# BF/U2 Topic 3 Expected Utility

The core concepts of expected utility theory involve preferences for one enterprise or venture over another when there are random prospects, with the enterprises or ventures being called “lotteries”.

This is commonly applied to gaming, but recent events involved financial ventures that were virtually gaming with risky investments based on probabilities of certain outcomes, such as mortgage failures. The outcomes of these high risk financial ventures had a huge impact on the world’s economies.

The probabilities are considered to be “objective”, or part of natural forces and not under any influence by the person. There is a matter of choosing among lotteries and trying to find the best choice. The “utility” is in the outcome or consequence of the choice. Given the probability that an outcome will be positive, the preference is for the lottery that has the best probability. However, preference can form over many lotteries or can be formed by participating in lotteries.

Expected utility theory originates with Daniel Bernoulli in 1738 and possibly earlier with Gabriel Cramer in 1728. Daniel Bernoulli attempted to solve his cousin’s “St Petersberg” paradox of infinite utility, which begins with people valuing the outcome from random ventures such as the toss of a coin that pays when “heads” comes up. Heads will come up with 50-50 odds of winning for each toss, even if the coins are tossed for an infinite period of time. There is an infinite 50/50 probability of winning, so people should find reasons to invest infinite amounts of money to play the random game of coin toss.

But Bernoulli found that wealth does not have a linear relationship to the utility that is related to wealth. In other words, there is over time, less and less of an increase in utility that relates to wealth.This is called “diminishing marginal utility”.

It is not the “win” or return that matters, it is the expected utility that matters when people assign value to a risky venture. Even though the expected return might be infinite, the expected utility causes a person to risk only a finite amount of money.

But that was not enough of a solution to the St Petersberg and similar paradoxes for John Von Neumann and Oskar Morgenstern . In 1944 the von Neumann-Morgenstern Expected Utility Theory brought in a new concept of of expected utility theory involving preferences for one enterprise or venture over another when there are random prospects, with the enterprises or ventures being called “lotteries”.

The probabilities are considered to be “objective”, or part of natural forces and not under any influence by the person. There is a matter of choosing among lotteries and trying to find the best choice. The “utility” is in the outcome or consequence of the choice. Given the probability that an outcome will be positive, the preference is for the lottery that has the best probability. However, preference can form over many lotteries or can be formed by participating in lotteries.

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