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Predicting Preferences

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Predicting Preferences
Prediction involves making a statement concerning the likely value of an event or action uncertain or unknown at the time of the statement. Since the theory of probability, (inaugurated by the French mathematicians Blaise Pascal and Pierre Fermat in 1654), was developed to quantify uncertain events in terms of their likelihood of occurrence, formal prediction is now viewed as a mathematical topic involving probabilistic modeling. Indeed, the mathematician Karl Pearson said in 1907 that the fundamental problem in statistics is prediction. Prediction, however, is usually not an end goal itself, but rather means to put probabilistic bounds on the relative frequency or likelihood of occurrence of future uncertain …show more content…

Bernoulli resolved the paradox by postulating that people do not make choices based on the expected rewards alone, but rather based on the value or pleasure that each individual pay-off is likely to yield to them. He said “The determination of the value of an item must not be based on the price, but rather on the utility it yields…. There is no doubt that a gain of one thousand ducats is more significant to the pauper than to a rich man though both gain the same amount.” He suggested there was a function U(w) (called a utility function) which describes the amount of value or utility that the individual gains by having an amount of wealth w. Rational individuals prefer more money to less money, so U(w) is increasing, but the incremental value of more wealth decreases as one becomes wealthier (decreasing marginal utility or value of wealth) so U(w) is concave. Bernoulli stated that people determined how much to pay for the game or gamble not based on the gamble’s expected value but rather it’s expected utility. Thus, if x1, x2, …, xn are the possible outcomes of an uncertain economic endeavor or gamble, and their probabilities of occurrence are p1, p2, …, pn then a decision maker with an initial wealth of W would make decisions based on their expected utility of their final wealth, U(W+x1)*p1 + U(W+x2)*p2 +…+ U(W+xn)*pn. Using this approach, one can predict preferences between two uncertain events by

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