Novelty and Collective Attention
Novelty and Collective Attention
Fang Wu and Bernardo A. Huberman
Information Dynamics Laboratory
HP Labs
Palo Alto, CA 94304
October 28, 2018
Abstract
The subject of collective attention is central to an information age
where millions of people are inundated with daily messages. It is thus
of interest to understand how attention to novel items propagates and
eventually fades among large populations. We have analyzed the dy-
namics of collective attention among one million users of an interactive
website — digg.com — devoted to thousands of novel news stories.
The observations can be described by a dynamical model character-
ized by a single novelty factor. Our measurements indicate that nov-
elty within groups decays with a stretched-exponential law, suggesting
the existence of a natural time scale over which attention fades.
http://arxiv.org/abs/0704.1158v1
The problem of collective attention is at the heart of decision making
and the spread of ideas, and as such it has been studied at the individual
and small group level by a number of psychologists [1, 2], economists [3], and
researchers in the area of marketing and advertising [4, 5, 6]. Attention also
affects the propagation of information in social networks, determining the
effectiveness of advertising and viral marketing [7]. And while progress on
this problem has been made in small laboratory studies and in the theoretical
literature of attention economics [8], it is still lacking empirical results from
very large groups in a natural, non-laboratory, setting.
To understand the process underlying attention in large groups, consider
as an example how a news story spreads among a group of people. When
it first comes out, the story catches the attention of a few ones, who may
further pass it on to others if they find it interesting enough. If a lot of
people start to pay attention to this story, its exposure in the media will
continue to increase. In other words, a positive reinforcement effect sets in
such that the more popular the story becomes, the faster it spreads.
This growth is counterbalanced by the fact that the novelty of a story
tends to fade with time and thus the attention that people pay to it. There-
fore, in considering the dynamics of collective attention two competing ef-
fects are present: the growth in the number of people that attend to a given
story and the habituation that makes the same story less likely to be attrac-
tive as time goes on. This process becomes more complex in the realistic
case of multiple items or stories appearing at the same time, for now people
also have the choice of which stories to attend with their limited attention.
In order to study the dynamics of collective attention and its relation
to novel inputs in a natural setting, we analyzed the behavioral patterns of
one million people interacting with a news website whose content is solely
determined by its own users. Because people using this website assign each
news story an explicit measure of popularity, we were able to determine the
growth and decay of attention for thousands of news stories and to validate
a theoretical model which predicts both the dynamics and the statistical
distribution of story lifetimes.
The website under study, digg.com, is a digital media democracy which
allows its users to submit news stories they discover from the Internet [9]. A
new submission immediately appears on a repository webpage called “Up-
coming Stories”, where other members can find the story and, if they like
it, add a digg to it. A so-called digg number is shown next to each story’s
headline, which simply counts how many users have digged the story in the
digg.com
past.1 If a submission fails to receive enough diggs within a certain time
limit, it eventually falls out of the “Upcoming” section, but if it does earn a
critical mass of diggs quickly enough, it becomes popular and jumps to the
digg.com front page.2 Because the front page can only display a limited
number of stories, old stories eventually get replaced by newer stories as the
page gets constantly updated. If a story however, becomes very popular it
qualifies as a “Top 10” and stays on the right side of the front page for a
very long time.
When a story first appears on the front page it attracts much attention,
causing its digg number, Nt, to build up quickly. After a couple of hours
its digg rate slows down because of both its lack of novelty and its lack
of prominent visibility (reflected in the fact that it moves away from the
front page). Thus the digg number of each story eventually saturates to a
value, N
, that depends on both its popularity growth and its novelty decay.
In order to determine the statistical distribution of this saturation number,
which corresponds to the number of diggs it has accumulated throughout its
evolution, we measured the histogram of the final diggs of all 29,864 popular
stories in the year 2006. As can be seen from Fig. 1, the distribution appears
to be quite skewed, with the normal Q-Q plot of log(N
) a straight line.
A Kolmogorov-Smirnov normality test of log(N
) with mean 6.546 and
standard deviation 0.6626 yields a p-value of 0.0939, suggesting that N
follows a log-normal distribution.
It is then natural to ask whether Nt, the number of diggs of a popular
story after finite time t, also follows a log-normal distribution. To answer
this question, we tracked the digg numbers of 1,110 stories in January 2006
minute by minute. The distribution of log(Nt) again obeys a bell shape
curve. As an example, a Kolmogorov-Smirnov normality test of log(N2 hours)
with mean 5.925 and standard deviation 0.5451 yields a p-value as high as
0.5605, supporting the hypothesis that Nt also follows a log-normal distri-
bution.
The log-normal distribution can be explained by a simple stochastic dy-
namical model which we now describe. If Nt represents the number of
people who know the story at time t, in the absence of any habituation,
1In fact, digg users are given the option to “bury” a story, which will decrease the
story’s digg number. Because this rarely happens, we ignore this possibility and simply
assume that a story’s digg number can only grow with time.
2The actual machine-learning algorithm used to determine whether a story qualifies to
appear on the front page is very complex and will not be discussed in this paper [10].
digg.com
diggs
0 1000 2000 3000 4000 5000
−4 −2 0 2 4
Normal Q−Q Plot
Theoretical Quantiles
Figure 1: (a) The histogram of the 29,684 diggs in 2006, as on January 9,
2007. (b) The normal Q-Q plot of log(N
). The straight line shows that
log(N
) follows a normal distribution with a slightly longer tail. This is
due to digg.com’s built-in reinforcement mechanism that favors those “top
stories”, which can stay on the front page and can be found at many other
places (e.g. “popular stories in 30 days” and “popular stories in 365 days”).
on average a fraction µ of those people will further spread the story to
some of their friends. Mathematically this assumption can be expressed as
Nt = (1 + Xt)Nt−1, where X1,X2, . . . are positive i.i.d. random variables
with mean µ and variance σ2. The requirement that Xi must be positive
ensures that Nt can only grow with time. As we have discussed above, this
growth in time is eventually curtailed by a decay in novelty, which we pa-
rameterize by a time dependent factor rt consisting of a series of decreasing
positive numbers with the property that r1 = 1 and rt ↓ 0 as t ↑ ∞. With
this additional parameter, the full stochastic dynamics of story propagation
is governed by Nt = (1 + rtXt)Nt−1, where the factor rtXt acts as a dis-
counted random multiplicative factor. When Xt is small (which is the case
for small time steps) we have the following approximate solution:
(1 + rsXs)N0 ≈
ersXsN0 = e
rsXsN0, (1)
where N0 is the initial population that is aware of the story. Taking loga-
rithm of both sides, we obtain
logNt − logN0 =
rsXs. (2)
The right hand side is a discounted sum of random variables, which for
rt near one (small time steps) can be shown to be described by a normal
distribution [11]. It then follows that for large t the probability distribution
of Nt will be approximately log-normal.
Our dynamic model can be further tested by taking the mean and vari-
ance of both sides of Eq. (2):
E(logNt − logN0)
var(logNt − logN0)
. (3)
Hence if our model is correct, a plot of the sample mean of log(Nt)− log(N0)
versus the sample variance for each time t, should yield a straight line passing
through the origin with slope µ/σ2. One such plot for 1,110 stories collected
in January 2007 is shown in Fig. 2. As can be seen, the points indeed lie on
a line with slope 6.947.
The decay factor rt can now be computed explicitly from Nt up to a
constant scale. Since we have normalized r1 to 1, we have
E(logNt)−E(logNt−1)
E(logN1)− E(logN0)
. (4)
0.0 0.1 0.2 0.3 0.4
sample variance
Figure 2: Sample mean of logNt − logN0 versus sample variance, for 1,110
stories in January 2007. Time unit is one minute. The points are plotted as
follows. For each story we calculate the quantity logNt−logN0, which is the
logarithm of its digg number measured t minutes after its first appearance
on the front page, minus the logarithm of its initial digg number. We collect
1,110 such quantities for 1,110 stories. Then we compute their sample mean
y and sample variance x, and mark the point (x, y). This is for one t. We
repeat the process for t = 1, 2, . . . , 1440 and plot 1440 points in total (i.e. 24
hours). They lie roughly on a straight line passing through the origin with
slope 6.947.
The curve of rt estimated from the 1,110 stories in January 2007 is shown in
Fig. 3(a). As can be seen, rt decays very fast in the first two to three hours,
and its value becomes less than 0.03 after three hours. Fig. 3(b,c) show
that rt decays slower than exponential and faster than power law. Fig. 3(d)
shows that rt can be fit empirically to a stretched exponential relaxation or
Kohlrausch-Williams-Watts law [12]: rt ∼ e
−0.4t
. The halflife τ of rt can
then be determined by solving the equation
e−0.4t
e−0.4t
dt. (5)
A numerical calculation gives τ = 69 minutes, or about one hour. This
characteristic time is consistent with the fact that a story usually lives on
the front page for a period between one and two hours.
The stretched exponential relaxation often occurs as the result of multi-
ple characteristic relaxation time scales [12, 13]. This is consistent with the
fact that the decay rate of a story on digg.com depends on many factors,
such as the story’s topic category, the time of a day when it appears on the
front page. The measured decay factor rt is thus an average of these various
rates and describes the collective decay of attention.
These measurements, comprising the dynamics of one million users at-
tending to thousands of novel stories, allowed us to determine the effect of
novelty on the collective attention of very large groups of individuals, while
nicely isolating both the speed of propagation of new stories and their de-
cay. We also showed that the growth and decay of collective attention can
be described by a dynamical model characterized by a single novelty factor
which determines the natural time scale over which attention fades. The
exact value of the decay constant depends on the nature of the medium but
its functional form is universal. These experiments, which complement large
social network studies of viral marketing [7] are facilitated by the availability
of websites that attract millions of users, a fact that turns the internet into
an interesting natural laboratory for testing and discovering the behavioral
patterns of large populations on a very large scale [14].
References
[1] Kahneman, D. Attention and effort. Englewood Cliffs, N.J.: Prentice
Hall (1973).
digg.com
0 100 200 300 400 500 600 700
0 100 200 300 400 500 600 700
0 1 2 3 4 5 6
log(t)
2 4 6 8 10 12 14
Figure 3: (a) The decay factor rt as a function of time. Time t is measured
in minutes. (b) log(rt) versus t. rt decays slower than exponential. (c)
log(rt) versus t. rt decays faster than power law. (d) log(rt) versus t
0.4. The
slope is approximately −0.4.
[2] Pashler, H. E. The psychology of attention. MIT Press (1998).
[3] Camerer, C. The behavioral challenge to economics: understanding
normal people. Paper presented at Federal Reserve of Boston meeting
(2003).
[4] Pieters, F. G. M., Rosbergen, E. and Wedel, M. Visual attention to
repeated print advertising: A test of scanpath theory. Journal of Mar-
keting Research 36(4), 424–438 (1999).
[5] Dukas, R. Causes and consequences of limited attention. Brain Behavior
and Evolution 63, 197–210 (2004).
[6] Reis, R. Inattentive Consumers. Journal of Monetary Economics
Vol. 53, 1761–1800 (2006).
[7] Lefkovic, J., Adamic, L. and Huberman, B. A. The dynamics of vi-
ral marketing. Proceedings of the ACM Conference on Electronic Com-
merce (2006).
[8] Falkinger, J. Attention Economies. Forthcoming in Journal of Eco-
nomic Theory (2003).
[9] How Digg Works. http://www.digg.com/how
[10] Private communication with the digg.com support team.
[11] Embrechts, P. and Maejima, M. The central limit theorem for summa-
bility methods of i.i.d. random variables. Probability Theory and Related
Fields, Volume 68, Number 2 (1984).
[12] Lindsey, C. P. and Patterson, G. D. Detailed comparison of the William-
Watts and Cole-Davidson functions. J. Chem. Phys. 73(7) (1980).
[13] Frisch, U. and Sornette, D. Extreme deviations and applications. J.
Phys. I France 7 1155–1171 (1997).
[14] Watts, D. A twenty first century science. Nature 445, pp. 489 (2007).
http://www.digg.com/how
digg.com
