Analysis of Decision Under Risk - Book Report/Review Example

Article Summary: “Prospect Theory: An Analysis of Decision under Risk” The article by Kahneman and Tversky (263) provides a critical analysis on the expected utility theory, which serves as an illustrative tool of decision-making. The development of a different option known as the prospect theory is also discussed. The standpoint of the article presents that the utility theory is an inadequate descriptive tool of decision-making in risky situations. The article suggests the use of another descriptive tool to be used under the risk. Options amid risky prospects demonstrate numerous prominent effects that do not follow general principles of the utility theory. Under the expected utility theory, the derivation of expected utility is based on three elements. These elements are expectation, asset integration, and risk aversion. This implies that this particular theory focuses more on final states instead on profits and deficits. To provide evidence that some situations negate the principles of the utility theory, hypothetical choice issues were provided to college students. Although the activity is described to be more qualitative than accurate in measurement of utilities, it shows inconsistencies in the said theory. Certainty Effect Another evidence, which shows the inconsistency of the expected utility theory, is the certainty effect. More specifically, individuals apply a little weight to results that are just probable as compared with results that are achieved with certainty. This manifestation, known as the certainty effect, provides the outcome of risk aversion. This makes people involve more on choices that assure gains rather than to choices that assure definite losses. A survey was applied to determine the certainty effect based on the proposition of Maurice Allais. Survey results show that the said theory does not conform to the preference of individuals. This is shown in the contrasting equations generated from the preference of respondents: Equation 1: u(2400) > 0.33u(2500)+ 0.66u(2400 Equation 2: 0.34u(2400) < 0.33u(2500) This can be explained by the fact that individuals tend to overweight the importance of certainty. It also illustrates that a change in prospect from a certain profit to a probable one may result in a diminished degree of attractiveness. This can be greatly manifested rather than the situation where both prospects are not certain. The reduction of probability in also winning affects the choice of respondents. They prefer more on the choice that gives them higher chances on winning. In such cases, where winning is impossible, the basis of choice is on the higher probability of taking gains. This negates the substitution principle of the expected utility theory leading to more inconsistencies. Reflection Effect In terms of relating the utility theory with negative prospects, the reflection effect is demonstrated. It is observed that the modification of result signs often lead to the reversion of choice. With the existence of negative prospects, people tend to enable people to perform riskier options. This form of effect negates the general idea that people tend to choose options, which shows a dislike to uncertainty because they opt to choose options with a higher variation. Isolation Effect Individuals commonly disregard elements that are allocated by all prospects. This manifestation is called the isolation effect. This results in erratic preferences when a similar option is provided in various types. This is explained through an example problem in which two stages are involved in a game. The first stage presents a 0.75 probability to finish the game winless and a 0.25 probability to proceed to the next stage. In the second stage, 78% of the correspondents opted for the (3000) rather than on (4000,0.8). A B (4000,0.8) 22% (3000) 78% This proves to show that people tend to choose the latter choice. This circumstance negates the Asset Integration element of the utility theory, which highlights the independence of final states with the people’s choice. Further, investigations show that people’s options rely more on the variations of wealth. This is a contradiction to the assumption of the importance of final states on the choice of individuals. This further proves the inconsistency of the utility theory in this manner. An alternative theory, known as the prospect theory, is created where values are designated to profits and deficits instead to final assets. Also, decision weights are used instead of probabilities. Decision weights are commonly more reduced in value as compared with probabilities. Putting much weight on low probabilities provide more desirability of insurance and gambling. Prospect theory involves two stages: the early stage of editing and the next stage of assessment. The first stage provides an analysis of the prospects suggested. In the next stage, the suggested prospects are investigated. The prospect with the highest measurement is selected. First Stage: Editing Stage The first stage, which is the editing stage, involves several activities that convert the results and probabilities into prospects. The following activities are coding, combination, segregation, cancellation, recognition of dominance, and simplification. Coding involves the definition of gains and losses in relation to a reference mark. This conforms to the present asset position used. The costs paid identify whether gains or losses are acquired. Combination is the integration of probabilities with similar results. Segregation is done by separating the prospects in terms of risks. Cancellation is related to the isolation effect where elements are disregarded--partaken by the suggested prospects. Another form of cancellation is the disregard of similar elements in result probability pairs. Simplification is the procedure of approximating probabilities/results of a prospect. Recognition of Dominance concerns with the investigation of suggested prospects to identify dominated options. Second Stage: Assessment Stage This is performed by assessing every edited prospect and selecting the highest valued prospect. The score of every prospect is indicated by the values v and . The v value signifies the subjective score of every prospect. It also determines the measure of deviations from the reference mark. The value signifies the relation of every probability with a decision weight. The assessment of exclusively positive and negative prospects involves the addition of all components with less risk. The difference between the results multiplied by the corresponding decision weight is further added. The Value Function This is a function based on two propositions: the reference mark and the magnitude of variation from the reference mark. In other words, it refers to the digressions from the reference mark. It is believed that the psychological reaction impacts the magnitude of physical modification. Sometimes, obtained value function does not present the clear behaviour towards money. There are cases where small deviations can impact the activity of gain or loss regions. Apparently, gains are presented in a concave illustration while losses are convex in presentation. Commonly, losses are considered a more powerful event than gains. This explains the steeper value function for losses as compared to gains. In addition, it also provides reason aversiveness heightens in accordance with the magnitude of the stake. The Weighting Function The decision weight () evaluates the effect of events on the attractiveness of prospects. Generally, it is equivalent to the event probability. Several elements of this particular function include: Overweighting - pertains to the over-approximation of unusual events. This functions properly with over-approximation because it heightens the effect of rare events. Subproportionality - signifies the closer unity of the conforming decision weights ratio on the circumstance where the properties have reduced value. Subcertainty on the relevant measure of probabilities. Risk Attitudes The elements, which negate the expected utility theory, are subproportionality and subadditivity. Subcertainty negates the independence principle. In accordance with the current theory, risk attitudes are identified by v and . They are not merely identified by the utility function alone. Reference Kahneman, Daniel, and Tversky, Amos. “Prospect Theory: An Analysis of Decision Under Risk.” Econometrica 47.2 (1979): 263-291. Read More