Game Development Reference
In-Depth Information
The guess receiving the largest number of votes (over 6%) was 33. Remember
that we had touched on 33 being a potential solution—but only if all of the other
votes were equally distributed between zero and 100, making the average guess 50.
So, some people were obviously thinking along those lines. However, their fatal
flaw was expecting that even distribution. Just as superrationality—the rationality
of all participants—is an unreasonable expectation, expecting that
all
of the partic-
ipants are completely
irrational
is just as flawed a premise.
The guess receiving the second-most number of votes—and, at 6%, only
slightly behind the 33 guess—was 22. Once again, the mindset seemingly at work
here is one that we touched on earlier. The people who guessed 22 were counting
on the fact that a large majority of the
other
folks were going to be guessing 33. They
were hoping some players would be at least thinking about their answer (unlike the
players who guessed 100, for example), but not thinking
too
much. By taking those
people into account, and then basing their actions on that information, people who
guessed 22 were, in fact, very close to the solution.
Measuring the Depth of Rationality
So, it would seem that assuming that at least a
portion
of the population was
partially
rational is a valid strategy that leads to an optimal solution. The question is, how
many of the participants are going to be rational and to what extent? We know the
answer lies between two extremes. Also, as we have seen, the answer presents itself
as a continuum that is represented by how many iterations people go through in
attempting to outguess the other people.
For example, we have the random players whose guesses are spread all over the
possible range from 0 to 100. Those players are not thinking at all about what any-
one else could do. This is evidenced by the fact that people are willing to even select
numbers of the impossible result threshold of 66.67. Let's give these people a ratio-
nality index of 0. In essence, they are simply randomly picking numbers.
Statistically, the average of their guesses should be close to 50 (Figure 6.3).
The next group of people takes the “zero rationality� folks into account. They
work from the assumption that people are going to be all over the map with their
guesses, figure that the average will be 50, and then guess around 33. They have per-
formed one level of iteration through the logic progression. Let's give them a ratio-
nality index of 1.
The people who are aware that the level-one people exist would also then take
those votes into account. With the presumption of the 33 vote being a big draw,
they would then guess 22. We will assign this group a rationality index of 2. They
have performed two iterations of thought—they assumed there would be level ones
who would count on the existence of level zeros.
