Alternatively, she can adopt an extremely conservative posture, rejecting every new project that comes along. Because she never produces a new line, she can never find herself in the box where she produced, but shouldn’t have. Thus, she never commits a false positive error. But now, false negative errors are certain. Whenever a product is profitable, she commits a false negative error because she necessarily rejects it. The more conservative her posture, the less likely is a false positive error and the more likely is a false negative error.
The following diagram shows the tradeoff. On the horizontal axis is the probability of making a false positive error, that is, going ahead with the project, given that the project is unprofitable.
On the vertical axis is the probability of making a false negative error,
that is rejecting the project, given that the project is profitable.
At point D, all projects are accepted so the probability of accepting a
project, given that it is unprofitable is 1. At point C, all projects
are rejected, so the probability of rejecting a project, given that
it is profitable, is 1. The tradeoff is shown by the solid line between
C and D. If some projects are accepted and some are rejected, then
the firm ends up at an interior point, like A. At A, some, but not
all, good projects are rejected, and some, but not all, bad projects
are accepted. How does the firm decide on which rule to choose?
If it is very costly to accept bad projects, the firm wants a more stringent
rule, which moves it toward C. If it is very costly to pass up a
good project, then the firm wants a more lenient rule, pushing it toward
D.
The goal is to enhance the information set so as to allow for less of each
type of error. If decisions were better informed, then the tradeoff
would be along the dotted curve, rather than the solid one. Note
that on the dotted curve, the firm can make less of each type of error.
Point B implies less of false positive error and less of false negative
error than point A. The firm would always prefer the dotted curve
to the solid curve, but for one thing: Information is costly. Decisions
are better along the dotted curve, but the cost of obtaining the dotted
curve might be more delay or more consulting fees.
We now return to job design and
authority patterns. By structuring the authority relations in different
ways, different kinds of errors are made more or less likely.
First, a worker can be told that she may reject any project, but does not
have the authority to accept any project on her own. All that she
can do is render a recommendation to accept. Her superior may then
be given the authority to make the final call. Such a structure works
in the direction of reducing false positive error and increases false negative
error. Workers cannot autocratically accept a project so they cannot
make a false positive error. Workers never accept bad projects; only
superiors do. But the rule does allow workers to reject projects.
This means that they may reject good projects before their superiors get
the opportunity to reverse the decision, which increases the likelihood
of false negative error.
Second, a flat authority structure results in a different combination of
errors than does a steep pyramid. The hierarchical firm has a different
decision structure than the flat firm. In the flat firm, both workers
do full reviews on projects. In the hierarchical firm, a supervisor
does not review a project until a subordinate already has reviewed it.
This means that fewer projects get full reviews than is the case in a flat
firm. But those projects that get positive reviews from the subordinate
get a second review from the superior. Which structure is better?
It is easy to show formally (see the appendix t Ch 16) that a hierarchical
structure will approve fewer projects than a flat decision structure.
The hierarchical structure makes fewer false positive errors, but more
false negative errors. Fewer bad projects are accepted by the
hierarchical firm, but more good projects are rejected. There are
two reasons. First, since the hierarchical structure requires two
approvals rather than one, the test that a project must pass is more stringent.
Second, since two persons are required for an evaluation, rather than one,
fewer decisions are made.
There is another possibility. The structure can be made flat, but
second opinions can be required. Rather than creating superior and
subordinate, the firm can simply require that every project reviewed by
I is also reviewed by II, and vice versa. If both agree, the
decision is obvious. If they disagree, then some other rule must
be used to reconcile the differences. There are a number of possibilities,
but for our purposes, the details of reconciliation are irrelevant.
It is always true, irrespective of the reconciliation rule used that a
second opinion structure is less stringent than a hierarchical structure,
but more stringent than a flat structure, where one worker has complete
authority to approve or disapprove. (The formal derivation of this
proposition is contained in the appendix to Ch 16).
The logic is this. The second
opinion structure is less stringent and approves more projects than the
hierarchical structure. Under the hierarchical structure, when I
rejects a project, II never even sees it. II only sees those
projects that I passes on. In the case of a second opinion
structure, II sees even cases that I rejects. If II likes the
project, then the two opinions must be reconciled. As long as some
of these reconciliations result in positive outcomes, projects that would
not have been accepted by the hierarchical structure will be accepted by
the second opinion structure.
The second opinion structure is more stringent than a flat, single decision
maker structure. This is somewhat less obvious than it seems.
It is true that a second opinion can sometimes reverse an initial to reject,
but it is also true that a second opinion can reverse an initial decision
to accept. The main reason that a second opinion structure is more
stringent is that when second opinions are required, more projects are
rejected without a serious screening at all. If it takes one for
one person to review a project, then the flat structure with a single decision
maker produces two decisions per week: one by I and one by
II. By contrast, the second opinion structure produces only one decision
per week since both I and II must review every proposal.
During week one, I reviews project A and II reviews project
B. During week two, they switch. By the end of the two week
period, only two projects have been reviewed by both managers, meaning
that one project per week is reviewed. Projects that are not reviewed
are rejected, by definition. The flat structure results in half the
rejections by failure to review and thereby is a less stringent criterion.
The flat structure increases the likelihood of making false positive errors,
but decreases the likelihood of making false negative errors.
Figure 7.2 augments figure 7.1 by showing location of the different job
authority structures with respect to false positive and false negative
errors. Hierarchical structures locate on the northwestern part of
the tradeoff curve. Hierarchical structures minimize the likelihood
of accepting a project that is bad, but maximize the likelihood of passing
by a project that is good. Flat structures with single decision makers
lie in the southeast section of the tradeoff curve. Flat structures
minimize the likelihood that a good project will be rejected, but maximizes
the chances that a bad project will be accepted. Second opinion structures
lie somewhere in the middle, neither minimizing nor maximizing the likelihood
of false positive or false negative errors.
Which do job authority structure should the firm choose? Since there is a tradeoff implicit in the choice, the decision on which authority structure to use depends on the payoffs associated with the job. Since three structures are identified, let us consider three types of payoff regimes. These are shown in figure 7.3, 7.4, and 7.5.
Figure 7.3 shows a payoff structure that has been labeled Exxon Valdez.
The losses associated with the oil spill ran into the billions of dollars.
The Exxon Valdez situation is typical of one variety of payoff structure.
Doing the job extremely well results in small gains relative to the expected
amount, but making a mistake can be disastrous. The upside of payoffs
is limited to $100,000 in figure 7.3, but the downside implies losses in
the billions.
When the payoff structure looks as it does in figure 7.3, the firm wants
to minimize type 1 error, and is willing to accept higher levels of false
negative error. Hierarchical decision making is appropriate here.
Figure 7.4 has a payoff function with a big upside and limited downside.
This corresponds to new firms. Most of the time, they fail, producing
negative or only slightly positive profit levels. Once every so often,
as is the case with Netscape, the innovators hit it big, earning in the
many millions of dollars. Which structure favors the upside?
The answer, summarized in figure 7.2, is that a flat structure with very
little supervisory veto power minimizes the amount of type 2 error.
Young firms often do give a great deal of authority to each worker.
It is sometimes argued that creative people do not do well in firms that
emphasize the hierarchy to heavily. Although true, it may not be
the people. Since a hierarchical structure tends to err in the direction
of caution, minimizing false positive error, and tolerating the rejection
of some good projects, a hierarchical firm does not encourage creativity.
Flatter authority structures, which allow each worker more choice, also
allow creativity to flower. Risky, wild ideas that would be rejected
in a hierarchical structure, are allowed to proceed in the flat, single
decision maker structure.
Most firms are neither in the Exxon Valdez category, nor in the Netscape
Category. Payoffs are more symmetric in most business, especially
established ones. Figure 7.5 shows a suggested payoff function for
a gasoline station in my town. Great performance and innovative work
are unlikely to generate the large upside that Netscape experienced.
Poor performance and shoddy workmanship may cost the firm some money, but
not the disastrous losses incurred by Exxon when the oil spill occurred.
In this case, the firm prefers tolerable levels of false positive error
and false negative error, minimizing neither at the expense
of the other. In the service station example, a mechanic who is uncertain
about a particular automobile’s problem asks his fellow mechanic for a
“second opinion.” But the setup tends to be non-hierarchical.
In Figure 7.1, two curves were shown. The dotted curve lies inside
the solid curve. Others things equal, it is better to face the constraint
of the dotted curve than of the solid curve because for any given level
of false positive error, the dotted curve implies less false negative
error than does the solid curve (except at the endpoints).
How does the firm move to the dotted curve?
Unfortunately, this cannot be done
without cost. Fewer errors are made along the dotted curve than on
the solid curve. To get to the dotted curve, it is necessary to improve
the decision process. There are a number of possibilities, all of
which are costly. First, the firm can attempt to hire better evaluators
by going for more able, higher priced workers. Second, the firm can
allow any given evaluator to take more time evaluating each project.
Third, the firm can make more information available to the evaluator, either
by hiring outside consultants or buying other services. Whether any
of these steps is profitable depends on how much is gained relative to
the amount lost by making poor decisions.