# Difference between revisions of "AD/BC problem"

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Ciphergoth (talk | contribs) (Briefly describe the opening example of "Risk Policies" in "Thinking, Fast and Slow") |
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Imagine that you face the following pair of concurrent decisions. First examine both decisions, then make your choices. | Imagine that you face the following pair of concurrent decisions. First examine both decisions, then make your choices. | ||

− | |||

− | * A. sure gain of $240 | + | * Decision (i): Choose between |

− | * B. 25% chance to gain $1,000 and 75% chance to gain nothing | + | ** A. sure gain of $240 |

− | + | ** B. 25% chance to gain $1,000 and 75% chance to gain nothing | |

− | Decision (ii): Choose between | + | * Decision (ii): Choose between |

− | + | ** C. sure loss of $750 | |

− | * C. sure loss of $750 | + | ** D. 75% chance to lose $1,000 and 25% chance to lose nothing |

− | * D. 75% chance to lose $1,000 and 25% chance to lose nothing | ||

</blockquote> | </blockquote> | ||

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− | AD. 25% chance to win $240 and 75% chance to lose $760 | + | * AD. 25% chance to win $240 and 75% chance to lose $760 |

− | BC. 25% chance to win $250 and 75% chance to lose $750 | + | * BC. 25% chance to win $250 and 75% chance to lose $750 |

</blockquote> | </blockquote> | ||

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. | 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. |

## Latest revision as of 05:31, 30 April 2012

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.