Situation X | ||

Option 1 | $1,000, | 1.00 |

Option 2 | $1,000, | .89 |

$2,000, | .10 | |

$0, | .01 | |

Situation Y | ||

Option 3 | $1,000, | .11 |

$0, | .89 | |

Option 4 | $2,000, | .10 |

$0, | .90 | |

Ball numbers | |||

1 | 2-11 | 12-100 | |

Situation X | |||

Option 1 | $1,000 | $1,000 | $1,000 |

Option 2 | $0 | $2,000 | $1,000 |

Situation Y | |||

Option 3 | $1,000 | $1,000 | $0 |

Option 4 | $0 | $2,000 | $0 |

Situation X | Option 1: | .01 u($1,000) | + .10 u($1,000) | + .89 u($1,000) |

Option 2: | .01 u($0) | + .10 u($2,000) | + .89 u($1,000) | |

Situation Y | Option 3: | .01 u($1,000) | + .10 u($1,000) | + .89 u($0) |

Option 4: | .01 u($0) | + .10 u($2,000) | + .89 u($0) | |

If we follow EU and prefer option 1 to option 2 (dropping .89 u($1,000)):

.01 u($1,000) + .10 u($1,000) > .01 u($0) + .10 u($2,000)

If we prefer option 4 to option 3 (dropping u($0)):

.01 u($1,000) + .10 u($1,000) < .01 u($0) + .10 u($2,000)

Prospect Theory will explain this inconsistency.

($30, .25) vs. ($45, .20)

Two stage game: ... If you reach the second stage, you have a choice between ($30) and ($45, .80). However, you must make this choice before either stage of the game is played.

.25 u($30) < .20 u($45)

u($30) > .80 u($45)

($1000, .001) vs. ($1)

(-$1000, .001) vs. (-$1)

Situation X | ||

Option 1 | $1,000, | 1.00 |

Option 2 | $1,000, | .89 |

$2,000, | .10 | |

$0, | .01 | |

Situation Y | ||

Option 3 | $1,000, | .11 |

$0, | .89 | |

Option 4 | $2,000, | .10 |

$0, | .90 | |

From California CIVIL CODE SECTION 1747-1748.7 :

"1748.1. (a) No retailer in any sales, service, or lease transaction with a consumer may impose a surcharge on a cardholder who elects to use a credit card in lieu of payment by cash, check, or similar means. A retailer may, however, offer discounts for the purpose of inducing payment by cash, check, or other means not involving the use of a credit card, provided that the discount is offered to all prospective buyers."

"Would you sell it for $0.25? for $0.50? ... for $9.25?"

Median $7.12

Buyers:

"Would you buy a mug for $0.25? for $0.50? ... for $9.25?"

Median $2.87

Choosers:

"For each amount, would you rather have that amount in cash or a mug?"

Median $3.12

(Choose good defaults.)

Confounded with omission bias and default bias.

Imagine that the U.S. is preparing for the outbreak of an unusual Asian disease, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimate of the consequences of the programs are as follows:

Program A: (200 saved)

Program B: (600 saved, .33)

Program A: (400 die)

Program B: (600 die, .67)

Inspector: Now, you wish to report a murder?

Depp: No, some people tried to kill me.

Inspector: I was told you were reporting a murder.

Depp: Attempted murder.

Inspector: Ah, that is not so serious.

Depp: No, not when you downgrade it from murder. When you upgrade it from room service, itâ€™s quite serious.

From "The tourist". Johnny Depp plays the title character.

If people follows EU, indifference curves will be lines like those drawn inside the triangle, all parallel, but possibly different in slope from those drawn here. If the slope is higher, people will prefer A to B and C, and they will prefer D to E. If the slope is lower, the reverse.

Thus, people prefer A to B, but they will prefer E to D, in
Allais' paradox. This is the *common consequences* effect.
Notices that this is dependent on a fixed *difference* in
the probability of the high outcome, traded off with a fixed
difference in the probability of the low outcome.

People likewise prefer A to *C* even when the prefer E to
D. This is the *common ratio* effect, as shown in the
diagram of the certainty effect, above. Here the *ratio* of
the probabilities if the *high* and *middle* outcomes
are the same. In the certainty effect as presented above, the
high outcome is $45 and the middle is $30.