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.