# The Truth Behind Expected Utility

*By: Jake Willms, Quantitative Analyst*

Utility is at the very foundation of economic theory: its what you get for receiving a good or service. Its very important to understand utility because this directly influences demand, price, and even supply. Expected Utility, which happens to the focus of this week’s trending piece, is the average of all possible outcomes for a good or service, typically weighted by likelihood or probabilities.

But what happens if the expected utility isn’t modeled correctly, and the “correct average” is something else than what is being priced into the economy?

Ole Peters, a renowned physicist and academic, is applying ergodicity, a model most commonly applied in thermodynamics, to economics in an effort to challenge the way we think about expected utility and help explain the disconnect between what economic theory suggests and what actually happens in real life. Peters believes that what you might expect on average has very little connection to what most people experience, therefore rendering the projection inaccurate.

Take his coin flip example. [1] Say you were given $100 and asked to participate in a simple game of chance. I will flip a coin 10 times in a row. Each time the coin is heads, your money will increase by 50%, and decrease by 40% on every tails. Probability would suggest you are expected to earn money in this case, so would you play the game?

Now, let’s say 10,000 people all decide to play the game 100 times each. Even though more than half of these gamblers would only have $1 at the end, the “average expected payout”, or expected utility for playing, would end up being over $16,000, thanks to the lucky winners who earned big.

What is happening here? Even though probability would ** expect **a positive return by playing, the majority of people end up losing big. Is this evidence that expected utility, one of the core concepts behind modern economics, is flawed?

Most economists would say no. Ergodicity economics, as Peters calls it, is a very simplistic application of expected utility. There’s even a running joke in the field of economics that every couple of years, a physicist shows up and tries to use a simple mathematical model to identify a problem that isn’t actually there.

In my opinion, I see Peters’ concept as interesting, but ultimately flawed since it fails to consider the weighted aspect of a true expected utility. Peters seems to only consider it as a simple mean average, whereas its use in true economic theory is far more complex. However, his theory does a great job demonstrating the disastrous effects of an inaccurate expectation and promote a healthy conversation surrounding expected utility’s use. Parlaying to finance, investors and financial analysts must ensure they have an accurate and reasonable means of estimating the likelihood of future events to prevent falling victim to an illusion.

**[1] **Peters, O., & Gell-Mann, M. (1970, January 01). Evaluating gambles using dynamics. Retrieved December 11, 2020, from https://aip.scitation.org/doi/full/10.1063/1.4940236

**[2]** Kochkodin, B. (2020, December). Everything We've Learned about Modern Economic Theory Is Wrong. Retrieved December 11, 2020, from https://www.bloomberg.com/news/articles/2020-12-11/everything-we-ve-learned-about-modern-economic-theory-is-wrong