Rational vs. Irrational Behavior - Behavioral Mathematics for Game AI - page 95

We were iteratively eliminating logically impossible answers and, in doing so, as-
sumed that the entire population of guessers would do so as well. Eventually, this
led us to the purely rational answer of guessing zero.
In our second attempt at solving the problem, we started with the premise that
the population was not superrational; that is, some people may be rational, but it is
not likely that everyone is. By taking away the aura of superrationality, it would
seem that our problems have been solved. However, we still had to decide how to
rationally proceed from that standpoint. As we showed, this can be done in stages—
which we labeled as index 0, index 1, and so on. The same caveat is in play, however.
If we proceeded on logically, we would eventually end up back in the territory of
guessing zero once again.
Both of these approaches lead us to the wrong answer. While we may have
wonderful proofs of the perfect rationality of guessing zero, it is simply not a good
answer to this problem. In the first method, our premise of superrationality was
flawed. Put another way, it is irrational for us to assume that everyone else is ratio-
nal. In the second method, we started with the right idea. We gave up on the notion
that everyone was rational (giving us the index 0 guessers) but still had to count on
the fact that at least some of them were (the index 1 guessers). So, it is rational to as-
sume that some other people are rational, but how far can we take that? At some
point, the seemingly rational chain of iterated processes has to be abandoned. We
can no longer assume that things will be the way they “should be� because, at some
point, other people will no longer be acting the way they “should.�
Therefore, it is in our best interests to, somewhere along the way, abandon the
rational method of arriving at an answer and say, “Enough!� We are logically con-
cluding that we are going to no longer be purely rational. It is logical to act irra-
tionally simply because the environment that we are making the decisions in is
irrational as well. If the other people involved aren't going to be completely ratio-
nal, then it is not logical for us to be completely rational. (I don't recommend using
that justification during an argument with your wife. And definitely don't do it
where your kids can hear… you don't want it coming back at you later!)
The whole idea can be summed up in a single quote from Mr. Spock, Star
Trek's renowned purveyor of logic and rationality. When Captain Kirk asked Mr.
Spock if a particular action was “the logical thing to do,� Spock replied, “No, but it
is the human thing to do.� And isn't this, after all, what we are trying to accomplish
in crafting our AI?