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Subjective Probability in Behavioral Economics and Finance: A Radical Reformulation

July 2015
Journal of Behavioral Finance 16(3):231-249

DOI:10.1080/15427560.2015.1065262

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Northern Illinois University

Behavioral finance depends intimately on the notion of subjective probability, which has been universally treated as one of the two forms of probability. A substantial body of work and recent experimental results show conclusively that this approach is invalid: subjective and objective probabilities cannot be treated as two sides of the same coin. This raises serious questions about calculations based on that assumption, decisions based on those calculations, and what to do if assigning numerical values and calculating expected values based on subjective probabilities is invalid. This paper presents a radical re-formulation of subjective probability, showing that what have been called “subjective probabilities” are properly formulated as uncertainty appraisals, re-descriptions of states of affairs carrying tautological implications for action. A novel formulation of the decision maker's field-of-view, based on the concept of Actor, Observer, and Critic roles, combined with the uncertainty appraisal formulation, is used to develop new methods for evaluating data, finding patterns in data, and integrating probabilities and uncertainty appraisals, that is, those aspects that have, until now, been called “subjective probabilities.”

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Subjective Probability in Behavioral Economics and

Finance: A Radical Reformulation

H. Joel Jeffrey & Anthony O. Putman

To cite this article: H. Joel Jeffrey & Anthony O. Putman (2015) Subjective Probability in

Behavioral Economics and Finance: A Radical Reformulation, Journal of Behavioral Finance,

16:3, 231-249, DOI: 10.1080/15427560.2015.1065262

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Subjective Probability in Behavioral Economics and

Finance: A Radical Reformulation

H. Joel Jeffrey

Northern Illinois University

Anthony O. Putman

Descriptive Psychology Institute

Behavioral ﬁnance depends intimately on the notion of subjective probability, which has

been universally treated as one of the two forms of probability. A substantial body of work

and recent experimental results show conclusively that this approach is invalid: subjective

and objective probabilities cannot be treated as two sides of the same coin. This raises

serious questions about calculations based on that assumption, decisions based on those

calculations, and what to do if assigning numerical values and calculating expected values

based on subjective probabilities is invalid. This paper presents a radical re-formulation of

subjective probability, showing that what have been called “subjective probabilities” are

properly formulated as uncertainty appraisals, re-descriptions of states of affairs carrying

tautological implications for action. A novel formulation of the decision maker’s ﬁeld-of-

view, based on the concept of Actor, Observer, and Critic roles, combined with the

uncertainty appraisal formulation, is used to develop new methods for evaluating data,

ﬁnding patterns in data, and integrating probabilities and uncertainty appraisals, that is, those

aspects that have, until now, been called “subjective probabilities.”

Keywords: Subjective probability, Decision theory, Homo commmunitatis, Probability

theory

Almost every decision in ﬁnance, whether by individual or

institutional investors, involves the use of what is called

“subjective probability,” either explicitly or implicitly. Vir-

tually every formulation of subjective probability treats it

as though it and objective probability were two sides of the

same coin, and accordingly essentially the same methods

for incorporating subjective and objective probabilities into

decisions have been employed: assign a numerical value to

a probability (whether objective or subjective), estimate or

calculate the value of the associated event, and calculate

the expected value (perhaps with adjustments to the proba-

bility values based on some form of prospect theory [Kah-

neman and Tversky (1979)]).

Unfortunately, a substantial body of work and recent

experimental results show conclusively that this approach

is invalid: objective and subjective probabilities address

entirely different things, and further numerical values for

subjective probabilities do not, in general, satisfy the axi-

oms of probability. “Subjective probabilities” are not prob-

abilities at all. As a result, any calculation based on treating

those numerical values as though they satisﬁed the axioms

of probability, such the expected value of a security or per-

formance of a market sector, are at best highly suspect. The

impact on quality of decisions involving those expected

values is obvious.

A new formulation of the factors that have been

known as “subjective probabilities” is clearly needed.

Equally necessary are new methods for incorporating

those uncertainties in decisions. The straightforward

expected value calculation outlined above is invalid, but

the uncertainties in the picture are inescapable; we need

ways to incorporate “subjective probabilities” and actual

probabilities. This paper addresses the need for a new

formulation (the second section) and presents several

new methods based on it (the fourth section). We

believe the formulation and methods have signiﬁcant

Address correspondence to H. Joel Jeffrey, Professor Emeritus, Depart-

ment of Computer Science, Northern Illinois University, DeKalb, IL

60115. E-mail: jeffrey@cs.niu.edu

THE JOURNAL OF BEHAVIORAL FINANCE, 16: 231–249, 2015

ISSN: 1542-7560 / 1542-7579 online

DOI: 10.1080/15427560.2015.1065262

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implications for behavioral economics and ﬁnance, both

academically and professionally.

APPROACH

Since the time of Daniel Bernoulli, economics and ﬁnance

have rested on two foundations: that decisions are based on

expected value of outcomes and probability. Previous work

(Jeffrey and Putman [2013], Jeffrey [2010]) extensively

analyzed the ﬂaws in the ﬁrst of these and presented an

alternative, homo communitatis paradigm, a rigorous articu-

lation of the full range of factors affecting human action,

thereby providing a basis for full analysis of economic

behavior. Homo communitatis is, to our knowledge, the ﬁrst

new formulation of choice since the inception of the study

of decision under uncertainty.

In this paper we use homo communitatis to re-formulate

“subjective probability.” We show that, contrary to the 17th

century formulation of objective and subjective probability

as two versions of the same thing, they are actually two

entirely distinct concepts applicable to two distinct phe-

nomena: Objective probability is a relationship between

two numerical states of affairs, whereas “subjective proba-

bility” is a relationship between an individual and an action.

Confusing the two phenomena is a serious error and has had

serious consequences. It has resulted, for example, in the

unwarranted conclusion that an experimental subject who

states, “Based on Sam’s personality, he is more likely to be

a ﬁghter pilot than an insurance salesman” is doing Bayes-

ian probability calculations, but doing them badly. Perhaps

more seriously, it also results in the assumption that state-

ments such as “It is unlikely that subprime mortgage default

will result in serious ﬁnancial disruption” are made more

precise by restating them numerically, rather than by identi-

fying possible actions and assigning them relative priorities.

Homo communitatis may be summarized by the follow-

ing 7 principles:

1. Choice is choice of behavior, of which outcome is

only one aspect.

2. “Behavior” means intentional action, formulated

parametrically as <I, W, K, Kh, P, A, PC, S>.

3. The paradigm case of human behavior is deliberate

action, that is, intentional action in which the individ-

ual knows what he is doing and choosing to do it, rep-

resented formally by including the behavior (by

name) in the speciﬁcation of the values of the K and

W parameters, respectively.

4. Behavior choices are made in light of the individual’s

reasons to engage in one behavior or another.

5. People choose what matters to them; that is, choices

reﬂect values, which are shown in the pattern of a

person’s choices over time.

6. Every behavior is an instance of engaging in a social

practice of a community.

7. For any person, a particular state of affairs may be

real, actually possible, or merely possible.

Though stated in ordinary English, these principles con-

stitute a formal articulation of the concepts of choice,

behavior, reasons for choice, value, and the relationships

between them, much as the axioms of Euclidean geometry

are stated in ordinary language but are an articulation of

geometric concepts and their relationships.

11,22

The term

homo communitatis reﬂects the centrality of the relationship

between behavior and community: every action is a case of

engaging in a structured pattern of actions, a social practice

of a community. The new paradigm yields novel insights

into several phenomena such as the Friedman-Savage

“paradox,” loss aversion, the endowment effect, and fram-

ing effects, by articulating the full range of factors involved

in each decision or behavior. The apparent “irrationality”

often attributed to economic actor is an illusion due to bas-

ing analyses on defective descriptions of the choices, much

as a fun-house mirror produces the illusion of peculiar body

shapes.

This paper is organized as follows. The ﬁrst section dis-

cusses the relationship between objective and “subjective”

probabilities, showing that they cannot be two sides of the

same coin. The second section uses the principles of homo

communitatis to give a new conceptualization of

“subjective” probability (and its equivalent “degree of

belief”). The novel conceptualization yields novel methods

for handling uncertainty, methods quite unlike traditional

ones, but in order to develop those methods we must ﬁrst

address the issue of an action as seen by the person when

they are acting, as contrasted with how the actorCaction

situation look to an observer, and we do that in the third

section. The fourth section develops the pragmatic implica-

tions of the new conceptualization in research and profes-

sional practice in economics and ﬁnance.

As is customary (see, e.g., Tversky and Kahneman

[1974], Kahneman and Tversky [1979]), while our interest

here is primarily behavioral economics and ﬁnance, we

develop the concepts and methods in the general context of

decision under uncertainty.

“SUBJECTIVE PROBABILITY” VS. ACTUAL

PROBABILITY

Two important themes run through the history of probabil-

ity since it emerged in Western scientiﬁc thought around

1660. One is that from the beginning it has been “Janus-

faced” (Hacking [1975]), dealing on one hand with states

of affairs involving relative frequency of outcomes of

repeated trials and on the other hand with a person’s

“degree of belief” in propositions. The second is that both

232 JEFFREY AND PUTMAN

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concepts have been considered fundamentally related to

decisions. In the language of philosophy, one aspect is

ontological, the other epistemological, but both are aspects

of making decisions. In this section we address the question

of whether it makes sense to consider relative frequency

and degree of belief as two sides of the same coin.

Frequency and degree of belief have come to be consid-

ered essentially interchangeable, with concepts and meth-

ods suitable for the objective used to address the

“subjective” and vice versa, without regard to applicability

of concepts, particularly in decision theory, psychology,

and economics. (Interestingly, this is much less the case in

engineering disciplines.) For example, it is currently com-

mon practice in behavioral economics to ask experimental

subjects degree of belief questions and then analyze their

answers by asserting that subjects arrive at their answers by

using sample sets and (defective) calculations based on

them (Tversky and Kahneman [1974], Barberis and Thaler

[2003], Camerer [2000]).

Similar language (e.g., “probable,” “likely”) is often

used to talk about the two concepts, increasing the confu-

sion. The work that ﬁrst introduced the concept and term

“representativeness bias” (Tversky and Kahneman [1974])

is a good illustration of the problem. The authors introduce

their discussion as follows:

Many of the probabilistic questions with which people are

concerned belong to one of the following types: What is the

probability that object A belongs to class B? What is the

probability that event A originates from process B? What is

the probability that process B will generate event A?

A few lines later, they continue:

Steve is very shy and withdrawn, invariably helpful, but

with little interest in people, or in the world of reality. A

meek and tidy soul, he has a need for order and structure,

and a passion for detail. How do people assess the probabil-

ity that Steve is engaged in a particular occupation from a

list of occupations?...In the representativeness heuristic,

the probability that Steve is a librarian...is assessed by the

degree to which he is representative of, or similar to, the

stereotype of a librarian....This approach to the judgment

of probability leads to serious errors... . (p. 44)

Thus, the initial discussion is in terms of membership in

a class of events resulting from processes, such as picking a

ball from an urn of blue and red balls or a spinning roulette

wheel. Actual processes are the basis of a sample space: a

set of elements with a probability distribution, from which

repeated samples are drawn. The same language is then

used to describe a task in which there is no sample space—

no repeated trials and no relative frequencies—and there-

fore one in which the objective probability is entirely inap-

plicable. Subjects’ answers are interpreted as though 1) it

were known that the subject understood the question as an

objective probability question, despite there being a number

of commonly recognized nonprobabilistic meanings to the

question; and 2) answers had been produced by selection

from a sample set. Subjects’ answers are then described in

terms of errors they would have been making, had they

been selecting an object from a sample set. The presenta-

tion, though, does not say they would have been making

those errors; it says they are. Thus, an initial discussion of

objective probability moves seamlessly to a case of

“subjective” probability in which the concepts of probabil-

ity do not apply. Describing experiments as though subjects

were literally selecting from a sample space, without regard

for whether there is such a space or samples from it, is stan-

dard practice in behavioral economics.

A similar but even more striking example is cited by

Barberis and Thaler [2003]:

Linda is 31 years old, single, outspoken, and very bright.

She majored in philosophy. As a student, she was deeply

concerned with issues of discrimination and social justice,

and also participated in anti-nuclear demonstrations. When

asked which of “Linda is a bank teller” (statement A) and

“Linda is a bank teller and is active in the feminist move-

ment” (statement B) is more likely, subjects typically assign

greater probability to B. This is, of course, impossible

[emphasis added]. (p. 1064)

Here, even when experimental results contradict the

mathematics of probability, the researchers are, in effect,

insisting on the use of the concept of probability to analyze

them.

Use of probability language to refer to situations in

which there is no sample space is by no means unusual, as

shown in Table 1. Such use often results in describing

“subjective probabilities” with numerical values that do not

satisfy the deﬁnition of probability. Speciﬁcally, it is not

uncommon for subjective probabilities assigned to disjoint

events to be subadditive (sum to less than one) or super-

additive (sum to more than one) (Macchi, Osherson, and

Krantz [1999], Mandel [2005]). In ﬁnance, law, political

science, intelligence estimation, and a number of other

ﬁelds ambiguity, a concept distinct from uncertainty, com-

monly results in situations in which, on considering all

available facts, both X and not-X appear likely. In such

cases the numerical representations of these “probabilities”

would sum to more than one. Quantities (or equivalently a

function from an event set to the positive real numbers) that

in general do not satisfy the axioms of probability are not

probabilities, just as 3-sided closed plane ﬁgure is not a dif-

ferent sort of rectangle. No sample set, no probability.

Objective and “subjective” probability have to do with

situations that are crucially different, depending on whether

or not a sample set is in use. They are, however, both ways

of talking about uncertainty. Further, as noted at the begin-

ning of this section, without exception they have to do with

SUBJECTIVE PROBABILITY IN BEHAVIORAL ECONOMICS AND FINANCE 233

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“decision under uncertainty,” which means a person decid-

ing what to do when uncertain about something relevant to

the decision. Uncertainty is a fundamental fact about the

world, while probability is not; the error has been to equate

the uncertainty with probability.

As decisions are central to understanding uncertainty,

and therefore to making sense of “subjective probability” in

light of the fact that it is not probability at all, let us look

more closely at decisions. Making a decision is depicted

below in Figure 1. Known as the CRJ diagram (Ossorio

[2006], p. 228, Jeffrey and Putman [2013]), it is a depiction

all the factors that pertain to a decision.

Discursively, the diagram represents the fact that person

P, in light of circumstances C

,...,C

, which constitute

reasons R

,...R

to do B

,...B

, chooses to do B

, reﬂect-

ing the relative priorities P assigns to the reasons. Or, less

formally: P’s circumstances give her reasons to do various

things, and the one she does reﬂects the relative priorities

she accords each reason. (It is important to understand that

Figure 1 does not depict a process of any sort. It is a recon-

struction of everything related to the decision, not a

sequence of steps, either overt or “internal.”)

As Figure 1 shows, the logic of a decision may be com-

plex, involving a number of states of affairs:

1. There are a number of behaviors, B

,...,B

that the

person has an opportunity to do.

2. Each behavior B

is described by 8 parameters, I

,Kh

,PC

3. The Circumstances C

,...,C

are those that the per-

son takes to be the case and to be relevant to the

decision. They are only those the person takes to be

relevant, not the perhaps-much-larger set an observer

might identify, and certainly not the enormously

larger set that could in some way be related to the

decision.

4. Each C

is appraised by the person as providing one

or more reasons to engage in one of the B

The entire

set of reasons to do one B

or another is R

,...,R

The C

are the relevant circumstances; the R

are how

each circumstance is relevant.

5. The reasons have relative weights w

,...,w

for the

person. These are the relative priorities the R

have

for the individual, in this case.

As discussed in Ossorio [2006], Jeffrey [2010], and Jef-

frey and Putman [2013], there are four kinds of reasons:

hedonic, prudential, ethical, and esthetic. As a result, the

entire value of circumstance C

to the person consists of

four incommensurate constituents, namely the total strength

of each of the four kinds of reasons. Mathematically, this

means that value is a four-element vector, and 4-vectors

cannot be ordered. As a result, current axiomatic treat-

ments, all of which are premised on value as a scalar, are

problematical.

What are circumstances? Circumstances here refer to

what the individual takes to be the case, the perceived facts,

with no connotations of correctness or degree of veriﬁca-

tion. The term is approximately equivalent to “beliefs,” as

that term is used technically, with the important proviso

that to say, “P believes X” is stating only that P takes X to

be the case and is prepared to act on it.

TABLE 1

Examples of Conﬂation of Objective and Subjective Probabilities

Phenomenon

Brief

description

Evidence subjects

used sample set?

Subjective or

objective

Presented as

subjective or objective

Representation heuristic Give personal description; ask occupation (Tversky and

Kahneman [1974]). Variation: ask occupation plus

group membership (Barberis and Thaler [2003])

NS O

Insensitivity to priors Give personal description; sample set present; ask

occupation (Tversky and Kahneman [1974])

NS O

Insensitivity to priors No personal description; sample set present; ask

occupation (Tversky and Kahneman [1974])

YO O

Insensitivity sample size Give M/F births at 2 hospitals; ask probable events at

each (Tversky and Kahneman [1974])

YO O

Insensitivity to priors Select balls from urns; predict outcomes (Tversky and

Kahneman [1974])

YO O

Misconceptions of chance Predict head-tail sequences (Tversky and Kahneman

[1974])

YO O

Insensitivity to predictability Present company descriptions; predict performance

(Kahneman and Tversky [1979])

NN O

Insensitivity to predictability Present teacher descriptions; predict performance

(Kahneman and Tversky [1979])

NS O

Anchoring Ask subjects to predict Dow Jones price (Kahneman and

Tversky [1979])

NS O

234 JEFFREY AND PUTMAN

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What are reasons? Reasons are a very precisely

deﬁned concept: valuing a state of affairs gives an indi-

vidual reason to act to try to achieve it. When an indi-

vidual has a reason to do X and sees an opportunity to

do X, he has motivation to do it. (This is the classic

concept of cause, but generalized to the case of an

action by a person rather than a physical objects and

processes.) Circumstances, by themselves, provide

opportunities to act, but they do not provide motivation.

Reasons provide the immediate connection to action:

reason to do B plus an opportunity to do B constitutes

motivation to do B.

How are circumstances and reasons related? Fundamen-

tally, the relationship between a circumstance and a reason

is a part-whole relationship. Circumstance C gives person P

reason R to do B when, and only when 1) C is a constituent

of state of affairs R, and 2) bringing about C will bring

about R.

Bernoulli’s example of a prisoner needing money to

purchase his freedom (Bernoulli [1738/1954]) is a good

illustration. If a man has 2,000 ducats, that is a circum-

stance; that he may win 2,000 more in a lottery is also

a circumstance, a possible state of affairs. If that man is

“a ... prisoner who needs two thousand ducats more to

repurchase his freedom”, the fact that he can win 2,000

gives him reason to play the lottery, as follows: having

2,000 and winning the additional 2,000 are constituents

of the larger state of affairs of having sufﬁcient ducats

to become free.

In general, circumstance C, together with other cir-

cumstances and the relationships between them, com-

prise larger state of affairs R that the person values.

That the C-R relationship depicted in Figure 1 is part-

whole, not probabilistic, has important implications in

articulating just what is meant by “subjective proba-

bility” in the section below.

Uncertainty

Figure 1 depicts all the factors that pertain to a decision.

Referring to it, we can see that a decision maker may be

uncertain about whether:

1. Circumstances-related issues:

a. Each of the circumstances is as perceived.

b. All the relevant circumstances have been

identiﬁed.

c. All circumstances identiﬁed as relevant actually

are.

2. Reasons-related issues:

a. Each circumstance actually gives the reason

identiﬁed.

b. All the reasons have been identiﬁed.

3. Priority issues: The relative priorities of the reasons

are appropriate.

4. Behavior-related issues. Each Circumstance C

appears in the speciﬁcation of the K parameter of the

behaviors – i.e., the speciﬁcation of the states of

affairs being acted on, and so Circumstance-related

uncertainty is uncertainty about what one knows (K),

but the person may also be uncertain about whether:

a. I: they are the correct individual to carry out the

action.

b. W: they actually want the result of the action.

c. Kh: they have the necessary competences for

one or more of the behaviors.

d. P: they can carry out the performance of one or

more of the behaviors, that they are carrying out

the performance of the chosen behavior cor-

rectly, or that they would recognize an incorrect

performance.

e. A: the performance of one or more of the behav-

iors will produce the intended state of affairs,

FIGURE 1 Circumstances, Reasons, and Judgment

SUBJECTIVE PROBABILITY IN BEHAVIORAL ECONOMICS AND FINANCE 235

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that they would recognize success or failure, that

they would recognize the relevant other conse-

quences of the behavior.

f. PC: they have the necessary personal characteris-

tics. These may be personality characteristics

(e.g., attitudes, character traits) or other relevant

facts about them, such as wealth or other

“external” attributes.

g. S: the larger state of affairs that would be

brought about by accomplishing one or more of

the behaviors; that they would recognize that

state of affairs if it did come about.

Objective probabilities have to do with a narrow subset

of these uncertainties: some of the circumstances and one

of the behavior parameters. Objective probability is a

numerical relationship between two numerical states of

affairs: ratio of occurrence of some kind to all possible

occurrences. It is therefore a circumstance—a state of

affairs relevant to the decision. As discussed above, the

relationship between circumstances and reasons is part-

whole, not a ratio of cardinalities; the relationship between

circumstances and reasons is not derivable via any proba-

bility calculation even when a sample space is present. Pri-

orities are a (partial) ordering on reasons, not ratios of

cardinalities. Thus, of the C’s, R’s, and w’s, only circum-

stances could possibly be probabilistic. Of the behavior

parameters, the only one that could possibly be a ratio of

cardinalities is whether achievement A will result if proce-

dure P is carried out, such as the probability that the out-

come of rolling the dice will be seven.

In his 1926 work Truth and Probability, Ramsey notes

that “...the general difference of opinion between statisti-

cians who for the most part adopt the frequency theory of

probability and logicians who mostly reject it renders it

likely that the two schools are really discussing different

things....” (p. 157). We can now see that Ramsey’s obser-

vation is correct: “subjective probabilities” have to do with

uncertainties that are not probabilistic.

In the following section we examine exactly what they

have to do with those uncertainties.

“SUBJECTIVE PROBABILITIES” ARE APPRAISALS

We have seen that “subjective probability” language cannot

be talking about the same concept as objective probability

language. What then is it talking about?

Pragmatic Assurance of Success

The paradigm case of human behavior is that a person rec-

ognizes that behavior B is called for and engages in it, and

the outcome of B is the desired state of affairs. Pace Aristo-

tle, I need milk for my cereal; there is none; I go to the store

and buy it; I come home; I put some milk on my cereal.

There is no uncertainty, nothing I am unsure of, and no

probability, whether objective or “subjective.” A great deal

of ordinary life and a great deal of economic behavior,

including ﬁnancial behavior, is of this sort—buying grocer-

ies, dining out, preparing dinner, teaching a class (including

answering interesting, not previously encountered student

questions), conducting a behavioral economics experiment,

going to a basketball game, celebrating an anniversary, and

so forth—almost ad inﬁnitum. In these situations, the indi-

vidual has what Ossorio [1981] terms pragmatic assurance

of success, which means that engaging in B results in the

intended state of affairs and no other behavior is called for

to ensure that W DA.

It is important to realize that “assurance of success” does

not refer to some sort of absolute guarantee, or that Proba-

bility(X) D1.0. “Pragmatic assurance,” of the success of B

or that X is the case, means only that P is prepared to do B,

or act on X, in one of the ordinary ways of doing B and

with no further actions to ensure the success of B. Saying,

“There is no uncertainty,” should not be taken as saying, “It

is guaranteed.”

When There Is No Pragmatic Assurance of Success

While the paradigm case is 1) to see that behavior B is

called for and 2) to do it, there is of course a large and

important class of behaviors in which there is uncertainty

about one or the other, or both of these. One may be uncer-

tain whether to buy a car or take vacation, whether to enroll

in college or get a job; one can engage in a series of actions

to checkmate an opponent, increase the value of an invest-

ment portfolio, win a hand of poker, launch an important

new product, etc., but each of these are courses of action:

one cannot simply do them and be assured of success, as

with buying milk. Games, including gambling games, are a

domain in which players routinely engage in courses of

action, and indeed this appears to be a sine qua non of

games.

Appraisals

We noted above that one may be uncertain about one’s cir-

cumstances, reasons, relative weights to give the reasons,

and each of the aspects of the possible behaviors. Each of

those items is a state of affairs. To say, “X is uncertain,” is

to say, “X cannot be counted on,” that is, “Acting on X has

no pragmatic assurance of success.” It is, in other words, an

appraisal of X: a re-description of X with tautological

implications for action (Ossorio [1990]). By “tautological,”

we mean that to re-describe X as Y is to say that Y consti-

tutes reason to act in certain ways, and not in others. To

say, “Driving drunk is dangerous,” is to say is to say that

one has reason to do some things and not do others; in

exactly the same way, to say, “Whether Greece will default

236 JEFFREY AND PUTMAN

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on its sovereign debt is uncertain,” is to say that one has

reason to engage in certain actions and not others with

respect Greek default. Similarly, to say one is uncertain

whether the circumstances are as perceived is to say,

“Certain ways of acting on these circumstances are called

for, and others are not.”

Danger is of course not an all-or-nothing concept, and

thus we refer to “mildly dangerous,” “very dangerous,”

etc., situations, calling for different actions, such as imme-

diate escape, casual re-evaluation, taking mild precautions,

and taking extreme precautions. The same holds for other

kinds of appraisals (e.g., enjoyable, unethical, wise), and in

particular it holds for uncertainty. “Probable,” “unlikely,”

“barely conceivable but not impossible,” etc., are distinct

uncertainty appraisals.

The answer to the question posed at the beginning of this

section is therefore:

Subjective probability language is language for expressing

uncertainty appraisals, that is, re-descriptions of facts, in

terms of nonprobabilistic uncertainty, carrying tautological

implications for action.

In other words, “X is probable,” “I believe X will

occur,” “X is unlikely,” “X is barely conceivable but not

impossible,” etc., are ways of stating uncertainty appraisals

of X, that is, re-descriptions of X that imply reasons to act

in certain ways in light of the uncertainty.

Appraisal is not to be confused with assessment. An

assessment is an evaluation or analysis of something in

order to determine its characteristics, implications, or other

related facts. One may assess characteristics of a situation

or some aspect of it, qualitatively or quantitatively; one

may derive other facts, empirically or logically; certain

kinds of facts permit assessment of probability of occur-

rence. Appraisals, in contrast, are a very particular kind of

evaluation: re-descriptions of circumstances as reasons to

do some things and not others.

The customary linguistic forms for expressing uncer-

tainty about the wide range of phenomena that are not prob-

abilistic are not imprecise language for something properly

expressed mathematically; they are customary forms for

stating uncertainty appraisals. “I’m unsure whether do X,”

“He’s not certain what will happen with Greek bonds,”

“I’m not sure whether the milk is spoiled,” and “I’ll move

my pawn, but I’m not sure that will work,” are appraisals of

possible facts, each of which refers, tautologically, so some

set of possible actions. In current usage, it is also common

to use the language of probability, even though the state of

affairs referred to is not probabilistic, and that is the lan-

guage of “subjective probability,” in all its forms: “There’s

a probability of 0.01 that Spain will default on its bonds,”

etc., “P’s degree of belief in X is 0.2,” “I’m 90% sure we

will complete this project on time,” and so forth.

“Subjective probability” language is probabilistic

language for referring to appraisals, not references to a dis-

tinct form or probability.

The particular appraisal constitutes reasons to act in cer-

tain ways and not in others, and the strength of those rea-

sons. The kinds of differences that may be involved are:

Performing one or more of the behaviors of the prac-

tice in a nonstandard manner. For example, a driver is

unsure whether he can make a turn without hitting the

curb, and makes the turn very slowly.

Assessing one or more of the factors about which one

may be uncertain, as enumerated in the previous sec-

tion, before, during, or after the course of action. For

example, an investor is unsure whether to buy an

offering of a company’s bonds, and investigates the

company’s ﬁnancial situation with unusual

thoroughness.

Pausing to assess whether to do a particular version of

the course of action. The frequent advice to persons of

a certain age to assess the status of their retirement

plans, in recognition of the fact that planning for

retirement has no pragmatic assurance of success, is

of this sort.

Pausing to assess whether to change to a different

course of action entirely, as in, “I took a look at my

job prospects with a philosophy degree, and changed

my major to computer science.”

Checking progress and avoiding dangers while engag-

ing in the course of action, including other practices

necessary to do so. The practices involved in testing

software during its development are a paradigm case.

More generally, there is rarely if ever a project in

business or industry for which there is pragmatic

assurance of success, and so in every ﬁrm one ﬁnds

the management practices of project management,

including monitoring and directing subordinates.

“X is likely,” “X is probable,” “X is barely possible,”

etc., are each uncertainty appraisals of X, that is, re-descrip-

tions of X that identify 1) that X is a possible state of

affairs; 2) P cannot count on X, that is, has no pragmatic

assurance of success of acting on X; 3) other behaviors,

which address the speciﬁcs of the uncertainty about acting

on X, are called for; and 4) those other behaviors have par-

ticular priorities for P.

Whereas objective probabilities are made precise by car-

rying out practices to determine more speciﬁc numerical

values, uncertainty appraisals are made precise by identify-

ing the behaviors called for in light of the appraisal and the

relative priorities those behaviors have. “Subjective proba-

bility” language, and uncertainty language more generally,

convey that acting on state of affairs S has no pragmatic

assurance of success. The central question then becomes,

“What behaviors are called for, and what priorities should

those behaviors have?”

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For example, Mandel [2005] reported that in a group

of 135 students at the University of Victoria the median

estimated probability of a terrorist attack within two

months was 0.10 while the median value the probability

of no attack was 0.50. The statements, “P(attack) D

0.10” and “P(no attack) D0.50” are cases of using

probability language to express uncertainty appraisals of

the two states of affairs, “attack” and “no attack.” Stipu-

lating the customary correspondence between numerical

values and verbal characterizations, this means the par-

ticipants, on average, appraised a terrorist attack as

“unlikely,” and appraised having no attack as “maybe-

can’t tell.” (Participants were instructed to express their

“estimates” as decimal values, with no verbal interpreta-

tions, so it cannot be determined whether participants

used the customary correspondence. Thus, we are stipu-

lating these verbal characterizations, for illustrative pur-

poses.) These appraisals tautologically indicate and

contra-indicate various actions, with various relative pri-

orities: changing one’s travel plans, investigating situa-

tions where terror attacks might occur, deciding whether

a location of interest is a terrorist target, and so forth.

(On Sept. 12, 2001, some residents of suburban Chicago

cancelled dentist appointments, having appraised a ter-

rorist attack in their area as highly likely.)

Consider a classic actual gamble, a sports bet. P decides

to bet $20 on the Cubs at 100:1. He does that, instead of

some other behavior with the $20—take the children to

McDonald’s, buy an inexpensive watch, buy his wife a

small present, and so forth. The circumstances include hav-

ing the $20, having other wealth in some amount W, how

his spouse will react to knowing about the bet, his personal

values, etc. Each of these circumstances gives P reasons to

bet or do something else, such as the prudential value of the

$2,000 that may be won, the hedonic value of betting on

the Cubs, or the esthetic (i.e., appropriateness) value of sup-

porting the home team. P’s appraisal of the odds constitutes

reasons to act in various ways, with various relative priori-

ties that reﬂect P’s personal characteristics. For many per-

sons, particularly those in “tight” ﬁnancial circumstances,

the 100:1 odds will result in the person assigning a low pri-

ority to betting the $20. If P said, “In our situation every

dollar counts, and my wife hates me gambling, but even

though the odds were 100:1 I took the bet,” it would call

for explanation. The kinds of explanation available are

either that the man had some other previously unrecognized

reason, or a that he was “just the kind of guy” to take such a

bet in such a circumstance (an attribution of a personality

characteristic, one which most in this culture would con-

sider pathological).

To summarize:

Objective probability refers to a numerical relation-

ship between cardinalities of event sets; “subjective

probability” refers to uncertainty appraisal.

The particular appraisal gives the person reasons to

engage in that behavior and others.

The person’s choice reﬂects the relative weights, or

priorities, of the reasons for that person.

RELATED WORK

Vagueness vs. Incompleteness

Verbal characterizations such as “likely,” “probable,” etc.,

have traditionally been considered vague or ill-deﬁned lan-

guage, to be replaced with numerical values. When talking

about objective probabilities, that approach is correct, but it

is not correct when talking about uncertainty appraisals.

The issue is one of complexity, not vagueness. Verbal iden-

tiﬁcations of appraisals, which are almost always single

words or short phrases, necessarily “encode” a great deal of

information, including all the practices either indicated or

contra-indicated and the relative priority of each practice in

the current context. In addition, practices are in general

complex and may be done in a number of ways, some of

which are consistent with the appraisal and others of which

are not, to varying degrees. All of that information is

“carried” in the brief terms such as “likely,” “probable,”

etc. The language is not vague; it is merely incomplete,

eliding a great deal of information about the connection

between the appraisal and a number of practices.

Degree of Belief

That “subjective probability” or degree of belief refers to

appraisals, and therefore indirectly to indicated or contra-

indicated behaviors, is consistent with Ramsey’s [1926]

characterization of degree of belief as “the extent to which

we are prepared to act on [the belief]” (p. 65). Ramsey

rather neatly disposes of the other interpretation, namely

that degree of belief is some kind of internal strength or

intensity:

We can ... suppose that the degree of a belief is something

perceptible by its owner; for instance that beliefs differ in

the intensity of a feeling by which they are accompanied,

which might be called a belief-feeling or feeling of convic-

tion, and that by the degree of belief we mean the intensity

of this feeling. This view would be very inconvenient, for it

is not easy to ascribe numbers to the intensities of feelings;

but apart from this it seems to me observably false, for the

beliefs which we hold most strongly are often accompanied

by practically no feeling at all; no one feels strongly about

things he takes for granted. (Ramsey [1926], p. 65)

Mathematical Treatments

Based on the observation that degree of belief can only be

deﬁned in terms of action, Ramsey used the idea of betting

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to deﬁne it: P’s degree of belief in X is the lowest odds P

would accept. de Finetti [1937] used the same concept to

axiomatize degree of belief, which, as Ramsey notes,

means the extent to which one is prepared to act on it:

Let us suppose that an individual is obliged to evaluate the

rate pat which he would be ready to exchange the possession

of an arbitrary sum S(positive or negative) dependent on the

occurrence of a given event E, for the possession of the sum

pS; we will say by deﬁnition that this number pis the measure

of the degree of probability attributed by the individual con-

sidered to the event E, or, more simply, that pis the probabil-

ity of E(according to the individual considered; this

speciﬁcation can be implicit if there is no ambiguity)....Your

degree of belief in Eis piff punits of utility is the price at

which you would buy or sell a bet that pays 1 unit of utility if

E, 0 if not E. (de Finetti [1937], p. 62)

The method derives a quantitative measure of how sure a

person is by directly asking, “To what extent are you will-

ing to act on what you take to be the case (the crude form

being, “Put your money where your mouth is”). The classic

sports bet, for example, “I’ll bet you $10 the Cubs will

ﬁnally win the World Series this year,” is an everyday

example. Professional bookies famously determine odds in

exactly this way. However, it is important to keep in mind

what these “odds” are: they are not a calculation based on

samples of a sample space; they are straightforwardly a

ratio of monies received.

Unfortunately, de Finetti’s axioms do not axiomatize the

phenomenon at hand because as noted in the ﬁrst section,

the numerical values violate ﬁnite, that is, “probabilities”

for disjoint events may sum to more or less than one.

ACTORS, OBSERVERS AND CRITICS

In order to develop the practical implications of the uncer-

tainty appraisal formulation, we need to articulate a particu-

lar aspect of the relationship between a person and what

they are doing.

It is a universal fact about persons that what a person

sees, and how they value what they see, depends on the

position from which they are seeing, that is, the role they

occupy. In the role of chess player, a person sees pieces,

conﬁguration, tactics and possible tactics, strategies and

possible strategies, opponent chess characteristics, possible

states of affairs on the board, and so forth, and we do not

wonder that a chess player, playing chess, rarely notices

anything outside what is happening or could happen on the

board. One simply does not see anything outside the

domain corresponding to the role. It is similar to but sub-

stantially more pronounced and stronger than, the widely

known phenomenon of ﬁgure-ground. What hold for chess

players holds equally for baseball players, ﬁnancial

analysts, economists, computer programmers, chief execu-

tive ofﬁcers, and so forth.

It also holds for three other roles, ones that an individual

always has: Actor, Observer, and Critic. Carrying out

actions in the world, including making decisions in the face

of uncertainty, requires three different kinds of tasks: one

must act, one must observe the act and how it is going, and

one must assess or critique the situation so as to be able to

change or correct how things are going as necessary. Act-

ing, observing, and critiquing each involve several tasks,

and require different knowledge and skills, so it is useful to

articulate them in terms of jobs and job descriptions, as

follows:

Actor: In the role of Actor, the individual’s “job” is to

act, to carry out the behavior called for. Doing will be

seen by someone in the observer role as constituting a

choice from among possible behaviors, as depicted in

Figure 1, but that reconstruction is not part of the

Actor’s job description.

Observer-Describer: The individual observes the

behavior and describes it via various concepts.

Critic: The individual assesses the description of the

behavior and gives “feedback” to the actor. (The term

“feedback” in this context originated with Norbert

Weiner, who observed that behavior has the character-

istic of the “feedback loop” in electronics; the term

has since become ubiquitous. Although the feedback

loop is a useful analogy to Actor-Observer-Critic

functioning, it differs in one very important way.

Unlike the operation of a feedback loop, ordinarily an

individual occupies all three roles, and does all three

jobs, simultaneously. An individual acts, observes

their action, and appraises it for corrective action all

at once.)

This distinction is well-known in economics. Moscati

and Tubaro [2009] point out:

...it is the economist who rationalizes the decision maker’s

choices as if they were generated by utility maximization.

Therefore, the utility function and its maximization are in

the economist’s mind rather than in the decision maker’s,

so that the psychology of the latter is not at issue. (p. 1)

In other words, decision makers act; economists make

sense of those actions and decisions.

Homo economicus is a set of observer concepts (self

interest, monetary quantiﬁcation of it, objective probability,

and expected value) and a principle for making sense of

choices. Homo communitatis is a different set of systemati-

cally related Observer concepts. An actor’s behavior con-

forms to the CRJ diagram, but in the role of Actor an

individual does not identify circumstances and their impli-

cations for action, identify what social practice they would

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be engaging in by carrying out some behavior, assess the

signiﬁcance of a behavior, consider their personal charac-

teristics and the priorities each reason should have, and so

forth. Figure 1 is a reconstruction, from the Observer per-

spective, of the factors involved in the individual’s action,

not a depiction of the world as seen from the perspective of

Actor.

The World from Actor and Observer Perspectives

The “job” of the actor is to moment by moment carry out or

continue a behavior (unless the actor recognizes it is no lon-

ger called for). What is relevant to fulﬁlling that “job

description” is the current behavior, possible behaviors,

and anything relevant to one or more of them: reasons for

or against one or more, presence or absence of anything

needed to do one or more, and whether or not anything that

must be so in order to carry out one or more is the case. We

may summarize this by saying that to the Actor, the world

appears as a ﬁeld of action (Ossorio [2006], p. 254).

The Observer’s “job” is to observe and describe. To ful-

ﬁll that job description with respect to behaving persons, an

Observer needs a set of concepts articulating the concepts

of person, behavior, and the real world. The principles of

homo communitatis are such an articulation, allowing an

Observer to re-describe what an Actor sees in terms of cir-

cumstances, reasons, relative priorities of possible behav-

iors, behavior itself being a multifaceted concept. Thus, an

observer watching a person pick up and drink a glass of

water describes it as, “He wanted a drink; he saw the water;

he picked it up and drank it.” The person, when drinking,

recognizes something to drink and drinks it. He does not

see the glass of water, somehow deduce the possibility of

drinking it, and enact that action. Nor does he recognize

each of the parameters of Intentional Action (Principle 2)

and then in some fashion deduce that the thing to do is

drink.

Actions take place in the real world. Looking at that

whole state of affairs, Actor-acting-in-world, we can

observe that there are two kinds of facts, facts about the

actor and the rest. Facts about the actor are aspects of the

actor in their position in their world; it is “how they are” at

that moment. The rest, the externals, are what the Actor, to

act, must ﬁnd out about by observation. Observers have no

access to actor facts, and so must, if they need to make

sense of an action, construct formulations using concepts

such as states of affairs, intentional and deliberate action,

states of affairs, and priorities.

Appraisals, as states of affairs, are parts of the world,

and like everything else look different from Actor and

Observer perspectives. Consider a familiar example: person

P asks friend Q for a favor; Q does the favor. An Observer

describes this interaction as 1) P and Q have the relation-

ship “friend”; 2) having that relationship is grounds for Q

to do the favor requested; 3) doing the favor has sufﬁciently

high priority for Q, in this case, that he did it. From the per-

spective of Actor, though, things look very different. As an

Actor, Q knows his reasons and how strongly they count for

him, sees actions and possible actions, and does the one

called for. Where Observers see circumstances, appraisals

of them, and priorities, Actors see what action is called for.

Now let us apply these principles to our topic of interest,

“subjective probability.” P observes that X (e.g., Greek

bond default) is “unlikely.” “Unlikely” is an appraisal of X

by P. That appraisal of X constitutes grounds for engaging

in various actions (e.g., sell euros, buy Greek bonds, moni-

tor the stock much more closely than they would otherwise)

and the relative priorities of those actions for him. In the

role of Actor, though, P sees possible actions, knows the

reasons and how much they count for him, and acts. If after

his ﬁrst observation P continues to act as an Observer, he

may construct the elaboration of the state of affairs of the

unlikely-but-possible event of Greek bond default just out-

lined. However, he may choose not continue as Observer,

and simply act. Asked “Why did you buy Greek bonds?” P

may reconstruct his action in term of circumstances, rea-

sons, and priorities, but he is then giving an account, as an

Observer, of what he did as an Actor, not reporting what

happened at the time of acting.

If P responds with, “Seemed like the thing to do” or “I

felt like it,” he is not voicing ignorance; he is refusing to

engage in the reconstruction. “I knew what to do, but I

didn’t know why,” “I couldn’t tell you why I did that,” “I

don’t know why, but I’m sure,” and the famous, “I had a

feeling” are all language for expressing knowing what to do

but not being able to articulate the reasons. They are Actor

language, that is, ways of talking about the world as seen

by the Actor. Probably the most famous of these is

“intuition”: the ability to discern, without being able to

articulate reasons.

The fourth section discusses new methods for decision

analysis, including ﬁnancial decisions, based on the refor-

mulation of “subjective probability” as uncertainty

appraisal. Several of these technique rely on the concept of

Actor perspective for dealing with decision making under

uncertainty. Since the Actor’s world looks very unlike the

Observer/Critic’s, the new methods in many cases bear lit-

tle resemblance to traditional decision-theoretic methods. It

is therefore signiﬁcant that the effectiveness of these meth-

ods has been repeatedly demonstrated via use in actual

business decisions.

IMPLICATIONS AND APPLICATIONS

The uncertainty appraisal reformulation has two kinds of

implications for research and professional practice:

addressing confusion and misunderstandings caused by

treating the objective and subjective as two sides of the

probability coin, and new methods for precise speciﬁcation

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and use of uncertainty appraisals. Since actual probabilities

are reﬁned by improving data and calculating a numerical

value, while uncertainty appraisals are reﬁned by improving

the speciﬁcation of actions potentially called for, reasons

for or against each, and relative priorities, integrating prob-

abilities and uncertainty appraisals requires integrating two

very different kinds of information, and therefore very dif-

ferent methods than simply doing an expected value calcu-

lation. (It is our view that adopting the term “uncertainty

appraisal” and avoiding the traditional term “subjective

probability” would be a valuable initial move on the part of

researchers and professionals who must communicate about

such phenomena, both to other professional and to lay

persons.)

Correcting Mistakes

Talking about and treating probability and uncertainty

appraisals as though they were versions of the same thing

has caused difﬁculties, sometimes serious ones, virtually

everywhere that the two concepts are involved, which is to

say virtually everywhere that persons make decisions under

uncertainty. The difﬁculties range from relatively simple

misunderstandings that are easily cleared up with a short

discussion to deeply embedded concepts and research prac-

tices yielding spurious conclusions and ﬂawed practices.

One kind of problem of this sort is failure to carefully

distinguish between estimating an (objective) probability

and clarifying an appraisal. An excellent example of this

error is the following:

There are situations in which people assess ... the probabil-

ity of an event by the ease with which instances ... can be

brought to mind. For example, one may assess the risk of

heart attack among middle-aged people by recalling such

occurrences among one’s acquaintances. Similarly, one

may evaluate the probability that a given business venture

may fail by imagining various difﬁculties it could encoun-

ter. (Tversky and Kahneman [1974], p. 1127)

Risk of heart attack among middle-aged people is a

probabilistic fact; the sample set is middle-aged people,

and the subset is those who will have a heart attack during

some speciﬁed period. Actual data can be gathered, and the

estimate compared to the result. By contrast, the probability

that this speciﬁc individual will have a heart attack, or the

probability that a given business venture may fail, are not a

probabilities at all, because there is no event set: the ques-

tion involves a speciﬁc individual, not a collection to be

sampled. These are cases of using probability language to

give an appraisal of the possible success of the business

venture. While there is a sample space of business ventures,

or business ventures having various characteristics, the

question—the central question in all decisions to buy or sell

a corporate bond—is whether the particular business

venture will fail, not whether some venture will. The

authors’ point, that persons often estimate poorly, is valid

and important, but they have illustrated it by citing entirely

different kinds of assessment, the ﬁrst a case of (actual)

probability and the second an uncertainty appraisal. What

the two assessments have in common is that they both

involve asking persons to identify facts or possible facts

(heart attacks or business difﬁculties), and the authors cor-

rectly note that that task is often done poorly. Unfortu-

nately, the authors’ well-taken point obscures the fact that

the estimates are of entirely different thing, numerical facts

and appraisals.

The ﬁrst section discussed a second problem, one exhib-

ited by a good deal of the foundational research in probabil-

ity fallacies and biases. This is the assumption that if an

experimenter asks a question using probability language,

such as “probable,” “most likely,” etc., subjects will inter-

pret the question as a probability estimation task and do

some kind of probability calculation on some sample space.

For example, that persons use representativeness is beyond

question; that it is a probability bias, as Tversky and Kahne-

man [1974] characterize it, is based on the assumption that

subjects take “What is the probability that Steve is a

librarian?” to be a probability question rather than, for

example, “Which occupation does Steve most resemble?”

There are similar problems with several other purported

errors in probability computations, such as the conjunction

fallacy (Tversky and Kahneman [1983]), availability bias,

and base rate fallacy.

Recommendations

Conﬂating measurement of actual probability, estimation of

actual probability, and giving uncertainty appraisals (n

“subjective probability”) is improper scientiﬁc procedure.

It has resulted in a great deal of confusion among research-

ers and practitioners, and signiﬁcantly impacted lay persons

in economics and in all ﬁelds dealing with risk and decision

under uncertainty, ranging from medical decision making

(Gigerenzer [2012]) to national intelligence estimates (Cen-

tral Intelligence Agency [1999]) to civil engineering (U.S.

Department of the Interior [2011]). In our view corrective

action is called for, at a minimum including:

Insistence by journal editors and reviewers on clear

identiﬁcation of which task—counting, estimation of

a count, or uncertainty appraisal—is the focus of an

experiment.

Insistence by journal editors and reviewers on speciﬁ-

cation of measures taken to verify that questions

couched in the language of objective probability are

actually interpreted by subjects as probability ques-

tions. In the “Linda” experiment, a favorite example

of many authors writing about heuristics and biases,

there are at least ﬁve interpretations of the question

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“Which of the statements [about Linda] is most like-

ly?” in addition to the probabilistic one assumed (Jef-

frey [2010]). Failure to take such measures is failure

to control a crucial variable, an elementary experi-

mental error.

Insistence by journal editors and reviewers that an

objective probability description of a “subjective

probability” question be accompanied by a speciﬁca-

tion of the sample space and the repeated trials, and

the justiﬁcation for assuming that the space is actually

being used by the subjects, that is, is a distinction on

which they are acting. In our view such speciﬁcations

are as fundamental as any other aspect of experimen-

tal procedure description, such as identiﬁcation of the

source of experimental subjects or statistical methods

used.

The above two items should be adopted as standards

to be met by all Ph.D. dissertation work.

New Methods

The elaboration of the principles of homo communitatis

above, particularly the Actor-Observer-Critic distinction,

yields a number of practical methods for addressing deci-

sions in the face of uncertainty, several of which have been

extensively tested in practice over the past three decades.

Three of these are presented below.

Pragmatic Evaluation (Putman [1980])

The traditional approach to decision making under

uncertainty, on which virtually all traditional methods are

based, is what might appropriately be called the “truth-

seeking” approach: evaluate the situation to produce a clear

picture, and when we have enough data, the choice will be

clear. The problem with this approach is that, as any num-

ber of sociologists, philosophers, anthropologists, and psy-

chologists have pointed out, data virtually never “speaks

for itself.” To make matters worse, as Gigerenzer [1994]

points out, in actual practice a person is looking at a partic-

ular representation of the data, and the representation

greatly affects whether the person can understand and act

on the data. Any evaluation, even the most systematic and

comprehensive, produces data that is a picture of the situa-

tion, and the picture cannot direct the decision.

Truth-seeking approaches to decision making proceed

by ﬁnding the data, assessing its implications, and then

seeking the correct relative weighting of the implications.

Pragmatic evaluation, by contrast, proceeds in the reverse

manner. It corresponds to going right-to-left on the CRJ

diagram (Figure 1), rather than the customary left-to-right:

1. An evaluation is always done for one purpose: to

enable an individual (or individuals) to make a

(behavioral) choice. Therefore begin by identifying

1) Who is making the choice, and 2) What choice are

they making? That choice will always be whether to

do Y (perhaps in lieu of doing Z, W, etc.): Do I invest

in security X? Do I increase my holdings in large-cap

mutual funds? Do I sell my Greek bonds? Do I rec-

ommend that a client re-balance his/her portfolio?

2. Individuals vary enormously in terms of what kind of

information they want, and in what form, for the par-

ticular choice they need to make. In deciding whether

to release a new version of a major software project,

for example, one manager may want extensive reli-

ability reports and analyses of the mathematical char-

acteristics of the history of the reliability data, while

another may value only the professional judgments

of three trusted subordinates. Having determined that

the evaluation of the situation is being done to enable

person P to decide whether to do Y, the second step

is to identify what kind of information “counts” for P

for this choice, that is, constitutes a reason, with a

particular P to act in one way or another.

“Information” here means both the state of affairs

that implies action and the representation of that

information. It is important to recognize that the

information that counts for P may be much broader

than the particular thing being evaluated. It may

include relationships between P and others in his/her

organization, P’s standing in his/her organization,

relationships between P’s organization and other

organizations, such as their customers, and so forth.

For example, a legal ﬁrm requests that a litigation

support provider do a pilot study evaluation of new

technology, but in deciding whether to hire the pro-

vider bases their decision in part on their legal cli-

ents’ reaction to the use of new technology in their

case.

This is perhaps the single greatest problem faced

by practitioners of behavioral ﬁnance. It is crucial to

know what kind of information counts for the deci-

sion maker, for this decision, and that may be quite

difﬁcult to ﬁnd out. It is also one of the common

sources of error in decision analysis, resulting in

inappropriate attributions of overoptimism bias and

sunk cost fallacy when an executive persists in a

course of action that does not succeed.

3. Having identiﬁed what P needs to know, and the form

in which it needs to be presented to him or her, the

evaluator (or decision maker) is now in the position

to ask, “What data—what facts and circumstances—

need to be gathered, and how does that data need to

be processed, to determine the information P needs?”

A number of practical considerations that must be

addressed to prepare for and carry out the data-gath-

ering and analysis, including cost, requisite permis-

sions, any necessary collaboration or cooperation,

etc., are addressed in this ﬁnal step, to ensure the

242 JEFFREY AND PUTMAN

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practicality of gathering and presenting to P the infor-

mation he/she needs for this purpose, that is, deciding

whether to do Y.

Complete Situation Analysis

The traditional approach of assigning “subjective” prob-

abilities numerical values and then calculating expected

values has the advantage that it neatly uses the same frame-

work for both actual and “subjective” probabilities and

appears to offer a straightforward way to approach complex

decisions. The major disadvantage is that as we have seen

“subjective” probabilities are not probabilities at all, and as

a result it is entirely unclear what the “expected values”

mean, or indeed whether they mean anything at all. This is

not “mere semantics.” It means that the numbers used to

represent “subjective probabilities” violate the deﬁnition of

a probability measure, and therefore the calculation does

not in fact produce expected values. Speciﬁcally, numbers

attached to distinct events of a set of possible outcomes

may add to more than 1.0 (Macchi [1999]) or less than 1.0

(Tversky and Koehler [1994]). Mandel [2005], for example,

found that in a group of 135 students at the University of

Victoria the median estimated probability of a terrorist

attack within two months was 0.10, while the median value

the probability of no attack was 0.50.

Tversky and Koehler [1994] state,

The major conclusion of the present research is that subjec-

tive probability, or degree of belief, is nonextensional and

hence nonmeasurable in the sense that alternative partitions

of the space [of possibilities] can yield different judgment.

...The evidence reported here and elsewhere indicates that

both qualitative and quantitative assessments of uncertainty

are not carried out in a logically coherent fashion, and one

might be tempted to conclude that they should not be car-

ried out at all. However, ...in general, there are no alterna-

tive procedures for assessing uncertainty.

They conclude,

...judgments of uncertainty ... play an essential role in

people’s deliberations and decisions. The question of how

to improve their quality ... poses a major challenge to theo-

rists and practitioners alike. (p. 565)

A relatively recent approach to the problem is the one

advocated by Gigerenzer [2005, 1994]. Health care pro-

viders frequently face a different form of the uncertainty-

relationship question: “What are my chances?” Similar

questions arise in all ﬁelds in which there is uncertainty:

“What are the chances this dam will fail?” or “What are the

chances this stock will go up?” and so forth. They are

uncertainty appraisal, not probability, questions because

they are single events; there is no sample space and there-

fore no probability.

Gigerenzer’s recommended approach is to respond to a

“single-event probability” question with a frequency

answer, for example, “Of 100 patients like you, 10 will

recover.” Frequency answers can always be given and they

are well-understood by professionals and lay-persons

(Gigerenzer [1994]). Unfortunately, the frequency-answer

approach does not address the challenge posed by Tversky

and Koehler, because a frequency response is not an answer

to the question asked. “What are my chances” is a question

about an individual; “What are the chances of someone like

me” is a question about a group. Giving frequency answers

is a method for changing the subject, not answering the

question.

Judgments of uncertainty matter because of their role in

decisions. The call for improving the quality of judgments

of uncertainty is a call for a better method for making deci-

sions involving actual and “subjective” probabilities, that

is, decisions involving both probabilistic facts and uncer-

tainty appraisals. Complete Situation Analysis addresses

that need.

The “presenting question” in Pragmatic Evaluation is,

“What are the facts,” and the ﬁrst step is to change that

question to, “Who is making what behavioral choice?”

With “subjective” or single-event probabilities the “who” is

the questioner, and the initial question is, “What should I

do,” or, more completely stated, “What should I/we do, in

light of these circumstances and these uncertainty

appraisals?”

Accordingly, we proceed in two phases, essentially

separating uncertainties from probabilities. In Phase 1,

after specifying the behavioral choice, the decision

maker identiﬁes the signiﬁcance of each alternative

action, incorporating all the factors unique to them and

their speciﬁc circumstances, including the uncertainty

appraisals (i.e., the factors the individual has “a degree

of belief” in). The result is a set of pragmatically com-

plete “Complete Situation” descriptions, each of which

identiﬁes the impact of each behavior in all the ways

that matter to the individual. (The point of the word

“complete” here is to emphasize the breadth of the out-

come-signiﬁcance analysis involved.) In Phase 2, the

actual probabilities are incorporated, thereby associat-

ing the probabilities with the Complete Situations, e.g.,

“20% chance of CS

and an 80% chance of CS

.”

Recalling that the core of the difﬁculty here is the dis-

tinction between “What are the chances of someone

just like me?” and “What are my chances?” Phase 1

builds an event set that takes into account all the rele-

vant factors unique to the individual and all the factors

about which they are uncertain (factors that have cus-

tomarily, and as we have seen, misleadingly been

described as having associated “subjective proba-

bilities”). Phase 2 applies actual probabilities to the

events in that set.

The method is:

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1. Specify the behavioral choice to be made, including

speciﬁcation of the actor or actors involved.

2. Identify the actually possible outcomes of each

choice.

3. Expand the descriptions of each action.

4. Associate the (actual) probabilities with each Com-

plete Situation.

5. Decide.

To elaborate the method a bit:

1. Specify the behavioral choice to be made, including

the actor. (Including speciﬁcation of the actor is a

pragmatic, not logical, necessity. The actor is known.

But the method is to be carried out by the person(s)

making the decision. An actor will frequently give

different answers to “Should I do this?” than they

will to “Should this be done?”)

2. Identify the actually possible outcomes of each

choice. The possible outcomes are the ones the

decision maker considers the relevant

possibilities.

3. Expand the descriptions of each action. The result of

these ﬁrst two steps is a list of names of actions and

possible outcomes. The crucial next step is to expand

the descriptions of each action to include:

a. The process involved in the action and any

facts speciﬁcally related to the process, such

as cost, time, other events that may occur dur-

ing the process, etc.

b. The signiﬁcance of each outcome, including

1) the larger practices the actor is doing by

doing each alternative action and 2) the

impact of each possible outcome on each

state of affairs of importance to the actor.

Those states of affairs will include effects on

other persons with which the individual has a

relationship that matters to them, choice prin-

ciples of any community the person is part

of, and, very importantly, the individual’s

place in those communities, e.g., their family,

their company, their church, etc. This speciﬁ-

cally includes the individual’s concept of

“what kind of person he/she is,” that is, self-

concept.

4. Associate the (actual) probabilities with each Com-

plete Situation: for each expanded actionCoutcomes,

ask: “What is the probability of this happening?”

5. Decide.

We illustrate with two examples. We begin with a health

care example, a decision widely recognized as involving

both actual probabilities and nonprobabilistic uncertainties,

that is, uncertainty appraisals. Consider a patient with a

diagnosed cancer whose doctor has recommended a course

of chemotherapy. The patient asks, “What are my

chances?”

1. The behavioral choice: do I undergo chemotherapy?

2. Actually possible outcomes:

a. Undergo chemo and survive.

b. Undergo chemo and live 6 months longer.

c. Undergo chemo and die within 2 years

d. Forgo chemo and die within 2 years.

e. Forgo chemo and recover.

(A different individual might distinguish dif-

ferent possible outcomes, e.g., living 3 months,

living 6 months, living one year, and recovery.)

3. Expand outcomes to Complete Situations:

a. Undergoing chemo and recovery means CS

Months of very unpleasant sickness, very low life

quality and inability to carry out normal duties in my

family and work.

I’m afﬁrming my self-image as a ﬁghter.

My spouse sees I did all I possibly could.

My spouse will see me suffering during the treatment.

I’ll be able to ﬁnish the research project I’m working

on, which means a lot to me.

I get to attend my daughter’s wedding in 10 months.

I may see grandchildren.

b. Undergoing chemo and live 6 months longer

means CS

Months of very unpleasant sickness, very low life

quality and inability to carry out normal duties in my

family and work.

I’m afﬁrming my self-image as a ﬁghter.

My spouse sees I did all I possibly could.

My spouse will see me suffering during the treatment.

I’ll be able to ﬁnish the research project I’m working

on, which means a lot to me.

c. Undergo chemo and die within 2 years means

Months of very unpleasant sickness, very low life

quality and inability to carry out normal duties in my

family and work.

I’m afﬁrming my self-image as a ﬁghter.

My spouse sees I did all I possibly could.

My spouse will see me suffering during the

treatment.

d. Forgoing chemo and dying in 2 years means

A 2-year decline.

Much better time with my family during the two

years.

I’ll be able to ﬁnish a research project that is important

to me.

I’ll have time to make peace with my passing.

I’m doing something that conﬂicts with my image of

myself as a ﬁghter.

My spouse will not see me suffering until the end.

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I’ll be able to ﬁnish the research project I’m working

on, which means a lot to me.

I get to attend my daughter’s wedding in 10 months.

e. e.

Forgoing chemo and recovery means CS

Moderate sickness and disability for 6 months.

I’ll be able to ﬁnish a research project that is important

to me.

Afﬁrms my self-image as a uniquely fortunate person.

I’ll be able to continue my life and all that implies: ﬁn-

ishing my research project, attending my daughter’s

wedding in 10 months, perhaps having grandchildren,

etc.

Relevant facts include: 1) I am much healthier than

the average person, 2) I have a history of medical

treatments being successful, and 3) I see myself as a

lucky person—things generally turn out well for me.

(We have deliberately presented here a mixture of the

kinds of factors typical of such a situation. two are

“objective,” empirical, facts; the third is a typical

expression of self-concept.)

4. Apply known statistics for survival rates for this can-

cer and this treatment regime to these Complete Sit-

uations, for example: p(CS

)D0.60; p(CS

)D0.30;

p(CS

)D0.10; p(CS

)D0.98; p(CS

)D0.02.

5. Decide.

Step 3 is the point at which the particulars of the situa-

tion, including the individual’s values, their relationships,

their “place” in their life and the impact on that place and

what they care about of the possible actions is taken into

account. Persons do not make decisions based simply on

outcome, a fact discussed extensively by Jeffrey and Put-

man [2013], and the immediate-outcome-only picture of a

decision situation omits most of what matters to an individ-

ual. In this step these other factors are re-incorporated. An

investor is not asking, “What is the probability that a stock

of this kind will go up 10% over the next 6 months?” out of

intellectual or academic interest; they are asking, “What is

the probability that this stock will go up 10% over the next

6 months,” and what they are doing by asking that question

is asking, “Do I invest this amount of money in this stock,

given my life circumstances, including but not limited to

the ﬁnancial ones?”

This step is an articulation of the impact of each out-

come on the individual, from the Actor’s point of view

(which is why we have stated the signiﬁcance of each out-

come in the ﬁrst person. Actor statements are ﬁrst-person).

The circumstances and values involved in those impacts

are, as illustrated in the example, highly speciﬁc to both the

decision maker and the facts of the situation. For example,

most decision makers in Western culture will eschew bet-

ting the family fortune on a 100:1 shot, but some, such as

persons whose self-image is, “That’s how it is for most, but

I’m a lucky guy,” or, “I’m the kind of guy who always goes

for it!” So it is with the person who agrees to the 1 in 100

chance of success of a particular treatment, or a 1 in 100

chance of their investment behaving in a certain way. A

particular uncertainty appraisal (“likely,” “barely possible,”

etc.) is, to the Actor, reason, with a relative priority with

respect to other reasons, to do X. That priority depends on

the decision maker’s personal characteristics and other cir-

cumstances, including cultural choice principles. If the

decision is an organizational one, the circumstances include

the organization’s choice principles. “X a long shot” is an

appraisal of X. To some, that state of affairs constitutes rea-

son to not do X; to others, it is the opposite.

Complete Situation Analysis is explicitly descriptive,

rather than prescriptive. Current standard practice is to attri-

bute acting in certain ways in the face of uncertain out-

comes to various cognitive errors, such as over-optimism

bias (Shefrin [2000]). While that may sometimes be the

case, it may equally reﬂect a particular personal characteris-

tic on the part of the decision maker, such as extraordinary

determination to succeed. It would not seem appropriate,

for example, to ascribe Eisenhower’s decision to proceed

with the D-Day invasion to a cognitive error. By contrast,

Complete Situation Analysis immediately clariﬁes

Eisenhower’s decision, the one shown clearly in his D-Day

Orders (Eisenhower [n.d.]): “the elimination of Nazi

tyranny.”

Now let us apply Complete Situation Analysis to a

ﬁnance decision, one involving, as in health care, probabi-

listic and non-probabilistic uncertainties. A bond trader

asks, “What are the chances that Company X, whose bonds

are rated BBBC, will go bankrupt in 6 months?” There are

well-known default statistics, but the trader is asking, “I

know the statistics, but I know how this company does busi-

ness and its ﬁnancials. What is its probability of default?”

The ﬁrst step is to recognize that the presenting question is

in the service of deciding, “Do I invest amount A in these

bonds?” Thus, we have:

1. The behavioral choice: do I invest amount A in Com-

pany X’s bonds?

2. Actually possible outcomes:

a. Invest and after 6 months bond price has

increased ppercent.

b. Invest and after 6 months X is bankrupt.

c. Forgo investment in X and after 6 months it has

increased ppercent.

d. Forgo investment in X and after 6 months X is

bankrupt.

3. Expanded outcomes:

a. I have afﬁrmed my image of myself as an a smart,

decisive trader; company X has performed as I

anticipated based on my knowledge of it; I have

made a proﬁt on X; my portfolio is increased in

value; my standing among my peers is improved,

though this is not very important to me; I am

SUBJECTIVE PROBABILITY IN BEHAVIORAL ECONOMICS AND FINANCE 245

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acting in accord with my organization’s culture.

In the cancer treatment example, the impor-

tance of including aspects of the situation related

to the individual’s character and values is obvi-

ous. It is perhaps not so obvious that one must

explicitly identify that range of facts in all deci-

sions, including ﬁnancial ones, perhaps because

of a belief that that decisions should be based

purely on “objective” (i.e., not personal) factors,

such as the ﬁnancial aspects. The ﬁnal item here

illustrates that the character of the speciﬁc per-

son is always a necessary part of identifying the

expanded outcomes. For many, the last statement

would be incorrect—standing among peers is

quite important to them. Equally important is

that people often not skilled at recognizing this

kind of fact about themselves, or have strong rea-

sons to not recognize them. For example, an

individual who has a strong belief they should

not be concerned what their peers think, or is

working in an organization that puts a high prior-

ity on assertiveness and independence, is

unlikely to recognize it when they do in fact

care. As a result, consultation with colleagues or

trusted friends can be very valuable in identify-

ing expanded outcomes. “Know thyself” is the

common recommendation, but it one that people

often require assistance to follow.

In the case of institutional investors, the

impact of organizational culture or choice princi-

ples on investor decisions (Jeffrey and Putman

[2013]) must always be taken into account. That

organizations vary along dimensions such as

aggressiveness/caution, degree of acceptable

risk, individualism/collaborativeness, etc., and

that these principles affect individual choices, is

universally recognized. These principles are as

much a part of the complete situation as the

ﬁnancials of prospective investment. Crucially,

“organization” refers to the immediate cohesive

work group the investor is operating as a mem-

ber of; this may or may not be the entire ﬁrm.

Differences in principles between different divi-

sions, even different supervisory groups, are

well known.

b. Company X has performed contrary to what I

expected, based on my knowledge of it; I am

less sure of my image of myself as an a smart,

decisive trader; the portfolio I manage has lost

value; my manager has some question about my

business judgment, though this is not very

important because I trust him to see the larger

picture; though it did not work out, this kind of

risk is expected of someone in my organization.

c. I have acted contrary to my image of myself as

an a smart, decisive trader; I see that I could

have made a proﬁt and I regret it; I have amount

A to invest in other companies; I have forgone

an investment I believe would have paid off, and

I really hate that; I am somewhat more deter-

mined to follow my own judgment next time.

d. I have acted contrary to my image of myself as

an a smart, decisive trader; I see that I would

have lost money and know I “dodged a bullet”;

I have amount A to invest in other companies; I

have foregone an investment I believe would

have paid off; I am somewhat less conﬁdent of

my ability to assess the ﬁnancial health of a

company; my manager sees me as having wisely

refrained from investing in X, and I value that,

though it does not carry huge weight for me.

4. Apply known statistics for ﬁnancial performance of

this kind of company to these Complete Situations: p

(CS

)D0.30; p(CS

)D0.70; p(CS

)D0.30; p(CS

)

D0.70.

5. Decide.

As in the previous example, the particulars elaborated in

Step 3 depend strongly on the individual, manager, and

organization. “Psychological” factors such as effect on self-

conﬁdence, regret or relief, and manager’s assessment are

included in this example because they are all universally

recognized as factors that affect ﬁnancial decisions. As dis-

cussed in Jeffrey and Putman [2013], any description of the

decision that omits them is seriously deﬁcient. “Degree of

belief” is an uncertainty appraisal; how one acts on those

appraisals in the presence of multiple reasons to act one

way or another is intimately related to the personality char-

acteristic of “decisiveness”; having the appropriate balance

of caution and decisiveness is an important part of any

adult’s self-concept and of how others in their organization

see them; and ﬁnally, “appropriate” means, “in accordance

with the individual’s values” and “in accordance with our

company’s choice principles,” in the cases of how an indi-

vidual sees themselves and how others see them,

respectively.

Experience with the Complete Situation Analysis

method has shown that its success requires inclusion of the

actor in the speciﬁcation of the behavioral choice in Step 1.

Omitting the pronoun in the sentence, converting “Do I

invest?” into “Whether to invest,” is particularly easy in a

domain in which decisions are traditionally viewed as

“impersonal” and personal factors as “irrational” inﬂuences

to be avoided. The method is, by design, speciﬁc to the per-

son making the decision and all of their reasons to act one

way or another.

We invite the reader to complete Complete Situation

Analyses for the following cases, with Step 1 as indicated:

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What are the chances of a recession during the next

year?

BDecision: “Do we (the Federal Reserve) raise

interest rates 0.25%?”

What are the chances of war with Iran?

BDecision: “Do I, the President, agree to deploy

Aircraft Carrier Eisenhower Strike Group to the

Persian Gulf?”

What are the chances that a Category 4 hurricane will

strike New Orleans in the next 10 years?

BDecision: “Do we, the U.S. Army Corps of Engi-

neers, request $30 billion to construct a levee sys-

tem for New Orleans capable of withstanding a

direct strike by a Category 4 hurricane?”

The ﬁnal question in this list illustrates the complexity

arising from the inescapable fact that different behavioral

decisions are likely to result in very different analyses of

“the same” question. Consider the following alternatives to

the question here:

BDo we, the United States Congress, allocate $30 bil-

lion to construct a levee system for New Orleans

capable of withstanding a direct strike by a Category

4 hurricane?

BDo I, a United States Senator from Louisiana, vote to

allocate $30 billion to construct a levee system for

New Orleans capable of withstanding a direct strike

by a Category 4 hurricane?

BDo I, a United States Representative from Idaho, vote

to allocate $30 billion to construct a levee system for

New Orleans capable of withstanding a direct strike

by a Category 4 hurricane?

BDo I, a candidate for President of the United States,

advocate the allocation of $30 billion to construct a

levee system for New Orleans capable of withstand-

ing a direct strike by a Category 4 hurricane?”

This kind of issue is present in many, perhaps most,

decisions of substantial signiﬁcance in organizations.

Finding the Pattern in the Data

People are often faced with a large number of observations,

facts, and possible facts with no recognizable pattern, that

is, no single description of what the many states of affairs

“add up to,” and ﬁnance is a prime example. There is an

immense amount of data in the ﬁelds of economics and

ﬁnance; the existence of a distinct ﬁeld, History of Econom-

ics, testiﬁes to the difﬁculty of ﬁnding patterns in that data.

Finding the pattern in the data is of central importance in

any ﬁnance policy decision and in many speciﬁc investment

decisions.

We do not look for a pattern, a summary description, as

an academic or intellectual exercise; rather, we do it as part

of a decision analysis. One common case in which this

arises is the brainstorm, which by design generates a large

number of observations that may have little coherence and

many of which are of little value when later evaluated criti-

cally. The standard method of brainstorming is to generate

ideas and then “distill” them via a voting procedure, in

which each participant is given a number of votes to distrib-

ute among the top nideas. If the brainstorm was done prop-

erly, this distillation procedure is typically very difﬁcult for

participants, because they are forced to allocate votes

among different concepts, multiple aspects of the same con-

cept, sometimes including between small but crucial details

of a concept and the overall concept itself. Consider, for

example, the dilemma facing a participant voting on fea-

tures of a software system for controlling elevators (Gause

and Weinberg [1989]), faced with brainstormed possible

functions including:

Display selected ﬂoors

Show passengers’ ﬂoor selections

“Scream” when passengers are assaulted

Trap assaulters in the elevator

Display directory information

Give directions for delivery people

Giving delivery directions is closely related to display-

ing directory information; displaying ﬂoor selections is

close to displaying passengers’ selections; both assault

measures are exotic and impractical, but “Provide a panic

button” is not, though it is not on the list. Voting among

alternatives provides no way to identify larger functions

that would encompass these speciﬁcs, and forces partici-

pants to allocate their votes among multiple aspects of one

larger one. The usual distillation is unsuitable for ﬁnding

patterns and making decisions.

It would seem natural, if the goal is to ﬁnd the pattern in

the data, to show participants the data and ask, “What is the

pattern?” Experience has shown that that procedure works

poorly. Participants ﬁnd it very difﬁcult to identify and

describe patterns in data, and it is quite rare for it to result

in a pattern that the participants agree on, other than grudg-

ingly. As Ryan and Bernard [2003] put it, “theme identiﬁ-

cation is one of the most fundamental tasks in qualitative

research. It also is one of the most mysterious” (p. 85).

Actor-based Distillation is a different approach, based

on the concept of Actor functioning. It has been has been

used in a wide variety of settings, from individuals formu-

lating psychological case studies to large complex software

organizational planning tasks, and has been found to be a

reliable and effective method for eliciting “the pattern”

from participants.

The procedure is to present the participants with a list of

the observations, facts, data, possibilities, etc., and ask

them to do a simple task: look at the list of what is known

and make simple observations about it and the items on it,

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in the form of simple declarative sentences. (Note the con-

trast with the customary question, “What is the pattern

here?”) Any observation is acceptable, as long as it is in the

form of a simple declarative sentence. (The sentence form

is essential, not a detail. Simple declarative sentences are

the customary English form used to identify overall states

of affairs, rather than re-statements of details. Long, com-

plex sentences identify perhaps-important details of the

overall state of affairs, not the state of affairs itself, and it is

that identiﬁcation that is needed.)

For example, consider once more the case of deciding

whether to purchase the BBBCrated bonds of Company X.

One way to approach that question is to ﬁrst ask, “What is

the pattern of X’s performance in the industry conditions

expected over the next six months?” An answer to that

question is developed by ﬁrst developing a list of facts,

observations, data, and possibilities involving X, its indus-

try, other companies in the industry, related industries, etc.,

that is, anything considered possibly relevant by a group of

participants with expertise relevant in some way to this

company or industry. (One would not expect, for example,

specialists in the paper products industry to have relevant

observations about the construction equipment rental indus-

try, but an individual might have accounting experience

with companies like X.) One then asks the participants to

look at the list of observations—ﬁnancial, accounting, com-

pany-speciﬁc, related-company, industry, related-industry,

macro-economic—and make observations in the form of

simple declarative sentences.

In practice, perhaps the most striking fact about this pro-

cedure is its speed: it typically takes only from 3 to 5 obser-

vations before some participant recognizes the overall

pattern and voices it. Less experienced moderators rou-

tinely report surprise at how quickly a pattern acceptable to

all the participants is articulated.

We have termed this method “Actor-based Distillation”

because it is based on the concept of Actor functioning,

while traditional methods are cases of Observer/Critic func-

tioning. Actor functioning is looking at a situation and act-

ing, without any kind of analysis or re-description, just as

one picks up a glass and drinks. The actor’s world is of a

ﬁeld of action, consisting in this case of the opportunities to

act deﬁned by the moderator’s initial request.

SUMMARY

The facts and concepts that have since the 17th century

been known as “subjective probability” are central to

behavioral economics and ﬁnance. In the last several years,

treating subjective probability as a form of probability has

been shown decisively to fail, both conceptually and mathe-

matically. Conceptually, objective probability is a ratio of

cardinalities of event sets, while what have been called sub-

jective probabilities are appraisals of the uncertainty of

possible facts. Mathematically, assigning numerical values

to subjective probabilities results in values that violate the

axioms of probability: they are sub- or super-additive. It is

no longer viable to think of objective and “subjective”

probabilities as two sides of the same coin, or treat them

that way. In particular, assigning numerical values to sub-

jective probabilities and then calculating expected values

with them is no longer a viable analytic method. The failure

of the concept of subjective probability means a new con-

cept and methods for analyzing and dealing with the uncer-

tainties that cannot be dealt with by assigning them a

number are needed. To address those needs, we have pre-

sented a complete re-formulation of subjective probability

as uncertainty appraisals, re-descriptions of states of affairs

carrying tautological implications for action. Whereas

probabilities are reﬁned by better speciﬁcation and methods

for collecting and using event set numerical data, uncer-

tainty appraisals are reﬁned by better speciﬁcation of the

actions tautologically implied by the appraisal and their rel-

ative priorities. Combining a concept new to economics

and ﬁnance, the difference between the Actor and Observer

perspectives, with the uncertainty appraisal formulation,

new methods for decision analysis have been developed,

including pragmatic (action-oriented) evaluation of data,

actor-based distillation of data into patterns, and Complete

Situation Analysis, which integrates probabilities and

uncertainty appraisals, which replaces the old approach of

calculating expected value on the basis numerical values

that do not represent probabilities.

NOTES

1. A formulation of the concepts of intentional action,

deliberate action, and community in mathematical

formalism may be found in Jeffrey [2010].

2. Poincar

e [1905/1970] noted that “axioms are deﬁni-

tions in disguise”; that is, they articulate the basic

relationships in a mathematical domain. The princi-

ples of homo economicus articulate the domain of

behavior. As Putman discusses in his introduction to

Ossorio [2012], this does not mean that the principles

function as postulates or assumed truths.

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