AND STERILIZATION OF MANAGERIAL-ACCOUNTING :
SOME TENATATIVE CONCLUSIONS
Arthur L. Thomas
Professor of Accounting
McMaster University, Canada
November 10, 1975
note: Arthur L. Thomas received a BA in philosophy from Cornell
University and an MBA and PhD in accounting from Cornell University
and the University of Michigan, respectively. He is the author of
four books and numerous articles on accounting topics. One of the
two books from which this paper stems was honored by the AICPA as
a notable contribution to the accounting literature.
A New York State CPA, Ontario CA, and Fellow in
Accounting Researchers International Association, he is a Professor
of Accounting at McMaster University in Canada and a member of the
editorial board of Abacus.
In Dr. Thomas' lecture, he will discuss
allocations in accounting, which he feels are ubiquitous. Financial
accounting's allocations generally suffer from a logical defect of
incorrigibility that renders them arbitrary. Those of managerial
accounting fall into two classes:
I plan to describe a few central themes of a research project begun
early last summer but unlikely to reach completion before 1977. As the
title indicates, my remarks will be tentative. I emphasize this because
although my role will be to sound positive, it's almost certain that
some of these remarks will prove, in hindsight, to have been mistaken
or, at least, misleading.
- Aggregations of two or more costs to single
cost objects. Whenever each cost is traceable to one (and only
one) cost object, these allocations are legitimate and create
no theoretical difficulties.
- Allocations of individual costs to two or more
cost objects. These are usually incorrigible and illegitimate.
Although such allocations can sometimes be rendered harmless by
a process designated as sterilization, managerial accountants
should cease perpetrating them.
The lecture will conclude with a survey of possible
explanations for the popularity of such arbitrary managerial allocations
To be able to explain a variety of phenomena consistently by a
simple theory is what we struggle to attain in theory construction.
Your role, if you will be so gracious, is to raise objections --
yet to be forgiving if I temporarily persist in what may seem to be
folly. Stanislavsky, the famous director, maintained that to act well
one must first suffer. Similarly, to theorize well one usually must
Throughout what follows, I'll use relatively simple, deterministic
models. For these illustrate the principles to be discussed quite
as well as complex, probabilistic models would, while saving time.
As far as I can tell, relaxing these simplifications would not affect
the conclusions that we'll reach -- though, of course, you're invited
to question this, too. (2)
In a recent article that summarizes research done for the American
Accounting Association, (3)
I claim that defense of allocations made in financial accounting de-pends
on one's being able to calculate the contributions individual inputs
make to the firm's productive processes, that such calculations inevitably
are incorrigible, and that therefore financial accounting's allocations
are incorrigible, too. The technical term incorrigible is one
used by logicians, and here signifies that these calculations and
allocations can neither be verified nor refuted and that, in consequence,
any one is just as good as any other.
These calculations and allocations are incorrigible because most
business inputs interact -- that's to say, they generate more
output working together than they would separately. It can be demonstrated
that in the presence of interaction any attempts to isolate portions
of output as contributions of individual inputs are as meaningless
as attempts, say, to attribute portions of an athlete's success to
his or her individual organs: legs, lungs, etc. The article illustrated
these claims by describing a process of manufacturing sourdough bread.
Anthony replied to a preliminary draft of this article as follows:
I must agree with you that if the problem is to "specify the
individual contributions of the inputs," then it is an incorrigible
problem. If, however, one considers a different, but nevertheless
important, problem, then it is possible to make some reasonable
statements about how to allocate costs, statements that certainly
are better than the assertion that one calculation is just as good
as any other.
This problem is that of measuring the cost of a cost objective.
In this problem, cost measures the amount of resources used for
the cost objective. The resources themselves are physical quantities
-- for example, ounces of flour, hours of labor services, and equipment
used in making the sourdough bread. Cost measures these amounts
in monetary terms so that they can be aggregated. The governing
concept -- which I think is a practical, defensible concept -- is
that the full cost of a cost objective is the sum of its direct
costs plus an equitable share of costs that are common to two or
more cost objectives.
With this concept we can measure quite closely the cost of the
materials and the labor, and we can measure approximately the cost
of the equipment that is applicable to one loaf of bread. If our
purpose is to measure cost so that each customer will pay an equitable
amount for the loaf of bread that he buys, no reasonable person
would argue that the customer who buys the first loaf should pay
the total cost of the equipment, while the customer who buys the
second loaf should pay nothing for the equipment used to make it.
There could, of course, be arguments about the appropriate amount
of depreciation, but it could not be said that each calculation
is as good as any other. (4)
This evening, I'll try to reply to these comments by Anthony and
clarify the circumstances in which allocations of costs to cost objectives
are theoretically legitimate, and explore characteristics that render
certain illegitimate managerial-accounting allocations preferable
to others. During the latter discussion I'll expand a concept of sterilized
allocations, introduced in earlier research, and will explore the
issue of allocations' corrigibility in more detail than was possible
in the article cited. Finally, though it wasn't written as such, this
paper serves as a reply to Anthony's recent article on cost allocation.
ALLOCATIONS OF TRACEABLE COSTS
In this section I'll argue that whenever an input is traceable to an
output allocation of its cost to that output's cost is legitimate and
corrigible. Unfortunately demonstrating this requires introducing a
Let's begin by defining a productive relationship, Y = g(Z1,
Z2, ... Zk, ... Zm) , between a
particular output, Y, and a set of inputs, Z1,
Z2, ... Zk, ... Zm, as one in which
the output would have been physically different (in quantity or kind)
had any of these inputs not been available to the production process
that generated it -- in short, a productive relationship is what a
lay person would call a cause-effect relationship. The detection such
differences requires two things that, for brevity, will be assumed
(since these assumptions don't affect the analysis): first, standards
of what characteristics the output, Y, should possess to be
Y, and second, standards of materiality, for deciding what differences
Traceability to Different Levels
All of a firm's costs are traceable either to waste or to its outputs
at some level of activity aggregation. This can be seen by beginning
at a high level of aggregation, then entertaining progressively more
and more detail. The following discussion, which assumes that the
firm is a manufacturer, is organized in the manner of a flowchart.
Level 1 Productive or waste. First, we might ask of any
cost that the firm has incurred during its lifetime to date: Is
there a productive relationship between the related input and any
of the firm's lifetime-to-date administrative, selling, or factory
Yes: The cost is traceable to the firm's total lifetime-to-date
No: (That's to say, these outputs would have been what they
were without the firm's incurring these costs): These costs should
be classified as waste.
Level 2 Year. If Yes, is there a productive relationship
between the related input and the firm's outputs in any one (and
only one) year?
Yes: The cost is traceable to the firm's total outputs during
that particular year.
No: The cost isn't traceable to this level.
Level 3 Administrative, selling, or factory. If Yes,
is there a productive relationship between the related input and
any one (but only one) of the three types of output (administrative,
selling, or factory)?
Yes: The cost is traceable to that particular kind of output
during that particular year.
No: The cost isn't traceable to this level.
Level 4 Responsibility center. If Yes, is there a
productive relationship between the related input and one (and only
one) department's (or other cost, profit, or investment center's)
production of that particular kind of output during that particular
Yes: The cost is traceable to that responsibility center's
total output during that year.
No: The cost isn't traceable to this level.
Level 5 Specific product or other output. If Yes,
does the center produce only one output of the kind in question?
Or, if not, is there a productive relationship between the related
input and one (but only one) output of the kind in question?
Yes: The cost is traceable to that specific output of that
center during the particular year.
No: The cost isn't traceable to this level.
Level 6 Unit of output. If Yes, is there a productive
relationship between the related input and some one (and only
one) unit of that specific output?
Yes: The cost is traceable to that particular unit.
No: The cost isn't traceable to this level.
Please note that an input's cost often will be traceable to two or
more levels of activity aggregation -- for these levels tend to assume
Waste and Side Effects
In practice, of course, accountants allocate to output various costs
that they should have assigned to waste, and misclassify as waste
other costs whose inputs do enter productive relationships. But such
misclassifications, the fruits of error, management's reluctance to
admit inefficiencies, and practical needs to minimize accounting costs,
don't affect the basic theoretical issues to be considered, and will
be disregarded henceforth.
Similarly, one can argue on theoretical grounds that some
waste is an inevitable concomitant of production and that, therefore,
some waste should be allocated to any output. Here, there's a bona
fide allocation problem (that accountants try to solve intuitively).
Again, I'll disregard it in subsequent discussion because it only
rarely has substantial impact on accountants' calculations.
Finally, when asking whether an input affects one and only
one year, type of output, responsibility center, specific output,
or unit of output, I'll respect accountants' customary materiality
rule and ignore minor, byproduct productive relationships. For example,
if a firm conducts a process that requires a minimum ambient temperature,
its labor input may slightly reduce its power consumption, since the
workers supply bodily heat. But we'll disregard such side effects.
The Corrigibility of Allocations of Traceable Costs
Whenever the cost of one or more units of a particular input is traceable
to output at one of the levels of activity aggregation just described,
at that level the allocation of that cost to output is corrigible.
The simplest reason why this is so is that the allocation can be verified
by simple, unequivocal counting: the units were devoted
to the particular activity, and their cost is known.
We may distinguish two kinds of allocations: physical distributions
of resources (with which, for instance, economists are concerned)
and notional assignments of costs and revenues (with which financial
accounts are concerned). In allocation traceable costs to output,
managerial accountants simply assign them in ways consistent with
the physical distributions of the related inputs. Doing so seems to
offer scarcely any more theoretical difficulties than does preparing
net-quick-assets funds statements -- which, similarly, merely require
counting physical distributions of cash and near-cash. In both cases
the association of dollar values with what's physically distributed
To be sure noncash traceable costs can provide a few allocation ambiguities.
For example, there are situations where labor costs of a particular
batch of product are influenced by other output (or lack of it) and
consequent availability (or lack of availability) of different grades
of labor, necessity (or lack of necessity) to use high-seniority (high-pay
and/or high-efficiency) employees, etc. But, once again, these ambiguities
will rarely be so material that they need concern us.
Nonetheless, physical distributions of inputs and notional assignments
of their costs are different things. With traceable costs, the physical
distribution is unambiguous. But why don't financial accounting's incorrigibility
problems arise for the cost allocations? Here are two reasons:
1. Any allocation of the input's cost to an output to which it
isn't traceable can be refuted on the simple grounds that
there's no productive relationship between the input and that output
-- refuted in exactly the same way that, if I give my son a slice
of bread, I can immediately confute any suggestion that the bread's
cost forms part of the costs of feeding the Prime Minister of New
Zealand. By multiple eliminations, allocation of the input's cost
to the one output with which it does have a productive relationship
is the only disposition to make of that cost that can't be refuted.
2. Financial accounting's incorrigibility problems arise from its
attempts to allocate single figures for total lifetime-to-date revenues
(or cashflows) first to individual years then to multiple inputs
within each year. Such allocations are just as irremediably arbitrary
as managerial accounting's joint-cost allocations (which attempt
to attribute single cost figures individually to multiple outputs).
With traceable costs, we reverse things and allocate from many to
one instead of from one to many. This reversal automatically eliminates
the factor that makes financial-accounting and joint-cost allocations
Indeed, one ordinarily would describe what's done with traceable
costs as cost aggregation, not allocation. Illustration 1
diagrams the difference between these two situations.
Allocations of Untraceable Costs
Incorrigibility becomes a potential problem in managerial accounting
whenever an input isn't traceable to one and only one output,
yet management or institutional considerations force allocation of
its cost. There are two main ways in which an input may not be traceable:
1. For convenience, and to minimize accounting expense, managerial
accountants don't bother to trace certain overhead costs that, in
theory, they could trace to individual outputs. For example, often
they can calculate with high precision the cost of electricity used
in manufacturing a particular batch of product. Under process costing,
managerial accountants often will allocate this cost to the product;
under job-order costing, they're apt instead to lump electricity
costs with other overheads -- that's to say, not try to trace
them. In the latter instance we once again see accountants invoking
a form of materiality rule.
We may perceive applications of such overheads proportionate to
direct labor hours worked (or some other index of activity) as a
surrogate for corrigible, traceable allocations: as attempts
to trace in an aggregated, statistical way costs whose tracing would
otherwise be impractical. Following this logic, overhead allocations
are illegitimate when accountants use the same index to apply other
costs that theory indicates are untraceable -- for instance,
to apply fixed overheads to individual units of product.(8)
2. The input is joint on two or more outputs at a particular level
of activity aggregation. Here, All the familiar dilemmas of joint-cost
allocation arise. We accountants tend to picture joint-cost problems
as occurring at Level 5 (Specific product or other output): as problems
of allocating costs of a single manufacturing process to its multiple
products. Yet, identical problems arise whenever we try to:
Level 2 Year: Allocate costs common to two or more years (such
as the depreciable base of a depreciable asset) to individual years,
Level 3 Administrative, selling, or factory: Allocate costs
common to administration, selling, and manufacturing (such as certain
head-office expenses) to these individual activities.
Level 4 Responsibility center: Allocate costs common to several
responsibility centers (such as those of building occupancy) to individual
responsibility centers, or
Level 6 Unit of output: Allocate costs common to a batch of
product (such as set-up costs) to individual units of that product.
Horngren suggests that accountants make such allocations for three
main reasons: pricing, income determination, and inventory valuation.(9)
The latter two are really financial accounting issues, and I've dealt
with them elsewhere. To pricing, I shall add one related concern:
whether or not to produce the product at all.
Decisions That Don't Require Allocations of Untraceable Costs
Let's begin by examining a situation in which allocations of untraceable
costs are clearly unnecessary and illegitimate. A group of investors
is considering organizing a firm to manufacture and sell a particular
product, x, for t years, then either liquidate this
firm or sell it to others. For simplicity, at first I'll disregard
taxes and waste, and assume stable input prices and that the investors
are profit maximizers. Also, I'll disregard uncertainty -- not
because uncertainty is unimportant, but because I wish to explore
other, even more fundamental, issues.
The project requires an initial investment of I. The investors
expect variable costs per unit of output to be v, and each
year's fixed outlays (exclusive of any amortization of I) to be fn
(n = 1, ... , t). The investors also envision some profit maximizing
strategy for marketing product x. This might involve selling all units
at the same price, p, or it might happen that profit maximization
requires selling different units, i, at different prices, Pi
Under either assumption the investors expect to sell some total number
of units of product, un, during
each year of the project's life. Of course, the u's and p's
are ultimately functions of the estimated demand characteristics of
the product and would be calculated without reference to any accounting
The investors won't undertake this project unless they expect to
obtain some minimum rate of return, r, on their investment.
Assuming a constant price for the product and that they anticipate
a scrap value of S from liquidating or selling the firm at
the end of year, t, the investors will undertake this project if and
only if its net present value, NPVx, is nonnegative:
( I )
If the product's price isn't to be constant, we must substitute
the expression for
(pi-v) for un
(p-v) in Inequality (I).
Since there's only one product, most of the firm's costs -- even
administrative and selling costs -- are traceable to its annual outputs
of product x, and allocating them to this output would be corrigible.
The only exceptions are:
1. Any components of the annual fixed outlays that interact with
other years' fixed-outlay components. (For brevity, I'll disregard
this possibility hereafter.)
2. The cost of the investment or, more precisely, its depreciable
base (I - S).
There's no theoretically legitimate way to calculate the full cost
(including allocated investment) of any individual year's output --
for doing so requires joint-cost allocation. But decision-makers have
no need to calculate such full costs. For you may verify that
whichever price assumption we make, neither the decision to undertake
the project nor the decision of what price(s) to charge for it require
any allocation of the initial investment's depreciable base (nor
any allocation of annual fixed outlays to individual product units,
either). You should also be able to satisfy yourself that there will
be no need to allocate untraceable costs even if Inequality (I) is
recast to provide for taxes, waste, price instability, uncertainty,
continuous compounding, or investors who seek satisfactory (or equitable)
returns rather than maximum profits.
Untraceable Costs Allocated Anyway; Sterilization
However, it may be that the investors, like many managers, are habituated
to basing their decisions on the kinds of full-cost data used in financial
accounting and, therefore, require allocation of the investment's
depreciable base. The article cited at the outset claimed that any
such financial accounting allocations would be incorrigible:
no allocation method can be verified because infinitely many other
methods are just as plausible as it is, yet no method can be refuted,
since each is just as plausible as any alternative. Here, matters
become slightly more complicated. Some possible allocations can be
refuted; the remainder will be incorrigible, unless unique.
Demonstrating this requires a concept introduced by my 1974 AAA
study: sterilization of an allocation method. In practice it's
fairly common for decision makers inappropriately to base their decisions
on allocated untraceable costs. The AAA study gave the example of
decisions whether or not to process joint products past their splitoff
points. Under circumstances specified there, management's decision
should depend upon whether product revenues, less costs to complete,
are positive. Yet, some managements may instead be concerned whether
revenues less full costs (including allocated joint costs)
The latter decision approach is inappropriate. However, one way
of allocating joint costs -- the familiar net realizable value (NRV),
or approximated relative sales value, approach recommended by textbooks
-- has an amiable characteristic. If management does make the mistake
of basing its decisions on full costs, but calculates these costs
by the NRV approach, its decisions will be identical with those that
it would have made had it used a correct approach that avoided
untraceable-cost allocations. That's to say, use of the NRV approach
ensures, under these particular circumstances, that inappropriately
allocating untraceable costs won't affect the decision one way or
another. Such a no-effect allocation is sterilized with respect
to the particular decision and circumstances.
Please note that sterilization is a rather odd concept. It doesn't
mean "right" or "good surrogate" or "possesses
high decision-utility." Indeed, it doesn't refer so much to the
allocation itself as to the relationship between an allocation and
a decision and set of circumstances. And even there, to say that an
allocation is sterilized merely means that, although it shouldn't
have been made, it does no harm because decision-makers who use it
will make the same decision that they would had they used appropriate
allocation-free data instead. (One really shouldn't consult fortune
tellers. But if their advice doesn't affect one's decisions, doing
so may be harmless.)
Similarly, it can be demonstrated that implicit-rate (economic)
depreciation of divisional assets is sterilized with respect to division
managers' decisions whether or not to invest in new capital projects
when these managers are evaluated according to divisional ROIs.
In general this notion of sterilization attempts to isolate what
research in progress indicates is a goal common to a great variety
of managerial-accounting behavior -- despite management's not being
conscious of following this goal. Thus, potentially, it offers a simple,
unified explanation of much that otherwise seems complex and disparate.
Earlier research made two more points about sterilized allocations
that are important for our purposes, and which I'll illustrate presently:
1. There's no reason to expect that an allocation method
that's sterilized with respect to a particular decision and set of
circumstances will continue to be sterilized for other decisions or
in other circumstances.
2. Often many allocation methods will be sterilized with respect
to any one decision and set of circumstances.
Sterilization and Corrigibility
Now, whenever a decision should be based on data free of untraceable-cost
allocations but decision-makers insist on an approach that uses them,
sterilized allocations are preferable to unsterilized ones. For an
unsterilized allocation could lead the decision-makers to make an
incorrect decision whereas, by definition, a sterilized allocation
couldn't. Accordingly, in such situations unsterilized allocations
aren't incorrigible -- for they can be refuted.
However, we should try to be very clear about what's going on here,
even at the price of repetition. Something has made management believe
that decisions should be based on allocated data. Yet decisions should
instead be based on data free of allocations. The only ground for
choosing sterilized untraceable-cost allocations is that they don't
affect decisions one way or another and are, therefore, harmless
errors. In no sense of the word does this "verify" sterilized
whenever more than one untraceable-cost allocation method is sterilized
with respect to a particular decision and set of circumstances, each
individual sterilized method is incorrigible -- for each is inappropriate,
yet each avoids affecting the decision.
I'll illustrate all this by the two decisions made by our investors,
assuming, for brevity, that the price charged for the product must be
constant. It should be emphasized that in both of the following examples
the investors are using foolish decision rules. For the purpose of these
illustrations is to show that even under a patently bad rule requiring
untraceable-cost allocations it may be possible to select sterilized
allocations that leave decision makers in the position that they would
have occupied had they been sensible.(13)
1. Perhaps the investors will decide whether or not to engage in
the project by first calculating the product's optimal price and
annual outputs (by the allocation-free analysis of potential demand
mentioned earlier ), then, for each year, comparing that price with
the full unit cost of the product plus a small markup for an equitable
profit. If price always exceeds marked-up full cost, the investors
will undertake the project; if it fails to do so in one or more
years, they won't.
Calculations of annual full costs plus markup require allocating
the initial investment's depreciable base to individual years. If
NPVx >= 0, any method
of doing this that results in each year's marked-up full cost being
less than the optimal price will be sterilized. If NPVx
< 0, any method that results in at least one year's marked-up
full cost exceeding the price will be sterilized. For, in either
event, any such allocation method will ensure that the investors
make the same decision that they would have had they followed the
correct decision approach reflected in Inequality (I) . On the other
hand, any way of allocating the depreciable base that isn't
sterilized could tempt investors to make a wrong decision and, therefore,
can be refuted in this particular context of decision to be made
and surrounding circumstances. (14)
As you may readily verify, whether NPVx
>= 0 or < 0, infinitely many allocation methods will satisfy
the rather modest requirements for sterilization here. Some might
be more familiar than others. But, with respect to this decision
and its particular circumstances (considered in isolation), each
will be as good as the other, and each incorrigible. Any rule to
choose among them must either be arbitrary or, as we'll soon see,
be based on some other decision to be made from the allocated
2. For our second bad decision rule, perhaps instead, the project
is so obviously profitable that the investors decide to undertake
it without first determining exactly what they'll charge for the
product. They plan to set this price by applying a percentage markup
(one regarded as equitable in the industry) to the product's full,
fast-year unit cost.
Any allocation method that generates the particular first-year,
full-cost figure that, in turn, yields a marked-up selling price
equal to the allocation-free, profit-maximizing price, p, will allow
the investors to follow their inappropriate decision rule yet simultaneously
maximize profits. Here, one allocation of the depreciable base to
Year 1 is preferable to all others, and any allocation method that
doesn't yield this Year-1 allocation can be refuted. But there will
be infinitely many ways of allocating the depreciable base over
the firm's entire life that satisfy this Year-1 constraint yet differ
in what's assigned to Years 2 through t; each of these will be as
good as any other with respect to this particular decision
By now, some listeners should have begun to feel uneasy. As Anthony
argued at the outset, in both examples surely some sterilized allocations
won't be as good as others; some, in fact, will be quite weird. For
instance, in the second illustration sterilization could be attained
by allocating the "appropriate" portion of the depreciable
base to Year 1, the remainder to Year 2, and nothing whatever to any
other year. Clearly (it could be argued) such an allocation approach
is inferior to other, less whimsical, ones. Thus, choice among sterilized
allocation methods isn't incorrigible.
The answer is simple. As emphasized earlier, a sterilized allocation
method is sterilized with respect to a particular decision and
set of circumstances. It may also be sterilized with respect to
other decisions and circumstances, but there's no reason to expect
this to be so. If the allocation method in question is inferior to
others, this must be because we perceive it interfering with sonic
other decision(s) -- perhaps by generating unsatisfactory Year-2
profits and thereby tempting decision makers to raise the product's
price (or to make some other inappropriate decision). But this merely
signifies that the subject allocation method isn't sterilized with
respect to other decisions.
Similar comments apply to rejecting otherwise-sterilized methods
of allocating untraceable costs for violating GAAP rules -- or, as
in Anthony's objections, for violating some concept of equity. Notions
of what's equitable vary so much from individual to individual and
situation to situation, and are so subject to unintentional bias from
self-interest, that one despairs of giving them analytical significance.
But any attempt to make them operational must specify that certain
kinds of decisions based on certain allocations are erroneous. For
instance, to use Anthony's example, one shouldn't allocate all equipment
costs to one loaf of bread, and none to the others, then decide to
base prices charged for loaves on the resulting book costs.
Of course, decision makers who set prices by an approach free of
untraceable cost allocations should never be tempted to make such
an inequitable pricing decision in the first place. Anthony's rule
against allocating all equipment costs to one loaf merely places decision
makers who inappropriately base their pricing decisions upon such
allocations in the same position as they'd have occupied had they
not allocated (though only, to be sure, with respect to this
This conclusion is equally applicable to any standards of
equity (for fairness) that someone might use to reject allocations
of untraceable costs that are otherwise sterilized. Either such standards
refute all of these allocations (in which case sterilization with
respect to all relevant decisions and circumstances is impossible)
or one ends up with a smaller set of allocations that now are also
sterilized with respect to the decision and circumstances implicit
in the standards of equity. Thus, all that such standards do here
is to impose additional sterilization criteria upon allocations that
shouldn't have been made in the first place; and nothing in Anthony's
observations or his article conflicts with the following conclusions:
1. Managerial allocations of untraceable costs (and other one-to--many
allocations) are either refutable or sterilized with respect to
one or more decisions and sets of circumstances. That's to say,
they're either demonstratably wrong or without effect.(15)
2. There's no guarantee that any allocation method will
simultaneously be sterilized for all the decisions that decision-makers
with to make and all circumstances in which they wish to make them.
3. When an allocation method is sterilized with respect
to one or more decisions and sets of circumstances, there's no guarantee
that it will be uniquely so.
4. When it's not unique, all sterilized methods will be
incorrigible though, of course, some or all of these could be refuted
if one invoked additional decisions or circumstances.
5. If more than one method is sterilized, the accountants' final
choice among them will depend upon such considerations as ease of
calculation, freedom from data problems or excessive sensitivity
to errors in parameter estimates, or familiarity.(16)
6. Finally, when one concludes that one-to-many managerial allocations
must be either refutable or sterilized, one is saying something
damning about them: at best, all that can be claimed in their favor
is that they're harmless excrescences.
Two or More Products
For simplicity, we've assumed that our imaginary firm makes only
one product. Let's relax this assumption now, first by supposing that
the investors contemplate the firm's making two products, x and y,
throughout its t-year life, and that sales of these products will
be independent. Each product will have its own traceable initial investment,
variable cost, annual fixed outlays, and (perhaps) scrap value. In
addition, there will be joint (untraceable) initial investment costs,
Ij, joint annual fixed outlays, fjn
and a joint component to the scrap value at the end of the year t,
Sj. (17) For
brevity, I'll assume that all variable costs are traceable to individual
products and that it's appropriate to apply the same rate of return,
r, to all calculations.
The significance of the net present value of an investment in either
product changes slightly; since the amounts of such net present values
may differ from what would be calculated in a single-product case,
I'll use the following notation for them:
As before, it may be necessary to substitute the expression
in the foregoing.
Once again, the investors will envision some profit-maximizing strategy
for marketing both products, and will undertake both only if:
( II )
The investors must now decide what prices to charge for each product,
and whether to product either x, y or both.(18)
Inequality (II) describes the criteria that these product decisions
should satisfy; none of its expressions are allocated magnitudes (
nor are any of the components of its NPV's ). Accordingly, despite
this situation's being more complex than the one reflected in Inequality
(I), it's evident that our earlier conclusions remain true: None of
the decisions that investors must make require allocation of untraceable
costs, and any such allocations that investors do make will be either
refutable or sterilized ( with all sterilized allocation methods being
incorrigible if more than one is available ). Listeners are invited
to satisfy themselves that as long as we continue to assume a limited-life
firm (and make our earlier assumptions), these conclusions hold no
matter how many products the firm manufacturers. Moreover, we can
relax the assumption that all such products are manufactured throughout
the firm's entire t-year life by substituting zero values for appropriate
un's and fn's,
and discounting any initial investments that are to occur after the
Indeed, it should be apparent that in theory none of the investor's
decisions require allocation of untraceable costs even were we to
go much further in relaxing assumptions and allow uncertainty, unstable
input prices, joint variable costs, multiple rates of return, interaction
of products, and an indefinite-life firm. However we should consider
two possible objections to this conclusion. At least one author has
implied that such allocations are a necessary response to a complex
decision environment. Also, the question inevitably arises: if such
allocations are unnecessary, why do so many managers make them?
Objection: Allocation as a Response to Complexity
It might be argued that once we relax Inequality (II)'s assumptions
and admit more complications, appropriate untraceable-cost-allocation
free calculations rapidly evolve beyond the capacities of most or
all decision makers ( perhaps because of limited channel capacity
and difficulties in making the necessary estimates ) -- and that,
as a practical matter, they must instead allocate costs that are joint
to various years, responsibility centers, and products. Wells seems
to imply this in his description of the origins of managerial accounting's
Specifically, it could be urged that firms must often calculate full
costs for products when bidding for new business or when deciding
whether or not to undertake new products whose selling prices are
given. For instance, a parts manufacturer preparing a bid may need
to estimate a minimum amount below which this bid shouldn't fall,
in the sense that if it bases all of its bids on parallel calculations
it will earn just enough to keep profits at a satisfactory level.
Calculation of any such floor price requires allocating untraceable
costs to individual jobs. I shall call this the UCA (for untraceable-cost
allocation) approach to such decisions.
Someone taking Wells' general view would go on to emphasize that
these are merely hypothetical allocations, made solely for specific
decisions, that they have no significance for other purposes, and
that nothing is served by booking them. Yet, if they are necessary
for practical purposes, doesn't this make them a legitimate part of
There are at least two answers to this question:
1. The UCA approach entails that firms will make product decisions
in series, as a way of simplifying complex decision environments
-- that's to say, make them one product or group of products) at
a time. But, if so, firms can legitimately simplify even further
by using a familiar variant of capital-budgeting analysis. Instead
of calculating individual NPV's for a multiplicity of products,
they need merely regard all products that they're currently producing
as though they were a single product, x, and the candidate product
as Inequality (II)'s product y. The candidate product should improve
the profitability of the firm as a whole; therefore, the criterion
for product decisions becomes:
( III )
For brevity, I'll call this the capital-budgeting approach
to deciding whether or not to produce a product and what price(s)
to charge for it. Under the capital- budgeting approach, these
product decisions are sensitive only to differential considerations.
Any complicating factors common to both NPV's drop out of the
2. The UCA approach doesn't escape any of the capital-budgeting
approach's remaining complications. For the UCA approach still
requires firms to estimate investment costs, scrap values, and
variable costs -- and to develop pricing strategies. Both approaches
require making the estimates of total output to be produced and
sold that Inequality (II) demands. (In particular, whatever way
the UCA approach charges untraceable costs to units of output
necessarily implies a total output over which all such costs are
to be recovered.) (20)
Similarly, the UCA approach's provisions for a minimum profit
require calculations that parallel Inequality (II)'s and (III)'s
need to specify a minimum rate of return. Other considerations
such as uncertainty, equity, unstable input prices, joint variable
costs, and interactions of products affect both approaches equally.
To be sure, the UCA approach might often disregard these. But
whenever doing so is legitimate, the capital-budgeting approach
can just as properly ignore them, too.
Thus, any supposed practical advantages of the UCA approach in complex
decision environments seem illusory. Instead, it mingles theoretically
illegitimate data (untraceable-cost allocations) with legitimate data,
thereby rendering an already complicated decision situation even more
Objection: The Widespread Use of Allocations in Practice
Accordingly, we may conclude on both theoretical and practical grounds
that managerial accountants should eschew allocations of untraceable
costs. Why, then, do we encounter such allocations in practice?
1. One reason often offered is that financial accounting's GAAP require
full-cost inventory figures. The UCA approach provides these; the
capital- budgeting approach doesn't. But this would be a satisfactory
reply only if GAAP arose independently of the managerial accounting
practices, which doesn't seem to be the case. (The same point applies
to any claim that we allocate untraceable costs because we've been
trained to do so.)
2. Many-to-one allocations are legitimate. It's a natural
error to suppose that one-to-many (joint-cost) allocations, though
admittedly "somewhat arbitrary," are legitimate, too.
Similarly, in our private lives we often feel confident of being
able to make meaningful profit and loss calculations on such things
as sales of securities or decisions to change employment. We feel
equally confident calculating profits for very simple business ventures
of the kinds that characterized capitalism until relatively recent
times. Such calculations require few significant allocations of untraceable
It's only natural that we should wish to make similar calculations
for today's complex business enterprises: why shouldn't it be just
as meaningful to calculate General Motors' profits, or the profits
of a responsibility center, as it is to speak of one's personal profits?
Of course, such calculations do require important untraceable-cost
allocations. But we go ahead and make them anyway, soothing any uneasiness
by reasoning that such profits must exist, and that there's no way
to avoid allocations if we are to calculate them: charging zero amounts
for relevant untraceable-cost factors seems clearly refutable, therefore
any systematic, consistent, plausible-sounding allocation method seems
preferable to no allocation at all.
I've argued elsewhere that this train of reasoning is defective
at its root: that profit, as commonly understood, cannot be corrigibly
calculated for large enterprises, and that the analogy from personal
profits is as misleading as the classic false analogy between prudent
personal savings behavior and surplus/deficit policies appropriate
to national governments. Nonetheless, as long as Society continues
to encourage this natural error, we may expect managers to continue
to request profit data for responsibility centers (rather than data
about their contributions), and thus accountants to continue to allocate
untraceable costs. (22)
3. Allocations of untraceable costs are required by both the cost theory
of pricing and the medieval notion of just price in which, presumably,
it originates. Neither of these will stand up to modem analysis, but
both seem deeply embedded in management thinking and in the terms of
many contracts (notably government contracts). This, and the previous
discussion, suggests that some reasons for allocating untraceable costs
reflect survivals from simpler eras of business organization that have
persisted long enough to become part of our habitual ways of thought
-- examples of what Schumpeter called the ancient truth that the dead
always rule the living. (23)
Unfortunately, by now any change to untraceable-cost-allocation free
accounting will require extensive reeducation and some dislocation.
This, of course, perpetuates our allocation fallacies. So does the
seeming absence of potential alternatives that stems from our inurement
to present practices and resulting failure to experiment with untraceable-cost-allocation
4. Many believe that the kinds of marginal or incremental calculations
involved in the capital-budgeting approach can lead a firm to financial
ruin. Here's an example. Let's suppose for simplicity that a firm manufactures
a single product and rents all of its plant and equipment. Variable
costs are $3 per unit and fixed costs $100,000 per year. The firm, which
has excess capacity, produces and sells 20,000 units per year. It must,
therefore, charge $8 per unit just to break even.
Incremental analysis assures us that if the firm could legally sell
additional units in a separate market without affecting its existing
sales, its total profits would increase at any selling price exceeding
$3. Yet, of course, if the firm applied this approach across the board
it would go bankrupt. Moreover, there's the additional danger that
sales in the $3+ market eventually could spoil sales in the $8+ market.
Therefore, many conclude that one should allocate untraceable costs
(the $100,000 of fixed costs, here) to individual units -- at least
as part of the firm's routine cost accounting.
But this conclusion simply doesn't follow. All that's really occurring
here is that the firm has an opportunity to substitute two different
pi's for p in the detailed expressions
that lie behind Inequality (III). In doing so, there's no chance that
choice of a low pi for the secondary
market will affect the primary market's $8 + pi
one way or another. And any dangers of leakage between the two markets
can be incorporated quite as well into Inequality (III)'s untraceable-cost-allocation
free, capital- budgeting approach as they can into the UCA approach.
What these fears really seem to boil down to is a concern that if
one gets used to thinking in marginal or incremental terms one may
end up disregarding fixed costs. Since the capital-budgeting approach
explicitly incorporates all fixed costs, this fear is groundless and
the reason for allocating untraceable costs collapses.
5. To many, the capital-budgeting approach may appear to be overly complex
and to require estimates of parameters that, as a practical matter,
are impossible to estimate reliably. Decision makers may therefore believe
that some rule-of-thumb approach to pricing, based on traceable costs
but charging an additional percentage markup to allow for imponderables
and profit, may be the best that they can do. Indeed, if reliable estimates
are impossible, such a rule-of-thumb approach may be best from a cost-benefit
standpoint. But please note that:
a. Although such a rule-of-thumb approach superficially resembles
the UCA approach, it's a retreat from it, too. For, as we've seen,
the UCA approach requires making the same kinds of estimates as
the capital- budgeting approach does and, thus, is equally complex.
b. There's no need for the rule-of-thumb approach to involve any
allocation of untraceable costs: all it requires is a percentage
mark-up over direct costs. To be sure, decision makers may speak
as though such markups were intended to cover both fixed costs and
profits, but that's merely symptomatic of the pervasive ideology
of profit calculation and untraceable-cost allocation, discussed
6. Relatedly, managers sometimes also believe that estimates of traceable
costs tend to be understated (or that dangers from understating them
exceed those of overstatement), and that therefore some "boot,"
or safety factor, should be allowed in marginal or incremental calculations.
But even if this is true, there's no need to allocate untraceable
costs in order to provide such a safety factor. Nor is there any need
to do so in order to make managers more aware of the costs incurred
and benefits offered by other parts of the organization --another
rationale sometimes given for allocating untraceable costs.(24)
7. Capital-budgeting approaches are generally less attractive
to decision makers than theorists might desire. This is partly for
the reasons just discussed, but partly also because of something identified
by Ijiri: a firm's divisions compete for investment funds from headquarters,
and tend to make overly optimistic estimates for long-lived projects.(25)
Although this affords an additional explanation for firms' preferring
rule-of-thumb approaches, it provides no reason for allocating untraceable
costs. For, once again, the UCA approach requires essentially the
same estimates as does the capital--budgeting approach.
8. As inspection of Inequality (II) should suggest, the untraceable-cost-allocation
free capital-budgeting approach is often best adapted to global decision
making by top management, whose resulting decisions are then imposed
upon responsibility centers. Such imposition may limit these centers'
sense of independence, thereby jeopardizing some of the lower-echelon
creativity and elan sought by decentralization.
The relevant question here is how much real lower-echelon independence
is possible under the UCA approach when joint input factors are significant.
The gloomy literature of transfer pricing suggests that allocation
of untraceable costs doesn't really help matters here.
9. Finally, it could be argued that accountants, as practical men, really
aren't trained to be terribly sensitive to logical issues, to worry
much about theory, or to be distressed by mere cognitive dissonance.
Thus, once in the habit of allocating the unallocable, we may be content
to continue to do so indefinitely, theory be hanged, as long as the
practical consequences of doing so seem bearable. If this paper has
been correct, the trouble with such attitudes is that major potentials
for reducing managerial accounting costs and confusions exist that won't
be realized until practical accountants come to worry more about the
intellectual foundations of their craft.
We've reached the following overall conclusions. Managerial accounting's
numerous many-to-one allocations often can be verified. Our allocation
problems are, instead, with one-to-many allocations. These are theoretically
illegitimate; in particular, Anthony's rationale for them and the
rationale that could be developed from Wells' work don't hold up under
One-to-many allocations fall into two types, depending on the nature
of the allocatee -- that's to say, upon what the cost is allocated
1. Allocations of total output to two or more inputs
that generate it. Conceivably, the inputs might have entirely
independent (linear) effects on the production process (as when an
individual's income equals the dividends that he or she receives from
two unrelated firms). In such cases, it's theoretically legitimate
to allocate the output to the individual inputs in proportion to their
separate effects -- the amounts of output that each allocatee
would generate in the absence of any other inputs.
Thus, accounting's basic allocation problem results from lack of independence
of allocatees. We call this lack of independence interaction
when the allocatees are inputs and jointness when they're outputs.
The extreme case of input interdependence occurs when all inputs are
essential (fixed input proportions); the extreme case of output interdependence
occurs when all outputs are unavoidable (fixed output proportions).
Most often, inputs and outputs are partly substitutable. But anything
materially short of full allocatee independence results in irremediable
Usually, though, inputs interact to produce output, and total output
differs from the sum of such separate effects. Here, earlier research
on financial accounting's allocations (together with this paper's
analysis) indicates that all allocations must be either refutable
or incorrigible. (26)
2. Allocations of total inputs to two or more outputs generated
by them. Conceivably, these outputs might be entirely independent
effects of the production process, freely substitutable for each other
and occurring in entirely variable proportions (as when one cuts either
3x5 or 4x6 filing cards out of 48x60 blank sheets). In such cases,
it's theoretically legitimate to allocate the total cost of the inputs
to the outputs in ratio to the actual quantities of each output produced.
Often, though, outputs are joint -- not independent; they
occur in proportions that are partly or wholly fixed. Here, we've
seen that all allocations must be either refutable or sterilized.
And if more than one is sterilized, each will be incorrigible. In
any event, it's widely recognized by writers on managerial accounting
that all such allocations are arbitrary.
The upshot for untraceable-cost allocations is that all will be
either refutable or sterilized -- and, if the latter, incorrigible
unless unique. Sterilization here signifies that these allocations
won't affect certain decisions made under certain circumstances. This
is the very best that can be said of them: they can be designed
to be ineffectual, to lack any decision impact whatever, to be tripe.
Since such allocations complicate analyses, waste time, and cause
misunderstandings, we accountants should stop making them -- especially
since research in progress indicates that untraceable-cost allocations
often can't be sterilized for all relevant decisions and circumstances
simultaneously. For if, at best, such allocations have no effect,
we can obtain this no effect easier and more safely by not allocating
at all. It's just that simple.
* Professor of Accounting, McMaster University. I wish to thank Robert
N. Anthony, Maurice Moonitz, Paul Rosenfield, Robert R. Sterling, and,
especially, Joseph G. Louderback, III, for comments on an earlier draft.
Be warned that not all of these individuals agree with what follows.
Also, much of this paper originated in reactions to a close rereading
of the first twelve chapters of Charles T.Horrigren, Cost Accounting,
A Managerial Emphasis. Third Edition ( Prentice-Hall, Inc., 1972 ).
(1) Yuji Ijiri, "Theory
of Accounting Measurement," Studies in Accounting Research
No. 10 (American Accounting Association, 1975). p.18.
(2) Finally, I've
made no attempt at this point to provide a scholarly bibliography.
(3) "The FASB
and the Allocation Fallacy, " The Journal of Accountancy
(November 1975), pp. 65-68. The research summarized appeared in "The
Allocation Problem: Part Two," Studies in Accounting Research
No. 9 (American Accounting Association, 1974), and "The Allocation
Problem in Financial Accounting Theory," Studies in Accounting
Research No. 3 (American Accounting Association, 1969), hereafter
SAR9 and SAR3, respectively.
(4) Robert N. Anthony,
in personal correspondence. (4a)
Robert N. Anthony, "The Rebirth of Cost Accounting," Management
Accounting (October 1975), pp. 13-16.
(5) The extractive
industries offer an exception: decisions whether costs of unsuccessful
exploration should be charged to, successful projects can have major
(6) It should be
repeated that this discussion disregards waste -- assumes, if you
prefer, that the firm's wastes have already been identified and that
all costs under consideration am waste-free.
(7) More precisely,
many-to-one allocations encounter such difficulties only when conflicting
ways to perform aggregations are available, only one of which can
be correct, and there's no conclusively defensible way to narrow down
the possibilities. The discussion under point 1, above, indicates
that this problem doesn't arise here. To be sure, as noted earlier,
costs that can defensibly be allocated at a particular level of activity
aggregation often can also defensibly be allocated at other levels.
But this poses no dilemma. For, unlike the aggregation of current-exit
values in the Appendix to SAR9's Chapter 7, hem we're not required
to choose one and only one figure. All are correct.
(8) Similarly, variance
accounting may often be a practical surrogate for elaborate investigations
whereby, at Level 1, costs could be allocated to productive output
or waste depending upon whether output would have been physically
different had the cost not been incurred.
(9) See Horngren,
op. cit., p. 88.
(10) Perhaps following
a strategy similar to that by which ball point pens were introduced
in the late 1940s: initially charging very high prices, then, once
demand at these prices has been tapped, successively lowering prices
to reach additional layers or demand).
(11) For background
to the following discussion, see SAR9, pp. 40-46 and 163-74.
(12) This point can
be subtle. Imagine, if you will, a situation where marginal or incremental
data are appropriate to a decision, and an allocation method generates
exactly these data. Their merit resides in their being what allocation-free
analysis would have provided; therefore, the allocation itself isn't
(13) For more familiar
(and plausible-seeming) bad decision rules, you may wish to refer
to SAR9's examples.
(14) Context is important
here. Ideally, an allocation method would have both features -- be
sterilized whether NPVx, was >=
or < 0. However, it may be impossible to devise such a method.
In that ewe, one would be forced to conclude that although it was
easy to sterilize the allocation with respect to the decision and
the specific circumstances NPVx
>= 0 or NPVx < 0, more general
sterilization happens to be unattainable.
(15) As a practical
matter, a general understanding that allocated data will be ignored
for certain decisions may be a satisfactory alternative to their sterilization.
This depends in part on style of leadership. Sterilization will be
of maximum value (such as that value is) where decision makers take
book figures very seriously, and less important where they temper
them with "non-quantifiable" considerations.
(16) Other criteria
may dominate particular cases. For example, in allocating direct materials
variances between price and quantity, desires for timely data encourage
calculating the price variance at actual quantities purchased or ordered,
thereby attributing price-quantity interactions solely to price. Accountants
then allocate the corresponding direct-labor price-quantity interactions
exclusively to price, too, apparently for consistency. (See SAR3,
pp.14-15, for the allocation issue here.)
(17) If the firm
is sold as a whole at the end of Year t, there may be no separate
scrap values for the investments in the two products.
(18) Please note
that even if NPVx or NPVy
< 0, it still might be more profitable for the firm to manufacture
both products than just one if they share facilities.
(19) See M. C. Wells,
" The Monetary Quantification of Inventory Stocks and Flows in
Multi-Product Firms: An Historical Perspective, "- unpublished
doctoral dissertation (University of Sydney, 1973), pp. 14-15, 46,
87, 107, and 122-23. My interpretation of Wells' position is based
in Part on personal correspondence with a proponent of his study,
and could slightly misrepresent Wells' own views.
(20) For example,
if untraceable costs are to be allocated equally to each unit of output
and total $120,000, a charge of 40C per unit implies a total output
of 300,000 units, a 240,000-unit output, and so forth.
(21) This conclusion
corrects my earlier tentative agreement with the claim that hypothetical
allocations are a legitimate feature of managerial accounting -- see
SAR9, p. 27n.
(22) For an extended
discussion of why the financial accounting allocations that underlie
our notions of profit seem plausible, seethe section headed "Why
Isn't This Obvious?" of my chapter in the Third Edition of Baxter
and Davidson's Studies in Accounting Theory, forthcoming. The
related question of why such allocations am, appropriate in economic
theory but not in accounting is discussed there and in SAR9, pp. 32-40,
47-48, and 141-44.
(23) Joseph Schumpeter,
"The Sociology of Imperialism," final sentence.
(24) Compare Horngren,
op. cit., p. 426.
(25) At least, ones
that are overly optimistic for periods beyond those during which the
individuals making the estimates expect to remain in their current
positions. Some of the payback approach's popularity results from
its avoiding much such bias -- see Ijiri, op. cit., p. 27.
(26) SAR9's Chapter
Six discusses the only clear-cut instance of sterilized financial
accounting allocations that I've seen to date. However, I hypothesize
that efforts at sterilization also explain many attempts to smooth
SELECTED QUESTIONS AND ANSWERS
Could you for my benefit and perhaps for other as well give us a simple
illustration of how an allocation becomes sterilized.
I wish I had some figures, because this is where figures becomes handy.
As an example, let's use the divisional depreciation calculation.
You have division managers with enough autonomy that they are allowed
to propose new capital projects. A division manager starts looking
around at possible projects, and he sees one that has a very high
internal rate of return. Let us say it's 30% per year; but in the
early years it has a rotten pay-out. The division manager hopes to
be promoted within three or four years. If he proposes this particular
project and it is approved by top management, he will have low cash
flows and revenues in the early years. His successor will receive
all the credit for the high ones. At the same time if the firm is
using straight line depreciation, he will be showing a very low rate
of return for this project. Again, his successor will be showing a
splendid rate of return. If the firm is using accelerated depreciation
for book and tax purposes, he may show a disastrous rate of return
on the project. In a situation like this, the division manager is
apt to make the incorrect decision of suppressing the proposal for
capital expenditure, even though the firm would benefit from it. Well
now if you use economic depreciation, the one that gives the same
book rate of return in each year, the division manager will never
be tempted into doing this type of censorship of an otherwise attractive
proposal. In that sense, the use of this particular allocation method
for depreciation makes him use the same criteria for selecting projects
and come to the same decision as if allocation, depreciation, and
divisional net income calculated on depreciation wasn't a factor at
all. In that sense, it's sterilized.
Again you can show with joint cost allocation that as long as products
don't have any positive or negative values at split-off and you use
the net realizable values approach, any product that should receive
further processing will have a positive book profit associated with
it and any product that shouldn't receive the processing will have
either zero or negative book profit associated with it. If management
is so unwise as to be made uneasy by carrying products that have negative
or zero book profits, then the best thing to be done is to use the
NRV approach. Whenever they do have negative or zero profits, these
are ones that management should discontinue anyway. Again you have
a case where management shouldn't be allocating at all, but should
figure whether to retain or get rid of products in terms of the contributions
they make. But if they use book profits for the products, you can
work out an allocation method for the joint costs that keeps management
from making mistakes.
You have given us a maximization rule for the firm. What notion do
you offer for performance evaluation and interim reporting?
The simplest answer is that you have a cash flows notion, or rather
a net quick asset flows notion. One can evaluate individual managers
or individual employees using a cash flows criteria rather than a
profit criteria. Again, I'm saying this in the abstract. In the world
in which we live since everyone is geared to think in terms of profit,
this is impossible. You know even the Russians in the last 15 years
have started to reintroduce the notions of profit. At the moment we
live in a society where profit is one of the central concepts in accounting.
How long it will take to get away from this I don't know. All I'm
saying in the long run, we will get away from it.
Don't you think you should emphasize the fact there really isn't any
problem in accounting if there is certainty? Shouldn't one view all
these responses as an attempt to deal with uncertainty?
It is always permissable to isolate in any scientific inquiry one
problem from other problems. I agree with you about uncertainty, it
is a very important problem. On the other hand if you're examining
meat for lead contamination, you don't have to simultaneously be examining
it for coliform bacteria contamination. They are two separate problems.
The uncertainty problem is being very adequately handled by people
such as Brief and Owen. I'm interested in a different problem. The
only way I can get into trouble is if the kinds of interaction problems
and incorrigibility problems that I'm worried about interact themselves
with uncertainty. I've tried to set things up tonight and in my other
research so that uncertainty isn't a problem. Even in a world of certainty,
the problems I'm talking about exist.