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?The purpose of this research paper is to demonstrate the functionality of traditional decision making procedures, under risk, in the context of the general naval and synonymous organizations combat tactics. First I will briefly explain the objective and types of decision theory. Second, I will explain what decision under risk is and the most reliable theoretical solutions for this problem and the types of situations it presents. Third, I will explain decision making, in the guidelines of the navy, and other similar organizations, in regards to combat. Fourth, I will provide an example of a warfare situation, and then show how decision theory and decision making in warfare conflict or not. Fifth, I will explain what a one-time game is and how it can or cannot apply in war, and if not what type of game is it. Sixth, I will explain how cultural norms can impact a conflict and change the way prescribed combat rules apply. Seventh, I will tie in all my discoveries and provide a conclusion on what I have found of warfare operations and its relation to normative decision under risk. ?First it is important to briefly describe the intent and guidelines behind decision theory as whole. Most of decision theory is normative, meaning how, theoretically, people ought to make decisions, and is concerned with deciding the action that will leads to the best possible outcome. What is meant by best, is the outcome that will provide the most utility or usefulness for the decision maker (Peterson, 3-4). However, people sometimes do not behave rationally and therefore do not follow the rules of normative decision theory and instead follow their ownapproaches. The study of this non-normative approach is descriptive decision theory and is focused on what people will actually do. Since the normative approach is focused on theoretical and the descriptive on practical, the two can often be tested against each other, as I will later in the context of warfare decision theory (Peterson, 3-4). ? First, it is important to demonstrate what a decision under risk is. Decision making under risk is essentially when the decision maker knows the probabilities of the outcomes, a simple and convenient example is flipping a coin and knowing that each of the two outcomes, head or tails, has a 50% chance each of occurring, with each outcome having some type of value behind it(Peterson, 64). Now when faced a decision under risk the main approach to handling it is maximizing the expected utility, keeping in mind the level of risk aversion the decision maker has. Before continuing I would quickly explain that utility is something with usefulness, in other words the ability of something to satisfy the decision makers particular needs or wants. Therefore the proposed theory is to choose the outcome that will result in the greatest expected value (Peterson, 65-8). However it must be kept in mind that some people have certain levels of aversion to risk and in a decision where there are accompanying risks associated with the greatest expected utility the risk averse might choose the outcome with less or no risk and the risk seekers will ignore the risk and focus on the expected utility (Peterson, 179-181.  Furthermore this theory features two different supporting arguments. The first argument, the Law of Large numbers, states that in the long run you should maximize the expected utility due to the mathematical principle that the results obtained from a large number of trials should be close, and become closer to the expected value (Peterson, 71-73). The second argument is an axiomatic approach, which focuses on independent decisions that will not last on the long run like the Law of Large numbers. The first axiom follows that the if all outcomes have a utility u then the utility of the act is u. the second states that if one act has more utility than the other than the utility of the first act trumps the latter, the third axiom states that a decision can be split into equi-probable states, and the fourth axiom states that if the utility of one act has dropped the overall utility can be compensated by adding some utility to the other outcome (Peterson, 74-7).  Furthermore choosing preferences among the various outcomes and their utilities can be explained by another set of four axioms completeness, asymmetry, transitivity, and negative transitivity to ensure the rationality of the agent’s choices. To briefly explain these axioms,completeness is when the decision maker has well defined preferences and can choose a preference between two decisions. Asymmetry holds that if a preference is true the opposite of the preference is not true. Transitivity holds that the preferences are consistent across any three options. Negative Transitivity is similar to transitivity but implies that indifference is transitive and it makes a higher claim to preferences across a few outcomes (Peterson, 92-4). Overall normative decision theories decision under risk, and its approach of expected value compared to how risk averse the agents are, is a wonderful too that promotes a wonderful theoretical way of making decisions under risk. Now I will demonstrate decision-making in combat for the navy and military and compare and contrast them with normative decision theory. The navy calls their evaluation of risk and decision making process as Operational Risk Management (ORM), which is a system that is characterized by them as a decision making tool used by all naval personnel to increase the effectiveness of their decisions by mostly focusing on identifying, assessing, and managing risks and not the utilities (U.S Navy, 1). The decision making process consists of five steps Identifying Hazards, Assessing Hazards, Making Risk Decisions, Implementing Controls, and Supervision. Before I begin let me quickly explain that a risk is expressed in terms of hazards, and a hazard is something that could potentially or actually cause various levels of damage, some examples being injury, death, property damage, mission degradation or environmental damage (U.S Navy, 2-3). The first step to this process, Identifying Hazards, involves creating an outline of all the major steps that need to be conducted in the operation, while simultaneously listing all of the hazards that could possibly be associated with each step of the operation, and their unique causes(U.S Navy, 2-3). The second step, Assessing Hazards, involves determining the associated degree of risk of the hazards in terms of the probability of them happening and the severity of the hazard itself. The third step, Making Risk Decisions, involves starting with the most significant risk and then selecting controls, measures that eliminate or reduce hazards, which will limit the risks as much as they can for a mission with the least amount of losses, basically choosing the tactics that would best suit the situation (U.S Navy, 2-3). The fourth step, Implementing Controls, is the actual employing of controls in three categories, engineering (e.g. temperature control), administrative (e.g. policies, training, and programs), and personal protective equipment (e.g. bulletproof vest, shields, fire resistant garments). The final and fifth step, Supervision, involves always having a superior at ready that can monitor for changes in the situations, whichmay require taking corrective action and actually implementing the plan (U.S Navy, 2-3). Now that the ORM process has been announced it is important to point out that there are various situations where there might be time constraints, which call for slight changes in the level of the process. In a time-critical situation the planning is done by experienced and trained operatives, whose level of training has allowed them to do a mental evaluation of the same exact five step process, despite being in a time-compressed situation. In an environment, which is, less critical officers use available data, diagram and analysis tools, and simulations to help evaluate the probability and severity of hazards within an operation. (U.S Navy, 3)Next it is important to discuss how the ORM focuses on four risk principles, Accepting Risk When Benefits Outweigh The Cost, Accepting No Unnecessary Risk, Anticipating And Managing Risk By Planning, and Making Risk Decisions At The Right Level, that help evaluate the formalization of risk within their operation guidelines (U.S Navy, 4-5). Accepting Risk When Benefits Outweigh The Cost essentially means that no matter what type of combat situation there is, there will be some type or risk associated with every mission and usually it has been found in war that with greater risk came a greater amount of gains. However it is important to note that ORM in the navy does not focus on gains or utilities in any way. In fact, in a war the missions are usually chosen for political and financial reasons that have been determined worthwhile by the upper echelons of the government or are simply so morally reprehensible that there is no choice but in preforming a mission, so the troops decision theory is not concerned with whether or not the utility of a mission is worthwhile or not because they would not be risking their lives unless for a good reason in the first place. Therefore as previously stated the ORM is primarily focused on just calculating and limiting risk and not on the utility of an operation (U.S Navy, 4) (Mason). The next principle, Accepting No Unnecessary Risk, is simple in that it points out that you should only accept risks that are necessary for the success of the mission, but becomes complex when you consider how you evaluate whether a mission is too risky for completion. For the most part it is found that if you find yourself in combat situation where you and you’re team are at risk of being killed you abort the mission, but at the same time there have been many situations in history where such safety was disregarded, such as the Battle of Normandy where the loss of life among the Allies was extremely high but the mission was carried out anyway because of the significance of the utility of severely weakening Germany was worth it. Therefore accepting risk for the sake of the mission is completely dependent on the situation that the troops are found in (U.S Navy, 4) (Mason). The third risk principle of ORM, Anticipating And Managing Risks By Planning, mainly states that no missions should be considered unless there is some modicum of information known about the potential hazards, essentially operations are usually never done blindly or colloquially on the fly. However in special cases where the information had been misleading or the response of the enemy combatants changed the situation, the highest supervising officer is in charge of doing a time-critical ORM of the situation and from there estimate whether they could complete the mission before all of their troops were killed and therefore accomplish nothing, or try and limit risks as much as possible with various controls, or retreat. What is important to note is that officers are usually expected to continue missions even in cases of a these type of hiccups due to the level of tactical training they should have simply retreating can have severe repercussions from commanding officers unless, as said before, there was literally no way of completing the mission before all of the troops were killed(U.S Navy, 4) (Mason).  This leads into the fourth and final risk principle, Making Risk Decisions At The Right Level, which simply follows that the leading officer must be ingrained with training, situation awareness and ORM experience to lead the troops, and know that in a situation where the risk management becomes too large and they have the ability to contact superior officers they should communicate with them to decide the best course of risk aversion for the operation (U.S Navy, 4-5). The final aspect of the ORM is the Risk Assessment Matrix (RAM), which is a system that uses two domains of hazard severity and mishap probability to create a primarily ordinal system of assigning hazards. The necessity of an ordinal over a cardinal system is that in a conflict the sheer amount of risks and hazards, and the possible surprises that come from the back and forth planning, attacking, and counter attacking of two enemy forces, who can only guess with some unquantifiable surety of each others tactics and responses, limits the ORM from using mathematical sureties (U.S Navy, 5) (Mason). The first domain, Hazard Severity, is essentially an assessment of the consequences that can occur as a result of a certain hazards. These consequences are mainly based on the degree of injury, death, illness, property damage, and loss of assets and is categorized by the severity of the hazard and formalized with roman numerals.  Category I involves death and/or damage to national interests. Category II involves severe injuries and illness and degradation of resources or environment. Category III involves minor injury and illness and degradation of resources or environment. Finally, Category IV involves negligible damage to resources, troops, and national interests (U.S Navy, 5). The second domain, Mishap Probability, is the probability that a specific hazard will result in a consequence, based on research of things like location exposure, relations with surrounding populations, experience of troops in a combat situation, and previous conflicts with enemy combatants. These probabilities are assigned in a system of sub-categories of A-D, D being the least likely to happen and A being the most (U.S Navy, 5). These two domains are then combined into something called the RAC or Risk Assessment Code, a table as shown in Figure 1-A, which uses these numbers, 1 being the most severe with 5 being the least, to prioritize which hazards should be focused on first in establishing controls (U.S Navy, 5).?An excellent combat example that embodies this ORM is the Battle of Bismarck Sea, specifically the Rabaul- Lae convoy situation, where General Kenney the Commander of the Allied Air Forces was expected to ambush a Japanese troop and supply convoy traveling from Rabaul to Lae. Step 1: The Mission General MacArthur ordered Kenney to intercept and inflict as much damage as possible on the convoy, keeping in mind that there was the possibility of skirmishes and naval mishaps (Haywood, 367). Step 2: Rain and poor visibility were predicted north of New Britain, and clear skies south of New Britain, while it was assessed that the Japanese would go of two routes from Rabaul to Lae (Haywood, 367). Specifically, they could sail north or south of that island, each route requiring three days of travel, while Kenney could respond to these hazards by sending planes north or south of these combatants resulting in four possible conflicts among them each with specific risks of visibility and unique combat responses that could increase or decrease the involved risks depending on their states, see figure 1-B(Haywood, 367). Step 3 & 4: Identifying, considering, and evaluating the four possible outcomes Kenney’s control of the situation, to limit risks and increase success, had him concentrating his reconnaissance on the northern route, where two days of bombing were surely to happen regardless of what the Japanese choose to do, see figure 1-B (Haywood, 367-9). Step 5: Kenney having completed the previous tasks and following the orders of his superiors, and being a highly trained officer himself, went through with his decision and concentrated his reconnaissance aircraft on the northern route (Haywood, 368-9). Now it is important to explain how ORM and this specific example seem to follow, for the most part, the basic guidelines of normative decision theory under risk. As stated before, decision under risk mainly involves having some knowledge and sense of the calculation of the risks involved, and then basically choosing the outcome that maximizes the expected value of utility. Now before continuing I believe it is important to note that one large difference between these operation theories and decision theory is that they do not focus on calculating the utilities of their decisions, especially through the use of the axioms, they just focus on choosing the outcome that will most likely achieve that utility with the lowest possible risk involved, truly higher ups like the Mission General MacArthur determine the utilities they require in a war through politics and common sense. Anyway from there it is, simple to see, that decision theory under risk and the principles of utility, the ORM and battle example focus all focus on calculating the risk in some fashion, usually on an ordinal scale in the operations case, and then among these possible actions choose the one that maximizes the expected utility. Operations managements main differences from decision theory under risk is that they go a bit further by considering how to possibly lower and manipulate risks and also having very arbitrary views of risk aversion, switching back and forth depending on the situation and the importance of the utility involved. Another aspect that is pertinent to warfare is the concept of one-time games. One-timegames are a concept in philosophy where there is a consideration that the agents will react differently if or if not there is a continued interaction among players. Essentially the theory is that in a prolonged series of games agents might act differently based on previous information and experiences gathered from the continued conflict, then they would act in a singular game with no more interaction afterwards (Nynka). In regards to war however the possibility of such a phenomena is unlikely. War tactics are completely based on previous battles amongst contending agents and even if it were possible for one agent to beat another agent in a single game, the outcome of that game will have been seen, analyzed and used by other agents in the world,which will in turn impact in other future games (Nynka). War is in fact usually considered as a two-person zero-sum game. Two-person meaning the conflict is between two opposing groups and zero-sum meaning that the utilities at the end of the game are give only to the players, with one group gaining the good outcome and the losing group the bad outcome (Haywood, 371).Essentially in war one must always be careful to never seem overly cruel or to fight irrationally or they risk possibly opening themselves up to more difficult conflicts with other agents (Nynka).Another consideration to consider with combat is the application of qualities such as cultural norms somehow affecting the guidelines of battle decision theory. Wars are often fought over differences in religion, cultures, and beliefs and therefore these views that are being fought over tend to infect the tactics of the agents fighting. For example in World War II the Japanese were known to fighting with a tactic called kamikaze where soldiers fought to the death in their conflicts, or even went a step further sacrificing themselves and their planes to maximize enemy damage. This style most likely arose from the ancient cultural belief of Bushid?, the code of the samurai, it stressed loyalty, strength, and honor to the death and under this ideal, if a warriorfailed to uphold his honor he could only regain it by performing seppuku (ritual suicide)(Nynka). Another example is the ideal in German culture that they idealized their own lives, and in a case where their loss was imminent they did the opposite of the Japanese and surrendered themselves to American soldiers. This cultural norm was so ingrained that American soldiers responded to it, and changed their battle tactics by in fact not forcing the Germans to relinquish their weapons when surrendering, a traditionally risky move that goes against the whole basis of operation management, so that their officers could control any of their soldiers who could possibly get out of line and risk the total chance of surviving for the entire German troop (Nynka). Basically what this all means in regards to operations management is that subjective principles such as cultural norms, that seem irrational and stand against all of normative decision theory, may in fact hold great sway over the tactics that the agents may act on and respond to (Nynka). ?Overall warfare is a horrible and usually chaotic affair, from all standpoints, and from what I’ve seen this stringency of following the rules seems, to me, to be man’s effort to apply some sort of foundation of order to what is a seething mesh of violence. In fact without these strict guidelines wars would, I feel, fall into the our ancestors original primal battles where only strength was measured in base acts of violence, where now calculation, cunning and precision can do so much more. Furthermore war has started and been evolving since the beginning of time and the fact that it is so similar to decision theory is not a surprise, because it seems to me it is the ultimate game, something written in history and or DNA, and is the best example and original reason for why philosophers studied something abstract as decision theory in the first place.