Difference between revisions of "AD/BC problem"

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(Briefly describe the opening example of "Risk Policies" in "Thinking, Fast and Slow")
 
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<blockquote>
 
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.
Decision (i): Choose between
 
  
* 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
 
 
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<blockquote>
AD. 25% chance to win $240 and 75% chance to lose $760
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* AD. 25% chance to win $240 and 75% chance to lose $760
BC. 25% chance to win $250 and 75% chance to lose $750
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* BC. 25% chance to win $250 and 75% chance to lose $750
 
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</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 04:31, 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.