The Allais paradox is a paradox about the psychology of decision-making. It presents two choices:

- Choice A: You have a 50% chance of winning $1,000 and a 50% chance of winning nothing.
- Choice B: You have a 99% chance of winning $1,000 and a 1% chance of winning $1,000,000.

Which choice would you make? Most people would choose the second choice because they perceive a higher probability of receiving some amount of money, despite the potential for a much larger win with Choice B.

However, when we evaluate the expected values of these choices, we find that they are not the same. Choice A has an expected value of $500 (0.5 * $1,000), while Choice B has an expected value of $10,000.99 (0.99 * $1,000 + 0.01 * $1,000,000).

The Allais paradox demonstrates that people sometimes make decisions based on factors other than expected value, such as the perceived risk of losing everything or the desire for a larger potential gain.

Which choice would you make? Most people would choose the second choice because they want to try to win the big prize, even though the expected value (the average amount you would win) is the same in both choices.

The Allais paradox shows that sometimes people don’t make decisions based on the expected value, but rather on other things like the chance of winning a big prize or the risk of losing everything. This can lead to decisions that don’t make sense, especially in situations where it’s important to make good decisions.

Put another way, the average person doesn’t crunch the numbers, use logical formulas, and identify what the optimal arithmetic decision is. Instead, they go off common judgement, assuming one choice is better. The second choice looks better because there’s zero chance of walking away with nothing, a very large chance of getting the max winnings of the first choice, and 1% of winning an extreme amount. However, a machine or AI would tell you that both options actually output the same amount over time.

This bias can hurt us in situations when we fail to see that both decisions are equal when they are. And this is just one example of many biases working together against you on a typical basis. The goal isn’t necessarily to be aware of all these biases, especially if your decisions don’t have to do with money. Instead, it’s to identify the big biases (affiliate link to a good book) and be aware of those.

I’m confused. How would both choices output the same amount over time? You only have a 50% shot of getting any money with the first choice. While with the second choice, you will get money every single time. Over time, the second choice will always get you more money in the long run.

Thank you for your thoughtful comment and for pointing out the oversight in my article regarding the outcomes of the choices in the Allais paradox. You’re absolutely correct that the expected values of the choices are not the same, and I appreciate your attention to detail.

The purpose of the article was to highlight how decision-making can be influenced by factors beyond pure mathematical calculation, but it’s important to ensure that the examples used are accurate. I will make the necessary updates to the article to reflect the correct expected values of the choices.

I value your feedback and constructive criticism, as it helps to improve the quality and accuracy of the content presented.