Will upvote all responses.
Lewis uses the word arbitrarily when he describes how he was assigned his Wall Street position and also when he describes how a leader was chosen in the cookie experiment.

In this context, arbitrarily means

Select one:
a. in a manner based on much consideration.
b. according to rules established by a judge.
c. in a manner determined by chance or whim.
d. as determined by specific qualifications.