**A LEXICON OF DECISION MAKING**

To the reader,

This short narrative is intended to provide, in non-technical terms and
in a readable way, definitions of the words most commonly used in a
decision making context. I have written this because I have found that
these words are frequently used incorrectly. In a sense,
misunderstanding language is more insidious than not understanding it at
all, in that it distorts meaning. Distortion of meaning, with its
attendant confusion of thought, deters us from the goal of good decision
making, which is clarity of action, the right action. I hope you can
read this in 10 minutes or less and benefit from it.

Several colleagues have contributed appreciably to the quality of this
document, and I would like specifically to mention Bob Clemen, Don
Keefer, Craig Kirkwood, Bob Nau, and Jim Smith. The reader has no way to
gauge their contribution, but I do. Thanks, gentlemen.

> Tom Spradlin
>
> 317-276-4311
>
> tomspradlin@lilly.com
>
> March 1997
>
> *It may not seem very important, I know,*
>
> *But it is, and that's why I'm bothering telling you so.*
>
> *\--Dr. Seuss*

**INDEX**

Alternatives 2

Certain equivalent 6

Clarity of action 4

Decision 1

Decision analysis 1

Decision maker 1

Direct values 5

Discount rate 5

Economic value 5

Expected value 4

Forecasts 3

Goal 1

Good decision 2

Good outcome 2

Indirect values 5

Mean 4

Median 4

Models 1

NPV 5

Objective 1

Option 3

Outcome 2

Portfolio 3

Prioritization 3

Probability distribution 4

Risk 6

Risk tolerance 7

Risk-averse 6

Risk-neutral 6

Sensitivity 4

Sensitivity of the decision 4

Sensitivity of the outcome 4

Simple decision 2

Strategy 2

10-50-90s 4

Trade-offs 6

Uncertainties 2

Utility function 7

Values 1

**A Lexicon of Decision Making**

**[Introduction]{.underline}**

A **decision** is an allocation of resources. It can be likened to
writing a check and delivering it to the payee. It is irrevocable,
except that a new decision may reverse it. In the same way that a check
is signed by the account owner, a decision is made by

the **decision maker**. The decision maker is one who has authority over
the resources being allocated. Presumably, he (or she) makes the
decision in order to further some

**objective**, which is what he hopes to achieve by allocating the
resources.

> *Key distinction: **decision** vs. **objective***
>
> *Example: To accelerate an R&D program is an objective, not a
> decision. To allocate the funds in an effort to accelerate the program
> is a decision.*
>
> *Why it's important: The decision might not succeed in achieving the
> objective. One might spend the funds and yet, for any number of
> reasons, achieve no acceleration at all.*

The decision maker will make decisions consistent with his **values**,
which are those things that are important to him, especially those that
are relevant to this decision. A common value is economic, according to
which the decision maker will attempt to increase his wealth. Others
might be personal, such as happiness or security, or social, such as
fairness.

The decision maker might set a **goal** for his decision, which is a
specific degree of satisfaction of a given objective. For example, the
objective of the decision might be to increase wealth, and the goal
might be to make a million dollars.

A decision maker might employ **decision analysis**, which is a
structured way of thinking about how the action taken in the current
decision would lead to a result. In doing this, one distinguishes three
features of the situation: the decision to be made, the chance and
unknown events which can affect the result, and the result itself.
Decision analysis then constructs

**models**, logical and perhaps even mathematical representations of the
relationships within and between these three features of the decision
situation. The models then allow the decision maker to estimate the
possible implications of each course of action that he might take, so
that he can better understand the relationship between his actions and
his objectives.

**[The three features of a decision situation]{.underline}**

At the time of the decision, the decision maker has available to him at
least two **alternatives**, which are the courses of action that he
*might* take. When he chooses an alternative and commits to it (i.e.,
signs and delivers the check), he has made the decision and then

**uncertainties** come into play. These are those uncontrollable
elements that we sometimes call luck. Different alternatives that the
decision maker might choose might subject him to different
uncertainties, but in every case the alternatives combine with the
uncertainties to produce the

**outcome**. The outcome is the result of the decision situation and is
measured on the scale of the decision maker's values. Since the outcome
is the result not only of the chosen alternative but also of the
uncertainties, it is itself an uncertainty. For example, an objective
might be to increase wealth, but any alternative intended to lead to
that outcome might lead instead to poverty.

> *Key distinction: **good decision** vs. **good outcome***
>
> *Example: Someone who buys a lottery ticket and wins the lottery
> obtains a good outcome. Yet, the decision to buy the lottery ticket
> may or may not have been a good decision.*
>
> *Why it's important: A bad decision may lead to a good outcome and
> conversely a good decision may lead to a bad outcome. The quality of a
> decision must be evaluated on the basis of the decision maker\'s
> alternatives, information, values, and logic at the time the decision
> was made.*

**[Types of decisions]{.underline}**

A **simple decision** is one in which there is only one decision to be
made, even though there might be many alternatives. An example of this
is the very limited consideration of purchasing collision insurance for
an automobile. The decision maker might be interested only in comparing
three alternatives, such as no insurance, insurance with \$100
deductible, or a policy with \$500 deductible. If at the same time we
attempt to add another decision, we have created a problem of

**strategy**, which is a situation in which several decisions are to be
made at the same time. Each of the decisions in the strategy will have
different alternatives, and the decision maker will attempt to choose a
coherent combination of alternatives. For example, if the decision maker
is considering whether to buy a new car or keep his 10-year old one, and
at the same time he is considering the insurance decision, he might
compare only two candidate strategies: keep the old car and not buy
collision insurance, or buy a new car and buy some level of collision
insurance.

> *Key distinction: **strategy** vs. **goal***
>
> *Example: Launching two new products a year is a goal. Investing in
> additional personnel, while at the same time stopping the funding of
> some stalled projects, is a strategy intended to lead to that goal.*
>
> *Why it's important: Strategy describes a collection of actions that
> the decision maker takes. The outcome of the actions is uncertain, but
> one of the possible outcomes is attainment of that goal.*

An important special case of a strategy problem is the **portfolio**
problem, in which the various decisions faced in the strategy are of a
similar nature, and the decision maker does not have sufficient
resources for funding all combinations of alternatives. An example is an
investment portfolio, in which the decision maker is aware of a good
number of investments he would like to make, but is unable to afford all
of them. Especially in situations like this example, people sometimes
address the problem as one of performing a

**prioritization** of the various opportunities. If one opportunity is
prioritized higher than another, then, in the case of limited resources,
the decision maker would prefer to invest in the former than in the
latter.

> *Key distinction: **decision** vs. **prioritization***
>
> *Example: To assert that one would rather fund development project A
> than development project B, and project B than project C, is a
> prioritization. Actually funding project A is a decision.*
>
> *Why it's important: A prioritization might be an intermediate step en
> route to a decision, and one might even use a prioritization as a tool
> to aid in a decision.*

Some decisions offer the opportunity to adopt a particular type of
alternative called an **option**. An option is an alternative that
permits a future decision following revelation of information. All
options are alternatives, but not all alternatives are options.

> *Key distinction: **alternative** vs. **option***
>
> *Example: To allocate the resources needed to drill an oil well is an
> alternative. To pay money now to reserve the right to drill after
> geological testing is done is an alternative that is also an option.*
>
> *Why it's important: Options, as an important type of alternatives,
> have the potential of adding value to a decision situation. A wise
> decision maker is alert to that possibility, and actively searches for
> valuable options.*

**[Uncertainties]{.underline}**

Decision making would be easy if we could predict reliably what outcome
would follow from the selection of which alternative. To this end
decision makers use **forecasts**, or predictions of the future, to
guide their choice of alternatives. They attempt to predict the outcome,
on all values of interest to the decision maker, associated with each
alternative that might be chosen. For example, the decision maker may
use forecasts of market size, market share, prices and production costs
in order to predict the profits associated with a new product. When the
quantities forecasted are uncertain, forecasters can describe their
uncertainty about these uncertainties using a

**probability distribution**. A probability distribution is a
mathematical form for capturing what we know about uncertainties, and
how confident we are of what we know. A probability distribution could
record, for example, that the decision maker (or his designated expert)
believes that there is a 30 percent chance of a product having less than
10 percent market share 2 years after its launch, and a 60 percent
chance of the product having less than a 30 percent market share. After
assigning probability distributions to each uncertainty, one can examine
the uncertainty associated with the outcomes of the decision situation.
For example, given probability distributions for price, market share,
market size, cost, etc., one can determine a probability distribution
for profits. Frequently in studying a probability distribution one
considers its

**expected value** (or **mean**), which is the average of the values one
would expect to obtain upon sampling from the distribution a large
number of times. The expected value weights each possible value by its
likelihood of occurring. Another way to summarize a probability
distribution is to consider some representative percentiles, for example
the 10th-, 50th-, and, 90th percentiles, or

**\"10-50-90s\"** for short. The 10th and 90th percentiles are possible
low and high values, respectively, for a given uncertainty, set so that
there is a 10 percent chance that the uncertainty, when revealed, will
fall below the 10th percentile, and a 10 percent chance that it will
fall above the 90th percentile. Similarly, the 50th percentile (or
**median**) is that number such that the realized value, when revealed,
is equally likely to be above as to be below. Given these percentiles,
we can test the

**sensitivity** of the decision to the uncertainties. Here we attempt to
answer the question whether the decision maker would choose a different
alternative if he could know that the uncertainty would have the low
(10th percentile) value from the one that he would select if he had
knowledge that it would have the high (90th percentile) value. This sort
of analysis helps to achieve

**clarity of action**. With clarity of action, the decision maker knows
what he *should* do, even if he does not know how it will turn out. This
is the aim of decision analysis.

> *Key distinction: **sensitivity of the decision** vs. **sensitivity of
> the outcome***
>
> *Example: The profitability of the new product we are developing is
> sensitive to the market share we achieve. However it may be the case
> that, as long as we achieve a market share within the range of our
> 10-50-90s, we would still choose to develop the product. In this case,
> our development decision is not sensitive to market share.*
>
> *Why it's important: Everyone wants the outcome to be as good as
> possible, and in that sense might be interested in knowing to what
> uncertainties the outcome is sensitive. However, if one is interested
> in achieving clarity of action, as opposed to predicting the future,
> one need only be concerned about those uncertainties which would
> change the decision if we could know in advance how they will turn
> out.*

**[Outcomes and values]{.underline}**

We consider decisions carefully because we care about the outcomes,
whose goodness we measure against our values. The most commonly studied
and discussed value is **economic value**, which we assume to be
measured in dollars. Given a stream of cash flows over time, people
often use the

**NPV** (net present value) to describe the current value of future cash
flows. The NPV is a calculation performed on cash flows over time,
allowing one to condense that stream of cash flows into a single number.
Decision makers often use the NPV of profits or cash flows as a measure
of the value of a project. The NPV calculation makes use of the

**discount rate**, which has several interpretations, but can be thought
of as a factor applied to future income to reflect the fact that it is
less valuable than income received now. It also reduces the impact of
future costs, since costs that can be deferred into the future are
preferable to those that must be paid now.

In thinking about the value of a scenario, it is helpful to distinguish
between **direct** and **indirect values**. Direct values are cash flows
directly related to a project, for example, the profits resulting from
the manufacture and sales of a new product. Indirect values are things
that the decision maker values that are not likely to show up in
accounting statements. For example, a decision maker may experience
\"pride\" or \"goodwill\" in producing some products and value such an
outcome beyond its direct economic value. These indirect values could
include costs associated with, for example, laying off workers, or
negative impacts on reputation. While some of these indirect values are
intangible, others are tangible but difficult to put a number on. For
example, increases in \"goodwill\" associated with one product may
result in increased sales of other products though this effect may be
hard to estimate.

> *Key distinction: **direct** vs. **indirect values***
>
> *Example: The direct value of a new product might be the current value
> of the future cash flow associated with the manufacture and sale of
> the product. The indirect value might include effects like increased
> goodwill or strategic advantage that come from having the product but
> are not directly associated with the manufacture and sale of the
> product.*
>
> *Why it's important: Typically, maximizing the NPV associated with a
> product is one of the decision maker\'s objectives. The decision maker
> might, however, assign value in excess of a cash flow based NPV, and
> that increment might be for what is sometimes termed "strategic
> value." These indirect sources of value must be included in the NPVs,
> if one is to think appropriately about values. It is better to put a
> rough value on these indirect sources (so it can be discussed and
> evaluated) than to assume they are worth precisely zero.*

Often the decision maker will have values other than economic, and in
this case he will have to make **trade-offs** between values, which are
judgments about how much he is willing to sacrifice on one value in
order to receive more of another. For example, in a personal context, a
decision maker may need to make a trade off between hours spent at work
(something he may wish to minimize so as to maximize the time he spends
with his family) and the amount of income he receives.

**[Risk]{.underline}**

As decision makers ponder the possible outcomes of their decisions they
often think about **risk**, which is the possibility of an undesirable
result. In discussing this, it is convenient to consider the notion of a

**risk-neutral** decision maker. Someone who is risk neutral is willing
to play the long-run odds when making decisions, and will evaluate
alternatives according to their expected values. For example, such a
decision maker would be indifferent between receiving \$1 for certain
and an alternative with equal chances of yielding \$0 and \$2, since
this is the average amount that the alternative would yield if repeated
many times. While an insurance company may evaluate individual policies
as if it were risk-neutral, for alternatives with substantial risks,
decision makers are often

**risk averse**, which means that they value alternatives at less than
their expected values. To make this definition of value precise, we
define the

**certain equivalent**, (or certainty equivalent) of an alternative as
the amount that the decision maker would be indifferent between (1)
having that monetary amount for certain or (2) having the alternative
with its uncertain outcome. For example, a risk-averse decision maker
might have a certain equivalent of \$500,000 for an alternative with
equal chances of yielding \$0 and \$2,000,000, even though the expected
value for this alternative is \$1,000,000. In thinking about risk
aversion, it is important to remember that different decision makers
have different attitudes toward risk. While this gamble with with equal
chances of yielding \$0 and \$2,000,000 may be very risky for me, a
billionaire or a big company may not view these stakes as large and may
have a certain equivalent close to the expected value.

Decisions where risk aversion holds can be analyzed using a

**utility function**, which encodes a decision maker\'s attitude toward
risk taking in mathematical form by relating the decision maker's
satisfaction with the outcome (or \"utility\" associated with the
outcome) to the monetary value of the outcome itself. These utility
functions can be indexed by their

**risk tolerance**, which is a technical term describing the decision
maker's attitude toward risk. The greater the decision maker\'s risk
tolerance, the closer the certain equivalent of a gamble will be to its
expected value. The risk tolerance is a mathematical quantity that
describes the decision maker\'s attitude towards risk; it is *not* the
maximum amount that the decision maker can afford to lose, though
generally decision makers with greater wealth will have larger risk
tolerances. The decision maker needs to think about his risk tolerance
only in cases where the stakes are large and he is not comfortable
basing his decision on the expected monetary value.

> *Key distinction: **certain equivalent** vs. **expected NPV***
>
> *Example: The certain equivalent for a risky new product is the
> smallest sum of money for which the decision maker would be willing to
> sell rights to that product. The expected NPV for the product is the
> hypothetical average NPV from numerous independent launches of
> identical projects.*
>
> *Why it's important: Most projects cannot be repeated and even if they
> could, when the stakes are large, most decision makers value gambles
> at less than their expected values. Precisely how much less than their
> expected value depends on the decision maker\'s attitude towards risk.
> This attitude towards risk varies from decision maker to decision
> maker and, even for a specific decision maker, may vary over time.*