## Introduction

Decision making is defined as the cognitive process that results in the selection of a conviction or a route of action among an assortment of possibilities. This process of identification and choosing between various alternatives is usually subject to preference, values, and the belief system of the person making the decision. The decision-making process is generally very complex and subject to cognitive shortcomings that are inherent of the human condition (Heilman et al., 2010). These cognitive limitations are as a result of the various shortcuts that the brain in order to arrive at a decision in a timely fashion or in order to reduce the complexity of a problem. These shortcuts are commonly referred to as heuristics. These heuristics, however helpful, usually predispose one to cognitive biases. Cognitive biases are formally defined as patterns of departure from what is considered a norm or rationality in arriving at a judgment. These biases usually lead us to succumb what would be regarded as an irrational thought. It can, however, be argued that cognitive biases are an effect of a process that is very vital in helping us navigate the world around us. This process helps us navigate the world with limited information. One of these cognitive biases includes confirmation bias where, for instance, when we meet an individual for the first time, we hold preconceptions pertaining to them. This type of bias is closely related to stereotyping, where we expect a member of a particular is expected to possess specific characteristics without having any information about the individual. This preconceived information is usually useful in determining the type of person, whether he/she is a threat or whether they can be trusted, and this information is oftentimes accurate. It can thus be observed that this process, however crude, can be perfected to yield better predictions. Referring to the example of meeting somebody for the first time, it can be said that the when one gets acquainted with them, they ask leading questions which are aimed to either confirm or disapprove the initial assumptions they made about the individual.

As we have observed, the human decision-making process is somewhat complicated and possesses rational pitfalls that are inherently fallacious. When the risk factor is added, then the process is bound to get exponentially complicated. Risk, in economics and psychology, is defined as the probability for uncontainable loss of something valuable. Values subject to the loss can be abstract or concrete. Abstract benefits include physical health, emotional health, or social status (Sheth & Stellner 1979). Physical health can be financial wealth or an item of great value. Perception of risk is a subjective judgment that people make about the possibility and the severity of a risk. This subjective judgment is subject to flux inter-personally. Any human undertaking can be potentially risky and with varying degrees. The individual must thus be at capacity, in the event of a risky decision, to evaluate all the available options and select the optimal solution all things considered. This is thus the aim of this paper, to explore this aspect of decision making in the presence of the risk factor.

Before we can get into utility theory, its shortcomings, and the works of Kahneman and Tversky, it is essential to recognize the relationship between heuristics and judgment or rather decision making. Heuristics, as we have encountered above, allows us to focus on the crucial aspects of a more complex problem. It allows us to focus on the essence of the problem while tuning out the gory details that constitute the complex problem. Heuristic preserves on time, energy and processing power, but they usually perform poorly when contrasted with logic, rational choice theory, and probability. This affirmation, however, neglects the critical dissimilarity between uncertainty and risk. Risk is constituted of scenarios and situations where all probable actions, their repercussions, and probabilities are well known. On the other hand, uncertainty precludes the fact that some information about the context scenario is unknown or potentially unknowable.

The expected utility theorem deals with the analysis of scenarios whereby individuals have to make a decision, devoid knowledge of the outcomes that may precipitate as a result of the decision. In theory, the individual has to make a decision under uncertainty. In a nutshell, the theory makes an estimate of the probable utility of action in the event, and there is uncertainty in the outcome (Cokely & Kelley 2009). The theory also elucidates that money utility is not automatically similar to the aggregate value of the money. The expected utility theory explains why people consider taking out insurance covers. Using this analogy, it can be said that the expected value from paying for a cover is losing out monetarily. However, catastrophic losses can lead to a critical deterioration in utility due to the thinning marginal utility wealth. Another example, for instance, suppose if one decided to study for a period of four years for a psychology degree. The common assumption is that a reasonable degree is a lot likely to result in a well-paying job except for the fact that there are no guarantees. The chances are that we might either fail in the degree or otherwise be frustrated by the market due to the overwhelming number of graduates we are competing with. Digressing into economics, it can be estimated that if one has a psychology degree, they possess a 0.6 chance of acquiring an extra $300,000 earnings in their lifetime, then the expected utility of a psychology degree is simply a product of the probability and estimated additional earnings.

The expected utility theory was propounded by Daniel Bernoulli while he was toying with the St. Petersburg Paradox. This paradox is based on a lottery game leading to a random variable having infinite expected value, however, seeming to be worth very little to the players of the game. The paradox points out a scenario or set of situations instead, where the naive decision criterion which only factors in the expected value and defines a course of action that presumably no actual individual would be willing to take. The theory introduces the utility function and the concept of the decaying marginal utility for incrementing the amount of money to resolve the paradox.

In the event of risky outcomes, a typical human decision-maker usually does not choose the alternative with the higher expected value investments as might be suggested by hindsight (Edwards 1954). As a good example, consider a choice where an individual is asked to choose between an assured payment of $1.00 and a stake in which the possibility of getting a payment of $200 is one chance in 80 is the alternative. The more likely outcome, 79 out of 80 times, is that the individual will get $0. The expected value of the former is 1.25, while that of the second alternative is 2.5. With respect to the value theory, one would be expected to follow the naive math at face value, i.e., take the $200 or nothing. This is in contrary to the expected utility theory tenets, which better model the aspects of reality more accurately. Some individuals are adequately risk-averse to make a preference of the sure thing irrespective of its relatively low expected value. Individuals in less aversion to risk will make the alternative high-risk gamble that has a higher expected value. This clearly shows the superiority of the expected utility hypothesis to the expected value theory.

Expected utility theory, as we have already encountered, is a theory that outlines strategies about how to formulate optimal decisions in the presence of risk. The theory is relatively old as it was propounded in 1944; thus, it encompasses a normative interpretation, mirroring the way the economists of the time thought it applied to rational agents. The theory now tends to be regarded as a way to obtain insights into first-order approximations. The theory itself, just like any mathematical model, say, Newtonian gravity is an abstraction aimed at making sense of reality by reducing it into math. The theory's mathematical consistency does not guarantee its reliability as a guide into human behavior and best practices. Its clarity, however, has aided scientists to construct various experiments to test its correctness and its scope.

The theory has been tested over time and its various shortcomings in describing human decision-making behavior in the presence of risk and provision of optimal behavior strategies, have helped to deepen understanding of how people arrive at decisions. Tversky and Kahneman presented their paper on prospect theory. The paper elucidates rather empirically how preferences are inconsistent among the same choices relying on how these choices are actually presented.

Expected utility theory was propounded as a theory to model the human decision-making process. The theory, however, falls short in realizing the subtle details in the thought process. The theory reduces the human thought to a linear process which is not exactly how the process works. Human beings simplify a complex problem heuristically, but that does not mean that this process in itself is not complicated. One of the main pitfalls of the theory involves the conservatism involved in updating beliefs. It is a well-known fact that human beings find logic to be hard to grasp, math even harder, and the tenets of statistics and probability even more mentally taxing (Ahlbrecht & Weber 1997). To illustrate, consider the Three Prisoners Problem, which is stated as thus; Three prisoners; X, Y, and Z have been placed in three separate cells and have been sentenced to death. The governor decides to pardon one of them, and the death sentence will be carried out to the rest of them. The prison warden knows the identity of the prisoner to be pardoned. Prisoner X pleads with the warden to disclose to him the identity of one of the two to be executed. Prisoner X adds that if Y is to be pardoned, then the warden should give him Z's name; if Z is to be pardoned then the warden should give him Y's name and in the event that it is he that is to be pardoned then the warden should secretly flip a coin to decide whether to name either prisoner Y or Z. The warden then goes on to tell prisoner X that Y is going to be executed. Prisoner X is thrilled as he believes that his chances of survival have gone up from the probability of 1/3 to as it is now between him and prisoner Z. Prisoner X then secretly tells prisoner Z the news; prisoner z reasons that X's chances remain unchanged at 1/3 but is pleased as his probability of being pardoned has gone up to 2/3. Which prisoner is accurate? The solution to the above problem is somewhat counterintuitive as one would imagine. Prisoner X does not gain any information about his own fate because, from the beginning, she already knew that the warden is going to give him somebody else's name. Prior to hearing the warden's answer, prisoner X estimates his chances to be 1/3, the same as the others. When the warden comes to give his answer, it can be either because; Y will be pardoned (probability of 1/3), or Z will be pardoned (probability of 1/3), or that the warden flipped the X/Y coin (having probability of ), giving a total probability of 1/6 for each case. Hence, when the warden tells Prisoner X that either Y or Z will not be executed, his estimate is halved than that of either Y or Z...

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