Communications - August 2010

diggs would be a scenario in which users pick stories randomly, never being influenced by what their idols did before them. If the observed fractions substantially exceed the random expectation, we can safely say that users indeed pick the same submissions as their peers.

We were able to test whether users digg stories according to the random null hypothesis by randomly shuffling their activities. We simulated a scenario whereby users made their diggs at exactly the same times as they would in real time to mimic the sessions when they’re logged onto Digg. However, we let the agents representing the users digg any story present in the system, rather than what users actually dugg. This approach ensured that the simulated agents picked a random story from among all the stories available to them. We maintained (important) the agents’ social links and corresponding user links, so we could observe the presence or lack of a social-network effect. After the agents’ selections were randomly made, we performed the same measurement as in Figure 7 to determine how agents might have been influenced by their idols to digg the same stories as their idols.

In Figure 7, the difference between
the random model (green line) and the
observed digging pattern (blue line) is
obvious: Users digging stories in the
“upcoming” phase were more than
twice as likely to digg what their idols
dugg than they would if there was no
social network—the same as picking a
story randomly. However, and most im-
portant, stories late in the “promoted”
phase get diggs from users who do not
watch their links at all; the random hy-
pothesis delivers the same fractions as
the real observations after about a day.
However, right after promotion, users
seem to do the opposite of their peers:
The probability that a new digger is a fan
of a previous digger of a story is signifi-
cantly less than one would expect from
random choice. The controversy in this
result might be resolved if we consider
that once a submission is promoted
to the front page (shortly after time 0
in the figure), it gains tremendous vis-
ibility compared to the “upcoming”
phase and is exposed to many casual
Digg users. These users do not actively
participate in discovering new submis-
sions but browse the Digg main page to
see what other users found interesting
(making up the bulk of the user base),
and, though they do not digg often,
their compounded activity dominates
the diggs a story gets at this stage. At the
same time, they are unlikely to have an
extended (or even any) social network.
Consequently, the observed probability
of peer influence is diminished.

figure 6. Representative example of a Digg-user social network. We randomly selected a user as origin and included every other user in the social graph with snowball sampling up to distance four from the user following breadth-first search. Diggers of a particular story are in red; non-diggers are in green.

figure 7. Probability that a digger of a story is a fan of a digger who dugg the same story (blue line) as a function of the time of the digg. Time is relative to the promotion time of the story, with the average calculated over all diggs on all stories. The vertical red line marks time 0 (promotion time), and negative times refer to the “upcoming” phase. The green line is the same measurement but with diggs randomly shuffled.