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Managerial Decision MakinNormative and Descriptive Interactions

David RodeDepartment of Social and Decision SciencesCarnegie Mellon University

Revision: March 3, 1997

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INTRODUCTION

Managers are invested with the task of making decisions which routinely affect the valueand viability of firms. Thus, managers bear the heavy burden of making optimal decisions. Over the

last fifty years, completely rigorous formal theories of decision making (e.g., expected utility theory,

game theory1) have been largely accepted as models of rational choice (Fishburn, 1988). One may

think that managerial decision making, then, comprises nothing more than calculating the output of

these normative models. What has not been so widely accepted however, is rational choice. While

the vast majority of managers do indeed attempt to make optimal decisions, clearly, there are

numerous impediments preventing them from actually doing so.

The behavioral decision theory and cognitive psychology literatures have cataloged

numerous deviations from perfectly rational behavior (Kahneman and Tversky, 1979; Poulton,

1994; Rode, 1995). Deviations from rational decision making have been observed in nearly every

facet of economic activity. This would be but an amusing theoretical question were it not for the

impact these suboptimal decisions have on the value of firms and thereby the economy. Thus, one is

left with two possibilities: managers actually don’t care about making suboptimal decisions or

managers aren’t aware they make suboptimal decisions. It is reasonable to believe that the second

possibility is, in fact, the situation. This paper develops a model for analyzing the interaction

between normative and descriptive models of decision analysis: namely options theoretic models

and prospect theory.

THE PROBLEMWITHMODELS ...

“The big problem with...models is that managers practically never use them.”

-Little (1970)

Little’s (1970) seminal work on a formal theory of management models (specifically,

computer-based models) remains highly accurate today. He describes models being used at

1Although numerous authors have significantly contributed to the foundations of expected utility theory,

this discussion would be incomplete without acknowledging the seminal contributions of von Neumann and

Morgenstern (1944) in decision making under risk and game theory and Ramsey (1931) and Savage (1954) in

decision making under uncertainty.

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corporations as being “irrelevant” to the problem at hand. In one case, managers repeatedly reran a

model under different assumptions until it resulted in output which the senior management found

intuitively appealing. The problem is not with the managers. If managers knew of the mistakes they

are likely to make, and knew how to avoid making them, they would indeed make “locally

optimal2” decisions. But information is not enough. The problem Little described is one of sufficient information but inadequate clarification. Any rational person cannot be expected to rely

on something which remains a mystery. Thus, it is important for managers to know not only what is

optimal in a given decision context, but also what the expected ( i.e., quasirational) outcome may be

and why. Fortunately, since the mid 1970s, an increasing interest has been taken in the analysis of

quasirational decision making under risk and under uncertainty. Several formal theories have been

proposed (e.g., Kahneman and Tversky’s (1979) prospect theory, Bell’s (1983) regret theory).

Recent advancements in management information systems (MIS) have also increased the ability of

managers to progress towards optimal decision making by reducing the two constraints identified

by Newell and Simon (1972): time (computational processing power) and memory (information

storage and retrieval). The typical MIS, however, makes the same mistakes that managers make

(only faster). For the most part, they ignore the impact of bounded rationality on managerial

decision making.

This paper proposes a decision support system (DSS) with the capacity to evaluate decision

contexts in parallel. Clearly, the system (and managers) must be able to identify and analyze the

optimal decision in a given environment. It is also important, however, to observe what the expected

outcome will be using a descriptive model. By observing these expected systematic deviations fromrationality, managers will be able to see where mistakes would be made and adjust for them. Most

importantly, however, managers will be able to learn why they make mistakes. As a result, they will

be less inclined to repeat them in the future once they are aware of them. Theoretical research in

information systems (Little, 1970; Gorry and Scott Morton, 1971; Kimbrough, 1994) has shown

that one problem with models is that users frequently distrust a “black box” approach and revert to

the adaptive heuristic behavior which guides unaided decisions (and leads to locally suboptimal

outcomes). Gorry and Scott Morton (1971) specifically address the importance of a DSS in

evaluating complex management decisions and their work remains the locus classicus. If managers

2It is important to distinguish between local and global optimality. Simon ( e.g., 1972, 1987) has

repeatedly shown that human decision makers are limited in their problem solving capacities even when they behave

rationally. This “bounded rationality,” as Simon terms it, virtually guarantees that any complex decision will result

in a less than (globally) optimal output. Global optimality, then, becomes the normative ideal - a goal to

continually reach for. However, managers make decisions by “satisficing” - setting an acceptable achievement level

and working towards it. Working towards this goal involves using heuristics to shape beliefs and adapt to new

situations.

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could see why mistakes were made, they would be more inclined to correct them by adopting the

normative suggestion.

Briefly, this DSS would behave as follows: A normative model (expected utility

theory/options theory) and a descriptive theory (prospect theory) would each be given the sameproblem. At each decision step, an output would provide the results and show the process until the

model had been completed. Managers could then review the normative model until they found a

particular result intuitively unappealing. They would then observe the descriptive model (which

ideally would confirm their intuitive unease) and see that their hesitation was typical and has a

quasirational validity. They would observe that the nonoptimal decision was made because of some

particular cognitive error which they could then adjust for and by doing so, feel comfortable

choosing the normative model’s conclusion. More explicitly, for example, managers may not be

able to discern the impact of incorrectly assigning a leptokurtic distribution to a real options model.

However, a descriptive model would indeed alert them to the problem of overweighting extreme

probabilities.

It represents a movement from the product of knowledge to the process of knowledge. For

all intents and purposes, options theory outputs a product. Normative decision making theories are

rarely found to have empirical support largely because they ignore the actual human decision

making process (see Albers and Laing (1991) and Rode (1995) in this regard). To wit, people solve

problems heuristically, not by maximization under constraints or by Bayesian updating. Cross

(1983), in his monograph, A Theory of Adaptive Economic Behavior, writes:

The methodological price for this approach [traditional statistical andmathematical decision analysis] has been extremely high, however,for it has become necessary to assume that individuals in thesemarkets can be represented as mathematical statisticians capable of solving specific problems that are often beyond the analytic abilitiesof professionals in that field. It also requires reliance on theassumptions that individuals follow optimizing rules of behaviorunder just those dynamic and risky types of situations for which theassumption of optimization has the least empirical support.

Thus, it is inaccurate and unfair to talk of the “failure” of the normative approach (of

expected utility and options theoretic models). The failure still lies with the decision maker, who, for

lack of better knowledge, makes the best decision he is capable of making. An integrated, interactive

paradigm takes a large step towards solving that problem.

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OPTIONS AND PROSPECTS

This section will describe the decision faced by managers in the context of two theories: the

normative options theory and the descriptive prospect theory. The options approach is seen as an

augmentation of the traditional net present value (NPV) analysis of project finance and decisionmaking. The additional benefits arise from the incorporation of values for the flexibility given

managers in a particular decision environment. Prospect theory adapts traditional normative models

of decision making to a descriptive theory by explicitly incorporating the systematic cognitive errors

routinely made by decision makers.

Problems frequently faced by mangers typically involve the decision whether or not to do

something given the condition of an expected result of their given choices. These environments can

include capital budgeting, resource allocation, strategic entry, and competitive strategy. Traditional

thinking claimed that the solution to these situations was available in the properly discounted

present values of expected future revenues. What is fundamentally ignored by this analysis is the

value inherent in not choosing something - in leaving one’s opportunities open (see Kogut and

Kulatilaka (1994a) for an application). These situations arise in determining whether to enter a

market immediately or to enter it later, whether to continue investment in a new project or to

abandon it. Even whether or not to forfeit these options for compensation of some kind.

Although the options approach is widely recognized (Dixit and Pindyck, 1994) as an

improvement over NPV models, it nevertheless suffers from the normative insensitivity toconstraints in the task environment and their impact on managerial decision making. It is interesting

to note that there appears to myopia in either direction. Kogut and Kulatilaka (1994b) claim that the

formulation of strategic investment decisions as real options alleviates the problem of myopic

behavior found in NPV analysis. However, one might also claim that options models are too

rational and can quickly grow too complex. Trigeorgis (1993) discusses the impact of real options

thinking when there are interactions among the various options considered. Clearly, if one is not

careful, everything could be viewed as an option. It is precisely this unwieldy potential that may

encourage myopic behavior. Managers can quickly be overwhelmed by options thinking and, with

the inherent mathematical complexity in more rigorous applications of it, renounce it entirely in

favor of simpler, but still “good,” heuristic rules.

It is important to note that the Kogut and Kulatilaka (1994b) paper clearly emphasized the

importance of options thinking - not necessarily the rigid quantification of every decision. As a

conceptual framework - a method of thinking - options thinking has substantial value. And yet, it

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still seems to be missing something. Although perhaps a more quantitative approach is needed to

clearly identify it, options thinking requires at some level an estimation of probability distributions

and assessments of value. Humans in general are notoriously poor at making these types of

judgments (e.g., Poulton, 1994). Further, humans do worse when the situations are at the extremes

and when tail-ends of the distribution are critically important. It would seem that such a pronenessto failure in those situations would be especially problematic for options theory. As a model of

managerial decision making, it is indeed problematic. But that situation is easily rectifiable through

the use of a descriptive theory and an integrative model.

Kahneman and Tversky’s (1979) prospect theory is a model of decision making under risk

that explicitly incorporates the cognitive errors that have been found to systematically occur in

decision contexts. Kahneman and Tversky note (1979) that classic utility theory (on which

normative models are based) defines the utility function exclusively on the final states - on the

outcomes - rather than gains and losses (or the progress towards some outcome). Experiments cited

in their paper show that gains and losses

are vitally important in the decision

making process. Briefly, they discuss

these violations of the axioms of expected

utility theory in two areas: editing and

evaluation. Editing refers to the process by

which the actual probabilities and values of

the decision are transformed by thedecision maker in order to simplify the

decision at hand. These operations involve:

Coding - classification of an outcome as a

gain or a loss. This has a significant effect

on how a prospect’s value is assessed.

Humans are typically risk averse for gains

and risk seeking for losses. Figure 1

Value

Losses

Gains

Figure 1

shows such a value3 function where zero

is defined as the reference point. Further, gains and losses are assessed from a reference point. This

point may change over time to reflect current asset positions rather than the initial asset positions.

Very often, it will even be different for contemporaneous, yet distinct, prospects; Combination - the

3It is important to note that this is not a utility function. Kahneman and Tversky deliberately use the term

value function here to indicate that this is the function which results from adjustments made to a utility function.

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aggregation of similar events into one event; Segregation - the disaggregation of events by

removing common features; lastly, Cancellation - the discarding of components that are identical

between any set of decisions.

It is not the intention of this paper to present an in-depth discussion of prospect theory,thus, without further background and without proof, the following formula is offered:

V ‡ x , p; y , q Ž = π ‡ p Ž v ‡ x Ž + π ‡ q Ž v ‡ y Ž

The first scale, π, attaches to each probability a decision weight π ‡ p Ž . π is not a measure of

probability and it is most likely that π ‡ p Ž + π ‡ 1− p Ž < 1 . Figure 2 graphically describes the

decision weights. The second scale assigns to each outcome, x, a value v ‡ x Ž which represents the

subjective value of thatoutcome from the

current reference

point. V represents the

value of the prospect

(or choice)

Figure 2

Decision Weight

π( p)

Stated Probability p

A Hypothetical

Weighting Function

0.0

0.5

1.0

0.0

0.5

1.0

between x

with probability p and

y with probability q.

Whereas expected

utility theory defines

the value of a choice

on the outcomes,

prospect theory

defines the value of a

choice on the

prospec t s . Tha t

terminology most

appropriately reflectsthe decision makers

“prospect” or

feeling for a choice, rather than some purely calculated number. Simply put, this prospect

formulation relaxes the expectations principle in utility theory and the editing procedure allows the

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violation of the substitution axiom.4

The areas in which prospect theory differ from expected utility theory are perhaps most

apparent by observing Figures 1 and 2. The value function [Figure 1] systematically

overemphasizes the relative importance of losses. This may explain, for example, why people areeager to purchase insurance contracts even though many are priced inefficiently ( i.e., premium

loading). It also incorporates a reference point. This incorporates the experimentally supported fact

that people often behave differently at different points. A company may initially choose a project

with a positive NPV. After receiving the positive NPV ( i.e., the value of the firm has increased), the

firm is presented with the identical project again with the identical expected value. The firm may

reject the project this time because it could deem the potential loss to great and wishes to protect its

recently acquired profits. The reference point of the decision maker has shifted to reflect the impact

of recent decisions.

With similar analysis of Figure 2, one may see the problems most important to an options

approach: probabilities. Decision makers tend to over-weight small probabilities, but under-weight

very large probabilities. Thus, if the ruin probabilities from accepting a certain project are near zero,

the decision maker may treat them as much greater than zero - despite the fact that the expected loss

in such an event may be substantial. Because the option theoretic approach, if applied quantitatively,

is critically dependent on the probability distribution assumptions (in a continuous model) and on

the probability assignments (in a discrete model), systematic deviations will color the results of an

options model unless the decision maker is made aware of these tendencies.

AN INTEGRATIONISTMANAGERIAL DSS

Management is increasingly recognizing the importance and power of using information

systems to aid the decision making process. Because this is the case, it is likely that managers can

easily find or create a system which analyzes investment and strategic opportunities within the

confines of NPV/options theory/expected utility theory. This paper has already discussed thepotential for danger in such an approach. It is important not to lose sight of the behavioral response

that is only natural among managers. By having a model which alerts the users to deviations from

4It is sufficient for the purposes here to define the expectations principle as requiring the expected value of

x, E ‡ x Ž= p A x + ‡1− p Ž A 5 x . The substitution axiom is violated if ( y, pq) is equivalent to ( x, p) then ( y, pqr ) is

preferred to ( x, pr ), where p, q, andr 0 0 ,1 . x and y are outcomes and { p, q, r } are probabilities.

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the normative model which have causation in cognitive errors, decision makers can learn from their

mistakes, understand the process of knowledge and decision making, and improve the product of

the decision making process. This section details several instances in which an option theoretic

model will conflict with the commonly expected intuitive response or prospect theoretic model.

Among the most prominent examples is adjustment in the treatment of probabilities. One of

the most valuable benefits of an options approach is its ability to capture value that lies only in

possibility, not probability (Kogut and Kulatilaka (1994b) refer to this as investing in opportunity).

That is, it allows firms to benefit from highly volatile, relatively unlikely events because they face no

downside risk (they don’t have to “exercise” the option). Consider the choice (prospect) of

investing in a project which would pay off 100 with probability 0.03 and 0 with probability 0.97. In

Kahneman and Tversky’s notation, this would be represented (100, 0.03). The expected value of

such a project would be 3 (100 x 0.03). Thus, if the project were to begin immediately (no

discounting) and the cost of entering into the project was 2, the project should be approved because

it has a positive NPV of 1 (3 - 2).5

Clearly, there is the potential for great value in that project. However, a manager is likely to

treat the small probability differently. During the editing phase (in a prospect theoretic model) the

decision weight assigned to the prospect would cause the probability to be rounded up. Decision

makers tend to overweight very small probabilities. This may lead to excessive optimism about the

project and a willingness to overpay to obtain the investment.

Another critical deviation from an options approach is the treatment of gains and losses.

NPV/options analysis uses a fixed reference point from which all other calculations are measured.

In addition, options theory suggests that it is valuable to consider incremental investments or

“platform investments” (Kogut and Kulatilaka, 1994b). The value here is derived from the fact that

such investments represent low entry costs should a new area become profitable or strategic in the

future. That is, there is potential and no downside. The cost (or premium) for such an option would

be the minimal investment required to maintain a presence.

From a behavioral standpoint, however, managers may not actually see the benefits of such

an approach immediately. Consider the following example. Management decides that Market X will

be an important market in the future. Therefore, they decide to invest some small amount in a

fledgling development firm. They sustain the smaller firm with the minimal capital necessary for

5Barring any other considerations such as payback period requirements, internal rate of return criteria, etc.

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several years with no tangible results yet - but still opportunity. The options approach would see the

annual payments as simply the premium for the right to renew the options contract for another year.

However, management may begin to shift the reference point this decision is being analyzed from.

Although normative models ignore sunk costs, human decision makers many times do not. The

repeated payments to the smaller firm begin to add up to the point where the potential benefits stillinherent in the smaller firm are overshadowed by the sunk costs and the new reference point. The

reference point may now indicate that a higher level of profitability is expected from the smaller

firm even though nothing in principle has changed. If that higher level of profitability is not

forthcoming, the larger firm may terminate the contract.

Lastly, consider the case of a firm Q. Firm Q is in a market that has become unprofitable. It

is beginning to lose significant amounts of money with no end in sight and is considering exiting.

There is the possibility, however, that the government may label the industry Q is in a “strategic”

industry for the U.S. and extend subsidies to the firms in the industry. These subsidies would

restore the firm to healthy profitability. However, there is only a 20% chance of that happening. If

no subsidies are forthcoming, Q will lose 100 per year until it goes bankrupt or exits. If the

subsidies are enacted, the profits will be 350 per year. Assume the value of the firm is 100. Thus,

the prospect is ((350, 0.20; -100, 0.80); (ε, 1.0)). The expected value of this choice is negative if the

firm stays and marginally positive if it leaves. An options approach may suggest that the firm

withdraw the majority of its operations, but leave a “representative” in place should the favorable

legislation actually occur. If it does, the firm could immediately get back into the industry and enjoy

sizable profits.

However, given the size of the potential gain in this case (3.5x the value of the firm), many

managers would be tempted to stay in the industry and attempt to get the larger gain. Prospect

theory specifies that utility functions for losses are steeply sloped and represent risk-seeking.

When people begin to lose money, they become less conservative. They try and “double up” on

investments to recover lost money. If managers were to follow such a model, they would stay in the

market until they either received the subsidy (statistically unlikely) or until the value of the firm was

diminished to such a degree that they had to choice but to leave or go bankrupt.

In each of these approaches, one can see the clear cut benefits of the options approach over

traditional NPV analysis. The search of possibility and opportunity is a powerful source for

creating value for firms. Managers who correctly use real options models can generate significant

value with their decisions. However, there is the potential for great misuse as well. The three cases

discussed here outline specific examples in which managers who do not know better can be led

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astray by following the options approach.

If managers routinely used a DSS which had the capability to evaluate these decisions in

parallel with normative and descriptive models, managers would be alerted to these traps before any

damage was done. Further, even if managers were uneasy about the output of an options modelalone, such a model gives no basis for defensible reasoning, or argumentation as Kimbrough

(1994) phrases it. The descriptive model gives managers some tangible evidence as to where and

why they make mistakes and how such mistakes can be avoided in the future.

CONCLUSION

This paper has outlined the structure of a DSS for managerial decision making. By

incorporating existing models of normative and descriptive decision making in investment analysis

and strategic planning, managers free themselves from the constraints of the black box. The DSS

becomes a tool to think with, rather than the “magic answer” generator.

Options theoretic models of decision analysis are extremely useful in managerial contexts

because so many of the decisions managers make involve estimating the potential of a project and

the possibility of events not considered yet. It is virtually impossible to incorporate such insight in

the traditional NPV framework. By considering the value these strategic real options give managers

in terms of flexibility, the overall value of firms can be increased.

This paper has also shown, however, that the potential for misuse is great. For managers to

effectively use options theory in the analysis of strategic decisions, they must have a careful

understanding of the biases and flaws in their heuristic decision making that can potentially distort

the value of the real options. There is no clearer way to visualize and control those distortions than

by delineating explicitly the steps of each model and identifying the incongruence.

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REFERENCES

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Cross, J. G. A Theory of Adaptive Economic Behavior (Cambridge: Cambridge University Press,1983).

Dixit, A. K. and R. Pindyck. Investment Under Uncertainty (Princeton, NJ: Princeton UniversityPress, 1994).

Fishburn, P. C. Normative Theories of Decision Making Under Risk and Under Uncertainty. In D.Bell, H. Raiffa, A. Tversky, eds., Decision Making: Descriptive, Normative and Prescriptive Interactions (New York, NY: Cambridge University Press, 1988): 78-98.

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Kahneman, D. and A. Tversky. Prospect Theory: An Analysis of Decision Under Risk. Econometrica 47 (1979): 263-291.

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Simon, H. A., et al. Decision Making and Problem Solving. Interfaces 17 (1987): 11-31.

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