Big brother is manipulating you

Big Brother is manipulating you: a stochastic
model of opinion control in social networks
Paolo Bolzern (Politecnico di Milano)
Patrizio Colaneri (Politecnico di Milano)
Giuseppe De Nicolao (Università di Pavia)

Outline
• Facebook: facts & figures and a quick primer
• The emotional contagion experiment
• Newsfeed control: from EdgeRank to ...
• A stochastic model of opinion dynamics
• The Leopard Theorem
• Simulation examples
• What’s next?

Outline
• Facebook: facts & figures and a quick primer
• The emotional contagion experiment
• Newsfeed control: from EdgeRank to ...
• A stochastic model of opinion dynamics
• The Leopard Theorem
• Simulation examples
• Conclusions

Basic ingredients
• The Newsfeed: posts that you see when you log
in
• Your personal page: you can publish your posts
and they might enter the Newsfeeds of your
friends
• You can ask friendship and admission to groups
• You can write on pages of friends and groups
• You can put “like”, “angry, “love” on posts
• ...

• Facebook’s News Feed—the main list of status updates, messages, and
photos you see when you open Facebook on your computer or phone—is
not a perfect mirror of the world.
• But few users expect that Facebook would change their News Feed in
order to manipulate their emotional state.
• We now know that’s exactly what happened two years ago. For one week
in January 2012, data scientists skewed what almost 700,000 Facebook
users saw when they logged into its service. Some people were shown
content with a preponderance of happy and positive words; some were
shown content analyzed as sadder than average. And when the week was
over, these manipulated users were more likely to post either especially
positive or negative words themselves.
• This tinkering was just revealed as part of a new study, published in the
prestigious Proceedings of the National Academy of Sciences.

“Two parallel experiments were conducted for positive
and negative emotion: One in which exposure to
friends’ positive emotional content in their News Feed
was reduced, and one in which exposure to negative
emotional content in their News Feed was reduced. In
these conditions, when a person loaded their News
Feed, posts that contained emotional content of the
relevant emotional valence, each emotional post had
between a 10% and 90% chance (based on their User
ID) of being omitted from their News Feed for that
specific viewing.”

Remarkable and unremarkable ...

A basic notion (that should be) taught in every
statistics course: the difference between
statistical and practical significance

the false belief
that [statistically]
significant results
are automatically
big and important
The significance fallacy

eliminating a substantial proportion of emotional content from
a user’s feed had the monumental effect of shifting that user’s
own emotional word use by two hundredths of a standard
deviation. In other words, the manipulation had a negligible
real-world impact on users’ behavior. To put it in intuitive terms,
the effect of condition in the Facebook study is roughly
comparable to a hypothetical treatment that increased the
average height of the male population in the United States by
about one twentieth of an inch (given a standard deviation of
~2.8 inches). Theoretically interesting, perhaps, but not very
meaningful in practice.
Tal Yarkoni

if the idea that Facebook would actively try to manipulate your
behavior bothers you, you should probably stop reading this
right now and go close your account. You also should
definitely not read this paper suggesting that a single social
message on Facebook prior to the last US presidential election
the may have single-handedly increased national voter turn-
out by as much as 0.6%).
Tal Yarkoni

“Our results suggest that the Facebook social
message increased turnout directly by about
60,000 voters and indirectly through social
contagion by another 280,000 voters, for a total
of 340,000 additional votes”

Markov chain model of a Facebook user

Friend #1
Friend #2
Friend #3
Friend #4
agent
Node = Agent = Markov Chain
arc = friendship
State of the chain = opinion
The stochastic social network

Friend #1
Friend #2
Friend #3
Friend #4
agent
Node = Agent = Markov Chain
State of the chain = opinion
The stand-alone model

The interaction model
Linear emulative interaction: the instantaneous
transition rates to opinion j undergo an increase
which is proportional through the constant lj to
the number of neighbors that share opinion j.
The case when all lj are equal goes under the
name of unbiased influence.

Friend #1
Friend #2
Friend #3
Friend #4
Influenced agent
influence = l2 x 3/4

Friend #1
Friend #2
Friend #3
Friend #4
Influenced agent
influence = l1 x 1/4

Markov property
• The aggregate of all agents that forms the stand-
alone model is itself a (bigger) Markov chain,
whose state whose state is the Cartesian
product of the agents’ states.
• What happens if we assume linear emulative
interaction?
• Answer: the overall network is still a time-
homogeneous Markov chain (good news)
• Bad news: the state of the master Markov
model with M opinions is of dimension MN ,
which soon renders its use prohibitive for the
evaluation of the probability distribution as the
number N of agents increases.

The “Leopard Theorem”
"everything changes so that
nothing changes”
(quote from the Italian novel “The
Leopard” by G. Tomasi di Lampedusa)

The “Leopard Theorem”
Theorem: For the unbiased influence linear
emulative model with an arbitrary network topology
and identical agents, the probability distributions of
the agents’ opinions reach asymptotically a steady-
state consensus represented by the steady-state
stand-alone distribution independently of the initial
probability distribution.
Moreover, if the initial distribution probabilities of all
agents’ opinions are equal, the equality with the
stand-alone probabilities holds also in the transient.

nothing changes?
Not properly: w.r.t. to stand-alone, now the
opinions of the agents are correlated.
Expectation of polls does not change ...
... but Variance changes

A special case: the peer assembly
• N identical individuals
• binary opinions (M = 2),
• interconnected by a complete graph (each
individual communicates with all others)
• initial opinions of each agent are independent
and identically distributed random variables
• linear emulative interaction is assumed
Such model can be “lumped” into a birth-death
Markov process so that formulas are available
for:
– marginal distributions
– mean and variance

Beyond the peer-assembly: other topologies

noninteracting
complete
star
smallworld
Beyond the peer-assembly: other topologies

Conclusions 1/2
• Agents as interacting Markov chains
• Overall system is still a Markov Chain
• Unbiased influence on identical agents: affects
variance but not mean
• Analytical results for the peer assembly
• Easy to simulate other topologies
• Next: agents’models drawn from a
distribution?

Conclusions 2/2
• Filters controlling users’ newsfeeds act as
influence intensities l
• Invisible bias on interactions
• Power to shape public opinion
• Control by Facebook is already justified as
countermeasure against fake news and
“influence operations” by governments
(Russia?) and non-state organization
• Lack of transparency

Information Operations
and Facebook
By Jen Weedon, William Nuland and Alex Stamos
April 27, 2017
Version 1.0
As our CEO, Mark Zuckerberg, wrote in February 2017:
“It is our responsibility to amplify the good effects and mitigate the bad -- to
continue increasing diversity while strengthening our common understanding so
our community can create the greatest positive impact on the world.”
«In brief, we have had to expand our security
focus from traditional abusive behavior, such
as account hacking, malware, spam and
financial scams, to include more subtle and
insidious forms of misuse, including attempts
to manipulate civic discourse and deceive
people. These are complicated issues and
our responses will constantly evolve, but we
wanted to be transparent about our
approach. The following sections explain our
understanding of these threats and
challenges and what we are doing about
them.»

Big brother is manipulating you

More Related Content

Similar to Big brother is manipulating you

More from Giuseppe De Nicolao

Recently uploaded

Big brother is manipulating you