The chapter "Risk Policies", in Kahneman's "Thinking, Fast and Slow", opens with this example, which makes vivid the pitfalls of relying on our intuitions in choosing between bets:
Imagine that you face the following pair of concurrent decisions. First examine both decisions, then make your choices.
- Decision (i): Choose between
- A. sure gain of $240
- B. 25% chance to gain $1,000 and 75% chance to gain nothing
- Decision (ii): Choose between
- C. sure loss of $750
- D. 75% chance to lose $1,000 and 25% chance to lose nothing
Most people, looking at both concurrently, choose A and D. Now consider this second choice:
- AD. 25% chance to win $240 and 75% chance to lose $760
- BC. 25% chance to win $250 and 75% chance to lose $750
Clearly, any sane person will choose BC here; it dominates option AD. However, AD is exactly the combination of options A and D, while BC is the combination of B and C.