decisions · paradox
Allais paradox
A sure thing changes your pick even when the extra chance is the same.
Pick one from each pair. The good choice by the money is the higher average.
Green is $1 million, yellow is $5 million, and red is $0. The line marks the shared 89%.
Pair 1
Pair 2
Pick one from each pair. The line on the picture marks the shared 89%.
Pair 1 is A or B. Pair 2 is C or D.
The good choice by the money is B and D. B averages $1,390,000 against A's $1,000,000. D averages $500,000 against C's $110,000.
The part left of the line is an 89% chance. In the first pair it pays $1 million. In the second pair it pays $0. That shared part should not flip your pick.
Right of the line, A and C keep a chance of $1 million. B and D keep a chance of $5 million. A goes with C. B goes with D.
Taking A and then D follows neither the higher average nor the safer pick. That switch is the Allais paradox.
Insurance premiums over many quiet years cost more than the insurer expects to pay, and one bad day can still cost more than you can lose.