Russian Roulette

Scenario 1: There is a gun pointed at your head. It has six chambers. There are four bullets inside. The chambers will be spun randomly before the gun is fired once.

Scenario 2: There is a gun pointed at your head. It has six chambers. There is only one bullet inside. The chambers will be spun randomly before the gun is fired once.

In which scenario would you be willing to pay more to have one bullet removed from the chambers?

Interestingly, according to economic theory you should be willing to pay more to reduce the bullets from 4 to 3 than from 1 to 0. Is this the case for you?


For those who are economically inclined, here is a brief sketch of the proof of the theory:

Where u(.) is a von Neumann-Morgenstern utility function, p1 is what you are willing to pay in Scenario 1, p2 is what you are willing to pay in Scenario 2 and Y is your income.

In Scenario 2:

u(alive, Y - p2) = 1/6u(dead) + 5/6u(alive, Y)

In Scenario 1:

1/2u(dead) + 1/2u(alive, Y - p1) = 2/3u(dead) + 1/3u(alive, Y)

Re-write Scenario 1:

u(alive, Y - p1) = 2/6u(dead) + 2/3u(alive, Y)

Comparing scenarios:

u(alive, Y - p2) > u(alive, Y - p1)

Therefore:

p1 > p2

QED