The Allais Paradox

1. a personal investment with a guaranteed profit of $3000, or
2. a personal investment with an 80% chance of yielding $4000 profit (and a 20% chance of returning no profit)?

3. a personal investment with a 25% chance of returning $3000 (and a 75% chance of returning no profit), or
4. a personal investment with a 20% chance of returning $4000 (and an 80% chance of returning no profit)?

To choose A and D is inconsistent with the “substitution” axiom of utility theory. C is equivalent to a 25% chance of receiving A, and D is equivalent to a 25% chance of receiving B: Given a choice between C and D, you'd choose D - but if the 25% chance comes to pass, you'll wish you'd chosen C! See this in pictures.

The fact that many people do choose A and D is known as the "Allais Paradox."

Lesson: The way we actually make decisions in the face of uncertainty is not necessarily the way a “rational” person would make those choices.