80: Possible-Worlds Accounting

    Suppose you go with a friend to a restaurant, and agree that
rather than splitting the check as usual, you'll flip a coin, and the
loser will pay.  You win the coin toss, so your friend pays for the
meal.  Do you feel guilty?  Some of us might intuitively say yes,
since after all, you just got away with a free meal.  However, if you
look at it like author Nassim Nicholas Taleb, you won't feel guilty at
all-- in a probabilistic sense, you have paid for half!
    Recently I've been reading Taleb's excellent book titled "Fooled
By Randomness:  The Hidden Role of Chance in Life and Markets."  One
of the most important concepts he discusses is the idea of
possible-worlds accounting:  when judging the wisdom of a particular
action that has a random factor, you should account for all possible
results in light of the expected random distribution.  In the case of
the dinner check, if you average your cost across all possible worlds
where you carry out the coin flip, it is equal to your half of the
dinner, so your actions are perfectly reasonable. 
    In a more serious scenario, imagine that you are choosing whether
to go to college, and you read that your high-school-dropout neighbor
won 10 million dollars in the lottery, making more money than you
would likely accumulate in your future career.  To judge whether your
neighbor made an intelligent decision, you should account for his
probability of actually winning that lottery, in relation to all
possible outcomes.  That probability, probably something less than one
in 10 million, multiplied by his total lottery winnings (of only one 10
million dollar jackpot), makes his probabilistic winnings across all
possible worlds much less than a dollar, so you probably should go to
college after all.  Of course, that's little consolation when you see
some bozo win the lottery instead of you, but maybe if you're nice and
don't throw these numbers in his face, your rich neighbor will let you
use his swimming pool.
    Another of Taleb's surprising anecdotes relates to an insurance
experiment.  Suppose you go to the airport and ask people how much
they would pay for a 1 million dollar insurance policy covering their
death for any cause during their trip.  Then you ask another group of
people how much they would pay for a million dollars of insurance
covering their death from a terrorist attack during their trip.
Viewing all possible results, clearly the first policy should be more
valuable than the second:  the possible worlds in which you would die
from any cause include the ones where you die from terrorism, plus
various others where you have a heart attack, slip on a banana peel,
or impale your forehead with your ipod because you're too eager to
listen to Math Mutation.  Yet when this experiment is actually done,
people are more willing to pay for the policy that covers terrorism
alone!  It looks like humans just aren't wired to judge probabilistic
situations rationally:  if you can paint a vivid picture or tap into a
primal fear, those situations appear much more likely.
    Anyway, Taleb's book is filled with these amusing anecdotes, and I
would highly encourage you to take a look.  Meanwhile, remember that
before you take chances in life, don't just optimistically look at
your successes: you must think about all possible worlds to truly
judge whether your actions are sensible.

Taleb's Website