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Graduating from the Infantry. Officers Basic Course, Ranger School, and Airborne School, his first assignment in. 1980 was at Fort Davis, Panama, where he ...
Typology: Summaries
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THESIS PRESENTED TO THE FACULTY OF THE SCHOOL OF ADVANCED AIRPOWER STUDIES, MAXWELL AIR FORCE BASE, ALABAMA, FOR COMPLETION OF GRADUATION REQUIREMENTS, ACADEMIC YEAR 1995–96.
Air University Press Maxwell Air Force Base, Alabama
August 1997
Disclaimer
Opinions, conclusions, and recommendations expressed or implied within are solely those of the author(s), and do not necessarily represent the views of Air University, the United States Air Force, the Department of Defense, or any other US government agency. Cleared for public release: distribution unlimited.
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Abstract
This is a study of the applicability of prospect theory to military decision making. Prospect theory posits that the decision maker’s reference point determines the domain in which he makes a decision. If the domain is one of losses, the decision maker will tend to be risk seeking, if gains, then he will be risk averse. The author proposes that if prospect theory’s propositions are correct, then it may be possible for the decision maker, by assessing his own domain, to make better informed decisions. One implication of this study is that if the decision maker can do the same for a subordinate or for an enemy, he may be better able to predict their responses in a given situation. The project’s goal is to develop a framework for assessing risk propensity. It does this by first describing the military decision-making process and concluding that it is a rational decision-making process. Second, this study describes prospect theory and matches the key aspects of the theory with the military decision-making process. Third, it proposes a framework for assessing risk propensity. The theory is tested in a case study of Gen Dwight D. Eisenhower’s 1944 decision to launch Operation Market Garden. This decision is analyzed in terms of Graham T. Allison’s three models for decision making and prospect theory to determine which model or theory seems to provide the best explanations for Eisenhower’s decision. The last chapter applies the risk propensity framework to the case study to test if it can predict risk propensity and its impact on decision making. The author concludes that prospect theory’s propositions are valid and that this theory provides a prescriptive way to consider decision making under risk. Although prospect theory does not predict the choice a decision maker will select, it should reveal his bias toward a risky or overcautious solution. This tendency may limit the types of alternatives developed or considered. The framework developed for determining risk propensity provides insights but its use may be limited by the time and information available. The author found that assessing the true reference point from which a problem is considered is problematic. Also, that knowing one’s risk propensity does not necessarily enable the decision maker to change his frame of reference or to consider the choice problem from different perspectives. Finally, additional study should be conducted in this area to further validate prospect theory’s propositions and refine techniques for improving decision making under risks.
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About the Author
Lt Col James V. Schultz (BS, USMA, and MPA, Auburn University at Montgomery) was commissioned through the United States Military Academy, West Point, New York, as an infantry officer in 1979. Graduating from the Infantry Officers Basic Course, Ranger School, and Airborne School, his first assignment in 1980 was at Fort Davis, Panama, where he served as a platoon leader, company executive officer, and as the battalion support and scout platoon leader. After completing the Infantry Officers Advanced Course, he was stationed at Fort Jackson, South Carolina, where he served as a company commander and battalion executive officer. Other assignments were as a platoon and company observer/controller at the Joint Readiness Training Center, an operations officer for the 1st Battalion 509th Airborne Infantry Regiment and the 5th Battalion 9th Infantry Regiment, a brigade logistics officer at Fort Wainwright, Alaska, and as the assistant chief of staff for training for the 6th Infantry Division (Light). In August 1996 Colonel Schultz was assigned to the US Army I Corps at Fort Lewis, Washington, as a plans and exercise officer.
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Introduction
If we now consider briefly the subjective nature of war—the means by which war has to be fought—it will look more than ever like a gamble.... In short, absolute, so-called mathematical, factors never find a firm basis in military calculations. From the very start there is an interplay of possibilities, probabilities, good luck and bad that weaves its way throughout the length and breadth of the tapestry. In the whole range of human activities, war most closely resembles a game of cards. —Carl von Clausewitz On War, Book One
If war is a gamble, then the operational commander must stack the deck in his favor. If he is wise, he accepts calculated risks but not reckless ones. With the former, odds are in his favor and he wagers only what he can afford to lose. But the commander who gambles plays against the odds and if the wager is too high and if the outcomes of an action go with the odds, he loses more than he can afford. How does he figure the odds? He uses his estimate of the situation, his experience, and his knowledge of himself and the enemy. Before hostilities, the commander assesses the situation and determines his goals and objectives. These are based on the guidance he receives from the national command authority and his higher headquarters, his personal understanding of the situation, and input from his staff. A multitude of players influence the commander as he develops alternatives to accomplish his goals. In turn, he influences what actions are to be taken by others through his discussions with those above him and beside him and the guidance he provides to those below him. As the commander formulates his plans, he considers the risks involved in the actions he might take. We assume the commander will select those actions that have the highest probability of success, that he is a rational actor. He will look at the costs and benefits of the proposed alternatives and select the one that maximizes benefits and minimizes costs. If this were true, then a commander’s risk propensity, his willingness to accept or decline risks, would only be a function of how he perceives the odds. It does not seem that simple in practice. A commander who is losing may be inclined to accept more risks than one who is winning. Gen Douglas MacArthur’s decision to conduct the Inchon landing during the Korean War serves as an example. Would he have considered the potential gains worth the risks if United States (US) forces were not about to be overrun at the Pusan perimeter? The purpose of this study is to determine how the situation
affects the commander’s risk propensity. The focus will be at the strategic and operational levels of decision making. The study discusses limitations of the military decision-making process with respect to the influence of risk propensity on output (decisions). Ultimately, a process for identifying risk propensity and its influence on decision making will be proposed. Military and political leaders assume that they make their decisions rationally. However, most decisions, when reviewed after the fact, clearly indicate that other nonrational factors affected decision making. Specifically, significant decisions do not always appear, in retrospect, simply to have maximized gains. For example, Graham T. Allison in his book Essence of Decision: Explaining the Cuban Missile Crisis,^1 attempts to explicate President John F. Kennedy’s actions in terms of three models: Rational Actor, Organizational Process, and Governmental Politics. Each model adds new insight into both President Kennedy and his administration’s decision-making process, but none explains or predicts how the situation itself may predispose decisions. Prospect theory (PT) postulates that the situation in which an event occurs significantly affects the decision-making process. In short, prospect theory predicts that people are more likely to take risks in bad situations and more likely to be cautious when times are going well. Understanding how the situation affects decision making should help decision makers to keep options open that otherwise might be discounted, options that if considered rationally, might lead to better solutions. This study argues that prospect theory allows a decision maker to assess his risk propensity. It follows that given the same information about a subordinate or an adversary in a given situation, one should also be able to assess others’ risk propensities. In the case of subordinate commanders, this knowledge could provide forewarning and possibly facilitate intervention, as appropriate. Toward an adversary, it should facilitate predicting enemy reaction to a selected course of action (COA). Intuition alone might suggest to some readers that a decision maker’s mind-set can influence the way he thinks about resolving a problem. This study shows that PT provides a means to determine that mind-set in terms of risk. This is important, because, even though a situation may rationally call for a particular solution, the decision maker’s perception of and reaction to risk may drive him to another choice.
Current joint doctrine provides a deliberate decision-making model that can be described as normative and rational. Doctrine describes how decisions ought to be made. The process is logical, scientific, and sequential. Doctrine recognizes the importance of the commander. It implies that the genius of the commander in applying operational art within the decision-making process is the essence of decision making. The apparent dichotomy between what “ought to be” and “what is” highlights the shortcomings of a purely rational normative model for military decision making. This study outlines a prescriptive process for identifying the impact a situation can have on a decision maker’s risk propensity and hence a means to assess that impact. Chapter 2 develops a framework for assessing the predictive power of prospect theory, identifies key predictive variables within the theory and
Military Decision Making and Prospect Theory
Introduction
The leading prescriptive and explanatory theory of decision making under risk is the expected utility model. For example, Allison used three models for analyzing the Cuban missile crisis.^1 Each provided a different perspective of the decision-making process but all assumed that decision making was ultimately rational. Allison’s Rational Actor model assumed a unitary decision-making individual or body and a rational decision-making process that was centrally controlled, completely informed, and value maximizing.^2 His Organizational Process model considered the dynamics of organizations and their impact on the decision-making process. His third and final model, Governmental Politics, considered the impact of decision making in a pluralistic body where compromise and bargaining lead to the selection of a decision. The second and third model seek to explain limitations to rational decision making but do not question the basic model’s validity. Prospect theory does not deny that individuals maximize utility but posits that this function is nonlinear. Decision makers tend to overweigh utility values while underweighing probability values. Expected utility models expect that preference ordering is constant but prospect theory posits that preference ordering can vary. This variance is caused by a key assumption of PT. Outcomes are not thought of as absolute states but as changes from a reference point. The reference point is determined by the way the decision maker edits and evaluates the decision problem. Editing and framing are dynamic processes, thus reference points can change. The changes in reference point can lead to changes in the decision maker’s perception of a given outcome as a gain or a loss. It is domain, gains or losses, that determines the decision maker’s risk propensity which in turn influences his decision. This chapter looks at the military decision-making process and concludes it is in theory a rational process based on expected utility. Next PT is described and its propositions are explained. The chapter concludes with recommendations about how to integrate key propositions of PT into the military decision-making process. In the next chapter, the resulting framework establishes the criteria for determining a decision maker’s frame of reference and risk propensity and is the basis for evaluating Eisenhower’s decision to approve Operation Market Garden in 1944.
Key Definitions
Goals and Objectives. The purpose toward which an endeavor is directed. Goals and objectives are translated into a preference function, which represents the value of alternative sets of consequences.^3 Gains or Losses. Gains or losses, in prospect theory, represent changes from a neutral reference outcome. Decision-making Process. A formal or informal procedure used by an individual or a group to analyze a problem, identify objectives and goals, develop alternatives, and determine consequences for each alternative. The result is a choice or decision. Decisions (Products). If the decision maker wants to optimize, the decision is a choice among the alternatives considered that seeks to maximize benefits or minimize costs. The decision maker evaluates options against each other to determine which choice has the most beneficial or the least detrimental outcome. On the other hand if the decision maker is interested in only finding an alternative that satisfies some external criteria, that person may select a choice that is merely acceptable.^4 Herbert Simon called this type of decision making “satisficing.” In either case, the choice is considered in terms of the outcomes each alternative is expected to produce based on the decision maker’s preferences and expectations. Rationality. Rationality refers to consistent, value-maximizing choice within specified constraints.^5 Decision makers choose among alternatives on the basis of their expected consequences, but those consequences are not known with certainty.^6 “Limited rationality recognizes that not all alternatives are known, that not all consequences are considered, and that not all preferences are evoked at the same time.”^7 Thus only a limited number of elements are considered and then only sequentially rather than simultaneously. The concept of limited rationality recognizes that human limitations do not allow exhaustive consideration of all alternatives and consequences. Further, as problems increase in complexity, information will be increasingly incomplete. Risk/Risk Propensity. Risk may be viewed as the potential for failure based on subjective evaluation of the probability for failure or success for a particular decision problem. Failure in this definition means that goals and objectives are not reached (outcomes fall short of expectations) or important criteria are not met. A risk averse decision maker will tend to select a sure gain over a smaller chance to gain an equal or larger amount. A risk-seeking decision maker will tend to select a choice that provides a chance to gain a larger amount over a smaller, more certain gain. Risks are the existence of factors beyond the decision maker’s control that affect the outcomes of choices. Degree of risk is a function of the size of the potential loss and the probability of that loss. In every risky decision something is at stake. The greater the stake, the greater the risk. There is some probability of loss. The greater the probability of loss, the greater the risk. Loss means becoming
its feasibility, adequacy, and suitability. He then compares identified advantages and disadvantages based on considerations specific to joint operations, other critical factors, and mission accomplishment.^15 Based on the results of the comparisons, the JFC selects a COA to be translated into a “concise statement of what the force, as a whole, is to do and [to] explain, as may be appropriate... when, where, how, and why.”^16
Expected Utility Theory
The estimate of the situation formalizes what is essentially a rational decision-making process for the military commander and his staff. The decision maker is expected to make choices that satisfy the requirements of consistency and coherence. The assumptions are that this process is consequential and preference based. In other words, action depends on anticipation of the future effect of current actions. Thus, COAs are considered in terms of their expected consequences. Additionally, COA selection is based upon the preferences of the decision maker, and COAs are compared in terms of the extent to which their expected consequences appear to serve the preferences of the decision maker. The preferences of the decision maker result from his experiences which form his norms, habits, and attitudes and from analysis of the context of the problem itself. The utility of a risky prospect is equal to the expected utility of its outcomes, obtained by weighting the utility of each possible outcome by its probability. A rational decision maker will prefer the prospect that offers the highest overall utility.^17 The following lengthy quote shows the utility of a risky prospect mathematically and integrates the assumption that value is seen in terms of final assets.
Decision making under risk can be viewed as a choice between prospects or gam bles. A prospect (x 1 , p 1 ;....;xn,pn) is a contract that yields outcome xi with probability pi, where p 1 +p 2 ...+pn=1. To simplify notation, we omit null outcomes and use (x,p) to denote the prospect (x,p;0,1-p) that yields x with probability 1-p. The (riskless) prospect that yields x with certainty is denoted by (x). The present discussion is restricted to prospects with so-called objective or standard probabilities. The application of expected utility theory to choices between prospects is based on the following three tenets. (i) Expectation: U(x 1 ,p 1 ;...;xn,pn)=p 1 u(x 1 )+...=pnu(xn) That is, the overall utility of a prospect, denoted by U, is the expected utility of its outcomes. (ii) Asset integration: (x 1 ,p 1 ;...;xn,pn) is acceptable at asset position w if U(w+x 1 ,p 1 ;...;w+xn,pn) > u(w). That is, a prospect is acceptable if the utility resulting from integrating the pros pect with one’s assets exceeds the utility of those assets alone. Thus, the domain of the utility function is final states (which includes one’s asset position) rather than gains or losses.^18 The expected utility model is based on several axioms that should govern the preferences of a rational decision maker.^19 The first axiom, transitivity ,
provides criteria for choice. First, if option A is preferred to option B and option B is preferred to option C then A will be preferred to C. Second, if option A is preferred to option B, A and C should be preferred to B and C.^20 The second axiom is dominance. If prospect A is at least as good as prospect B in every respect and better than B in at least one respect, then A should be preferred to B. The third, invariance , requires that the preference order between prospects not depend on the manner or order in which they are described. Fourth, cancellation is the property that allows the representation of preferences between prospects as maximization of expected utility. It is “the key quality that gives rise to expected utility theory” and means “the elimination of any state of the world that yields the same outcome regardless of one’s choice.”^21 “The main argument for cancellation is that only one state will actually be realized, which makes it reasonable to evaluate the outcomes of options separately for each state.”^22
Allison’s Models
The following is a review of Allison’s three models of decision making. They are presented in terms of the estimate process. The rational decision-making model is the estimate process without modification. The estimate is changed for the second and third models to reflect the impact each has on decision making. They are used in the case study to provide perspective. The models give insight into the goals, preferences, and values of the key players.^23 Rational Actor Model. The decision maker follows the steps listed in table 1. That person identifies goals and objectives based on the mission analysis. The decision maker then analyzes the situation to determine strategic context, characteristics of the operational area, friendly and enemy situation, restrictions, assumptions, and deductions. Based on this analysis, the decision maker then develops COAs. Each COA is analyzed for suitability, adequacy, and feasibility. Each COA is modified as required and advantages and disadvantages are listed. COAs are then evaluated based on their advantages and disadvantages and then compared. The best COA is selected
Table 1 Estimate
based on fixed values for military operations such as the principles of war, other critical values deemed to be important, and mission accomplishment. Organizational Process Model. Unlike the previous model, this model recognizes and incorporates the impact of multiple actors. Processes internal to the decision maker’s organization are as influential in decision making as
and thus tendencies toward a particular type of solution. It is the changing of the reference point that leads to violations of the expected utility theory axioms, notably invariance. In the evaluation phase the decision maker is assumed to evaluate each of the edited prospects. Evaluation involves two scales, one linked to probability, the other to subjective value.^28
The first scale p, associates with each probability p a decision weight p(p), which reflects the impact of p on the over-all value of the prospect. However p is not a probability measure... The second scale assigns to each outcome x a number v(x), which reflects the subjective value of that outcome... The overall value V, is expressed in terms of...[these two scales].^29
The individual makes a choice either by detecting that one option dominates another or by comparing their values.^30 According to Tversky and Kahneman, prospects have the following relationships to outcomes and probabilities.
Let (x, p; y, q) denote a prospect that yields x with probability p and y with probability q and that preserves the status quo with probability (1-p-q). According to PT, there are values v(•), defined on gains and losses, and decision weights p(•), defined on stated probabilities, such that the overall value [V] of the prospect equals p(p)v(x) + p(q)v(y).^31
A typical value function (v(•)) is shown in figure 1.^32 The value function, as proposed by the authors, is defined on gains and losses. Outcomes are ex- pressed as positive or negative deviations (gains or losses) from a neutral reference outcome, which is assigned the value of zero. The curve, which is generally concave for gains and convex for losses and steeper for losses than
Figure 1. Typical Value Function
for gains, reflects that individuals respond to losses more extremely than they do to gains. Coined as “loss aversion” by the authors, it simply means that “losing hurts more than a comparable gain pleases.”^33 The S-shape of the curve also reflects another important property of PT. Marginal changes are valued less the farther they occur from the neutral reference outcome for gains or losses. This means, for instance, that an individual attributes more value to a change in gain from $100 to $200 than he would from $1,100 to $1,200, even though the difference in both cases is $100.^34 This property is also reflected in figure 1. Note that the relative differences for values v 1 and v 2 are greater than for v 3 and v 4. This is even more pronounced for values when in the realm of losses. Again, note that the relative differences for values va and vb are greater than for vc and vd. Changes in the neutral reference outcome affect preferences. This reference point is determined by how an individual frames the problem he faces. Shifts may occur by different decompositions of outcomes into risky and riskless components. The authors also demonstrate that shifts can occur by how outcomes are labeled. The effective carriers of value are gains and losses, which are relative. This means that a gain or loss is not considered in absolute values but in terms of change from the reference point. The authors observed two common patterns of preference. Outcomes stated in positive terms elicit risk averse choices and those stated in negative terms tend to produce risk-seeking choices.^35 We now come to the weighting function. The authors point out that in expected utility theory, the utility of each possible outcome is weighted by its probability. Not so for PT. Instead, the value of an uncertain outcome is multiplied by a decision weight p(p). It is a monotonic function of p but is not a probability.^36 In the words of the authors, the weighting function has the following properties.
First, impossible events are discarded, that is, p(0) = 0, and scale is normalized so that p(1) = 1, but the function is not well behaved near the end point.... Second, for low probabilities, p(p) > p, but p(p) + p(1–p) £ 1 (subcertainty). Thus low prob abilities are overweighted, moderate and high probabilities are underweighted, and the latter effect is more pronounced than the former. Third, p(pr)/p(p) < p(pqr)/ p(pqr)/ p(pq) for all 0 < p, q, r £ 1 (subproportionality). That is, for any fixed probability ratio r, the ratio of decision weights is closer to unity when the prob abilities are low than when they are high, for example, p(.1)/p(.2) > p(.4)/p(.8)... The major characteristics of the weighting function is the overweighting of probability differences involving certainty and impossibility, for example p(1.0) – p(.9) or p(.1) – p(0), relative to comparable differences in the middle of the scale, for example, p(.3)
A typical weighting function is depicted in figure 2 and demonstrates the properties as described by Tversky and Kahneman.^38 Decision weights, according to these authors, are not probabilities in that they do not obey probability axioms. They reflect the impact that the probability has on the overall value of the prospect. Decision weights measure the impact of events on the desirability of prospects and not merely the
