Preferences, Choices, and Expected Utility Theorem

The main assumption in Economics (and also Finance) is the expected utility. In academic world, by using this assumption, economics is more known as conventional economic.  In a very simple way, this assumption states that human behaviour reflects rational self-interest. Individuals look for and pursue opportunities to increase their pleasure, happiness, or satisfaction obtained from consuming a good or service in rational way (McConnell, 2009).

It also implies that the decision is made based on the logic of thinking and rationality. To have an effective decision in choices and preference, a person must be able to forecast the outcome of each option as well and based on all their preferences.
For instance, when you are confronted by a choice that affect you personally such as going to Paris or London for holiday, there are nearly always benefits and costs associated with each choice. Where will you go for holiday? It will depend on answering “how do you decide to go?”. Von Neumann and Morgenstern (1947) propose an approach called Expected Utility. This theory address that usually humans will try to maximize their pleasure or satisfaction which is the subjective value we attach to an outcome.
In reality, the decision making of choices and preferences has to confront various factors associated with each option. For instance, in deciding between Paris or London for holiday, Paris may be preferable to London because it is a loveable city, good scenic, better weather, and more romantic. However, holiday in Paris will cost more expensive and language constraints. In such circumstances, according to Expected Utility, people are supposed to calculate the utility or disutility of each choice.
However, the choice between Paris and London has three basic properties: First is completeness, meaning that you can always completely understand and can always making up your mind about the desirability of any two alternatives. The assumptions rules out the possibility that individual can report both that Paris is preferred to London and that London is preferred to Paris.
Second assumption is Transitivity. If you report that “Paris is preferred to London” and that “London is preferred to Prague”, then you must also report that “Paris is preferred to Prague”. This assumption states that the individual’s choices are internally consistent. The last assumption is continuity. If you report “Paris is preferred to London” then situations suitably “close to” Paris must also be preferred to London. This rather technical assumption is required if we wish to analyze individuals’ responses to relatively small changes in income and prices.

The purpose of the assumption is to rule out certain kinds of discontinuous, knife-edge preferences that pose problems for a mathematical development of the theory of choice. Assuming continuity does not seem to run the risk of missing types of economic behavior that are especially important in the real world (Nicholson, 2003).

(Conventional) Economists believe that individual will not behave randomly in their decision and does not have selfishness. Individual will choice Paris not because of they just randomly pick it, but because they have their preferences and trade-off. Individual also will not choice Paris because of the altruism or egocentric thinking of individuals.
Choosing between Paris and London is easier for individuals as it has certain information to make decision. However, in the reality, individual often faces uncertainty choices, for example in choosing “head” or “tail” in coin flipping. Economics use the concept of probability and expected value to answer this issue.
In a fair game, it is so easy to calculate the expected value of doing coin flipping. However, people are generally unwilling to play the fair games. You may at times agree to flip coin for small amounts of money, but if you were offered the chance to wager $10,000 on one coin flip, you would undoubtedly refuse.
An example for unfair games in choice is St.Petersburg Paradox which was firstly investigated rigorously by Daniel Bernoulli. He found that in some sense even though the expected value is infinite, the game is not worth its expected dollar value.

His solution to this paradox was to argue that individuals do not care directly about the dollar prizes of a game; rather they respond to the utility these dollars provide. If we assume that the marginal utility of income declines as income increases, the St. Petersburg game may converge to a finite expected utility value that players would be willing to pay for the right to play. Bernoulli termed this expected utility value the moral value of the game because it represents how much the game is worth to the individual. Because utility may rise less rapidly than the dollar value of the prizes, it is possible that a game’s moral value will fall short of its monetary expected value (copy-paste from Nicholson, 2003).

John Von Neumann and Oscar Morgenstern are the scholars who developed mathematical models for examining the economic behaviour of individuals under conditions of uncertainty. They investigated the decision under uncertain condition and write it in “The Theory of Games and Economic Behavior” book. To understand these interactions, it was necessary first to investigate the motives of the participants in such “games.” Because the hypothesis that individuals make choices in uncertain situations based on expected utility seemed intuitively reasonable, the hypothesis could be derived from more basic axioms of “rationale” behavior. The axioms represent an attempt by the authors to generalize the foundations of the theory of individual choice to cover uncertain situations.
They surmise that in uncertain situations, individuals are concerned with the expected utility associated with various outcomes. If individuals obey the von Neumann-Morgenstern axioms, they will make choices in a way that maximizes expected utility.

This expected utility theorem is important to learn and understand as it is the basic of economics and finance theory. The main point of this essay is just to show that individual is assumed acting rationally in decision making. But, does individual always act rationally all the time? Do emotion, experiences, fear, and greed will not affect the decision making? Have you ever go to a luxury and fancy restaurant because the emotion attachment? Have you ever buy something because it was a trend? If the answers are yes, it implies rational behaviour is not always working. I will discuss about it in another essay.

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