe.
But there is no alternative to making such probability estimates.
Decision-makers1 do not enjoy estimating probabilities. Physicians, for example, often say it cannot be
done. But there is plenty of evidence that people will and can estimate probabilities with some accuracy.
Sometimes it is necessary to push hard on oneself, or on someone else, to extract the probability estimates -- a process
neatly called "executive psychoanalysis." The devices sketched out in this section should, however, help you to extract
meaningful and useful probability estimates.
The probability-estimation process discussed here is intended for use in all kinds of decision-making -- business, politics,
war, or other policy or action situations. Estimating probabilities for use in "pure" science is a subcategory of the estimation
procedures described here, and is subject to special limitations to which probability estimation for decision making is not
subject. More later about probabilities in science.
PROBABILITY ESTIMATION BY THE DECISION MAKER
The operational estimate of a probability (or probability distribution) begins with an overall estimate by the decision maker
or deputy. For example, consider the situation in which the firm is making a decision about whether to raise its price, and the
likelihood of the main competitor's responding with a price raise is a crucial aspect of the price decision. The estimate of that
likelihood will then probably begin as a rough horseback judgment by the executive in charge. If she is experienced and wise, the
initial estimate may be sound; if not, not. The wise decision maker uses all knowledge and mental facilities, taking everything
into account that she can think of. This sort of estimate is informal and follows no explicit rules. But if the executive forces
herself to organize her thinking on paper or for presentation to other people, she may thereby improve her thinking very greatly.
This suggestion to use pencil and paper (or computer) may be the most useful one in the chapter.
If the decision is an important one, and if the decision maker is willing to do some even harder thinking, he may be able to
improve his estimate by some mental gimmicks whose purpose is (1) to make sure that his thinking is consistent, and (2) to explore
his mind for thoughts that have not yet come to light. We will first discuss such gimmicks for a yes-no probability estimate,
such as that the competitor will raise his price in response to a price raise of ours. Then we shall move on to the job of
estimating sets of probabilities (probability distributions) that contain more than two possibilities, such as the estimation of
demand, which can have many possible sales quantities.
In addition to using the gimmicks below, your estimates of probabilities can benefit from keeping in mind the kinds of
pitfalls in thinking discussed in Chapters 4-5 and 4-6.
Gimmick 1. Make sure that the mutually exclusive probability estimates add to unity. It is, of course, just a convention
(an agreed-upon definition) that probabilities add to 1, but all our probabilistic reasoning is based upon this convention.
Therefore you must arrange your estimates -- in the simple two-possibility case, the probabilities of "yes" and "no" -- to add to
1.
It is often helpful to estimate separately the probabilities of "yes" and of "no." This check often reveals inconsistency.
For example, the executive might estimate the probability of a competitor's price raise as .40. If his assistant then asks him
the chance that the competitor will not raise his price, the executive may say, "50-50." This reveals an inconsistency, because
.40 and .50 do not add to 1. Further thinking to resolve the inconsistency and make the probabilities add to 1 should improve the
estimate.
Gimmick 2. If you find it difficult to form a numerical probability estimate, it may help to proceed in stages. For
example, first ask yourself whether the chance is more or less likely than 50-50. If less than .50, next ask yourself if you
think the probability is closer to 0 or to .50. And so on. Gimmick 3. Sometimes it is useful to compare your situation
to a clearcut gambling machine, such as a 32-slot roulette wheel. You might first ask yourself whether the likelihood in your
situation is about the same as the probability of the ball falling into one of the 32 slots. If you feel that the probability is
greater than that, then ask yourself whether the chance is about the same as the ball falling into one of two given slots of the
wheel, or three, and so on. Then convert to probabilities.
Gimmick 4. As a consistency check, try actually making a small wager with a friend on the matter to be estimated. See
whether you would be willing to bet $3 to $1, say, that the competitor will raise his price if you raise yours. After you find
the worst odds at which you would be willing to take a bet that he will raise his price, turn the bet around and figure the worst
odds you would take that he will not raise his price. Together these two sets of odds give an estimate for your decision. (It is
worth noting that many people who say it is impossible to make probability estimates of business events, because there is no
"scientific" basis to go on, have no reluctance or difficulty in making a bet on a football game.)
Gimmick 5. Use the "bet-yourself" technique, another consistency check.2 Imagine that you will
receive a big prize -- say, a trip around the world -- if you are
right about whether an event will occur. Then ask which side of
a wager you would pick concerning the probability of that event's
occurring. For example, assume that you are trying to estimate
the distribution of breakdowns that you can expect in the factory
next year, and you must begin with an estimate of the median.
You first guess that the median number is ten. Now ask yourself
if you would bet on more, or on less, than ten breakdowns, with
the round-the-world trip as a prize if you are correct. You
answer that with considerable confidence you would bet on more
than ten breakdowns. If so, your best guess of the median is
more than ten, because you should be undecided about which way
you would place the bet when the median has been correctly
chosen. So now move your estimate of the median to, say, eleven,
and ask which way you would then bet to get the prize. If you
are then undecided, you can stop. But if you are still pretty
sure you would bet on more than eleven, you must next consider a
number higher than eleven as the median, and so on, until you
reach the point at which you really are undecided about which way
you would bet to receive the prize.
Gimmick 6. Sometimes it helps to ask yourself what
proportion of such events would be "yes" if the same situation
were to be rerun 1,000 times. This mental trick may produce an
acceptable estimate even when it seems very difficult to attach
an estimate to a single event in isolation.
Gimmick 7. Sometimes it helps to ask yourself -- or the
decision maker you are assisting -- for a range of probability
estimates, rather than just a single point estimate. For
example, you may find it easier to estimate the probability of
the competitor's raising his price, if you raise yours, as
somewhere between 30 and 50 percent, rather than a point estimate
of 40 percent. If the range is thus fairly narrow, you can
safely work with the midpoint in subsequent calculations.3
Gimmick 8. As is true of other approximations, it is often wise to break the estimation job into constituent parts if there
are several identifiable important aspects to it. For example, you might wish to estimate the probability that a competitor will
bring out a plastic contact lens if you do so. And you know that the likelihood of his doing so depends heavily on his being
willing to invest money in research and development to develop the necessary new technology. Instead of estimating in one jump
the probability of his bringing out the plastic lens, you might separately estimate the probabilities for the two stages. After
you estimate these sets of probabilities separately, you can use the multiplication rule to get an unconditional probability
estimate for the overall event.
If there are more than a very few identifiable events that may have an influence on the outcome, you may be better off
estimating the probability of the outcome in a single jump, rather than building a fairly complex tree composed of many
probabilities, all of which are uncertain. But on the average breaking a complex sequence of events such as a plan into its
constituent parts has been shown to lead to more accurate estimation.4 Estimates made directly
about the probability of success for a plan tend to be more
biased toward a successful outcome than are estimates that take
into account the probabilities of the individual events that must
occur if the plan is to succeed. Perhaps this is because when
one makes an estimate of the probability of success directly, one
tends to focus on the first event that must occur, and then lets
that number influence the overall estimate. For example, assume
we are estimating the probability that a building will be
completed a year from now. The number of hitches that can occur,
contingent on one another, is very large. But if we do not take
each of them into account very explicitly, we may find that the
high probability of the first event -- acquiring the land, which
has a probability of, say, 70 percent influences our immediate
view of the overall success of the project.
In the previous example, the estimation task was broken into
separate sequential stages. Another situation where it may be
wise to break up an estimation job is where there may be several
alternative events to the one you are interested in. Consider
the example of the firm bidding on the contract to produce 2,500
Puritanian flags (Chapter 1-4). Assume there are five other
possible competitors. One might simply estimate directly the
likelihood of none of them bidding lower than some specified bid
-- say, $20,000. Another procedure is to estimate the
likelihoods for each of them individually, and then to combine
the probabilities.
Perhaps you estimate their probabilities of not bidding
under $20,000 as follows:
Firm Probability
A .7
B .8
C .7
D .9
E .9
If so, the probability of none of them bidding under $20,000 is
.7 x .8 x .7 x .9 x .9 = .32, and that is your probability of
your making a successful bid at $20,000.
It is interesting and useful to know that if you do not
break up a sequential situation, such as a construction plan,
into stages, you tend to overestimate the likelihood of a
"success" occurring. But if you do not break up a simultaneous
event, such as a bid, into the various other events, you tend to
underestimate the probability of a "success."5 Gimmick 9.
Ask some other qualified people inside or outside the firm to
estimate the probabilities, and find a consensus by comparing the
estimates. The best people to choose (and obviously, the hardest
to find) are those who are well informed but have no emotional
involvement in the situation.
The Delphi technique is a systematic technique for
developing the consensus of a group of people. First, people are
asked for their individual estimates of the probabilities. Then
they are presented with the estimates of all the other people and
asked how they will change their own estimates, if at all. If a
respondent's new estimates are still far away from the group's
previous average, the respondent is required to offer an
explanation. Then the process is repeated, a total of perhaps
three or four times. There is some reason to believe that the
last set of probabilities is better than the first set in many
cases, if only because people have had to think harder about
their estimates as time goes on. Of course, the possibility
exists that some of the people who hold "far out" views are right
and the majority wrong, in which case the Delphi process could
lead to progressively worse estimates. So the process is
imperfect -- but so is life.
The use of experts will be referred to again toward the end
of the chapter.
We have been working with the yes-or-no type of probability
estimate. In many cases one works instead with the estimation of
a probability distribution with a wider variety of possibilities.
Demand and cost functions are common examples. But this
technique may be left to more technical works (e. g. Simon, 1980,
Chapter ?).
It may be instructive and useful to keep a record of your
own probability estimates, and then examine how they compare with
actual outcomes. This is especially useful if you are engaged in
estimating some series of repeated events, such as the demand for
various kinds of musical performers. If you find out that you
systematically overestimate or underestimate, you can try to make
corrections in advance for your propensity.
Perhaps the most pervasive cause of bias is the estimator's
emotional state -- his hopes and fears, his optimism and
pessimism, the rewards and punishments that he expects contingent
upon various possible outcomes. One device suggested earlier to
get around this bias is to solicit judgments from people who are
not involved actually or emotionally. But often this device is
not feasible. Perhaps the best tactic in estimating
probabilities when one is involved is to make explicit to oneself
what one's feelings are. And the best way to do this is by
writing them down, as honestly as one can. Once the feelings are
out in the open and labeled, one can try to counteract them in
the estimates.
SUMMARY
Estimating probabilities is difficult, but it must be done.
The better one's information about the situation, the better the
estimate is likely to be. Sometimes the probability estimate can
be made on the basis of existing information. Sometimes experts
should be consulted on scientific research undertaken.
Various devices can help you extract reasonable probability
estimates from yourself. You should separately estimate the
probabilities of both "success" and "failure" to see that they
add to 1. You may proceed in stages, beginning with the midpoint
and then estimating midpoints between other points. You may make
wagers with yourself or with others to make the matter more
immediate and to check your feelings. And often it is useful to
make a range of estimates -- or "high," "low," and "medium"
estimates -- instead of just a single point estimate. And if the
planned alternative has several events in sequence, or if there
are several possible alternative outcomes to the one you are
interested in, it is helpful to estimate the probabilities of the
separate events and then to combine them.
There are many possible sorts of biases, some of which may
be mitigated by the various devices discussed in this chapter.
But the greater danger comes from one's emotional situation --
one's hopes and fears, expected rewards and punishments,
influencing one's judgment. The only antidote is to make one's
feelings explicit in as honest a manner as possible.
EXERCISES 1. Estimate the
probabilities that you will find employment at various salaries
when you next look for a job, and tell the bases for your
estimation.
2. How would you go about estimating the probabilities of
various quantities of this book being sold next year? After it
is revised the next time? 3. A man and wife teach psychology
and physics respectively at Bluewater State University. They
want to move to the University of Hawaii. How should they
estimate the probabilities of their both finding jobs there? How
about if they both teach psychology?
4. If Ford puts an airbag into next year's cars as a
standard item even though the law does not require it, what is
the probability that General Motors also will in the following
year at the latest? Chrysler? Both? How should Ford go about
making its estimate?
FOOTNOTES
1This material is more fully covered in Robert O. Schlaifer,
Analysis of Decisions under Uncertainty (New York: McGraw-Hill,
1969), especially when read in connection with Howard Raiffa,
Decision Analysis Reading, Mass.: Addision-Wesley, (1969). Many
of the ideas in this chapter have been drawn from these two
sources.
2William A. Spurr and Charles P. Bonono, Statistical
Analysis for Business Decisions, rev. ed. (Homewood, Ill.: Irwin-
Dorsey, 1973), pp. 117-20 discuss this technique at length.
3A similar comment has been made about all estimations,
probabilistic and non-probabilistic, by Enthoven:
We have found that in cases of uncertainty, it is often
useful to carry three sets of factors through the
calculations: an "Optimistic" and a "Pessimistic" estimate
that bracket the range of uncertainty, and a "Best Estimate"
that has the highest likelihood. These terms are not very
rigorous. A subjective judgment is required. But it is
surprising how often reasonable men studying the same
evidence can agree on three numbers where they cannot agree
on one. In fact, one of the great benefits of this approach
has been to eliminate much senseless quibbling over minor
variations in numerical estimates of very uncertain
magnitudes. Alain C. Enthoven, "Economic Analysis in the
Department of Defense," American Economic Review, LIII, May,
1963, 413-23.
4Amos Tverky and Daniel Kahneman, "Judgment under
Uncertainty: Heuristics and Biases," paper written for the
Fourth Conference on Subjective Probability, Utility, and
Decision Making, Rome, 1973 discuss this matter.
5Ibid.
6Tverdky and Kahneman, "Judgment under Uncertainty."
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