THE LIMITS OF
RECOMMENDERS
AND THE ROLE OF SOCIAL TIES
ALESSANDRO PANCONESI, SAPIENZA UNIVERSITY OF ROME
JOINT WITH: MARCO BRESSAN, STEFANO LEUCCI, PRABHAKAR RAGHAVAN, ERISA TEROLLI
THEGOODOLDDAYS
RS’s are now quite
standard on the web
Ecommerce sites: try to optimize revenue by
getting users to buy more.
News and media sites: try to keep the users
interacting with content, because it generates
(advertising) revenue.
Users would get more utility if they receive
recommendations they find valuable and
trustworthy.
RECOMMENDER SYSTEMS, THE MAIN GATEWAY TO ONLINE CHOICES
AS SUCH THEY ARE BECOMING POWERFUL ECONOMIC ACTORS
TO WHAT EXTENT CAN A
RECOMMENDATION SYSTEM ALTER
A MARKET?
DIGITAL FOODS: TURNING
BITS INTO BITES
Market shares, before RS
KDD FOODS: TURNING BITS INTO BITES
Market shares, after RS
KDD FOODS: TURNING BITS INTO BITES
Different approaches
User studies / social psychology experiments
Data mining with real data
Mathematical modelling
A MATHEMATICAL MODEL
Main Ingredients
the more successful an item, the higher the
probability of being recommended
social forces: recommendations are made by
friends
PRODUCTS
USERS (or BUYERS)
Users are connected via a
network
0.4
0.6
0.6
0.3
0.8
0.7
1.0
0.5
0.1
0.3
0.1
0.7
0.5
0.1
0.3
0.7
Trust
0.49
0.01
0.48
0.01
0.01
Personal inclinations
0.2
0.1
0.05
0.4
0.1
0.25
The purchasing process
Items are bought in a
sequence, when a
purchase is made a
buyer is chosen at
random
Following
recommendations
Recommendation
1
↵Shreck
↵Shreck
fShreck
Following
recommendations
0.01
Shreck is the current buyer
and he will follow Wile Coyote’s
suggestion
The weight of history
bought at
time t
0.01
Shreck is the current buyer
and he will follow Wile Coyote’s
suggestion
The weight of history
bought at
time t
0.01
Shreck is the current buyer
and he will follow Wile Coyote’s
suggestion
A natural condition: The
past fades away
If eventually we put zero probability on the item
purchased at any fixed time <t, we say that the
past fades away.
E.g., uniform on all past purchases, or..
truncated beyond recent history (e.g. consider
only last 10 items), or..
recency effect, weights are 1, 1/2, 1/4, ..etc.
START THE SYSTEM. WHAT
HAPPENS?
MAIN RESULT
If the past fades away, then the
system will converge to a unique
steady state
MAIN RESULT
…furthermore, the shape of the
market at the limit is given in
closed form
A bit of notation
t
xu (p)
fraction of times that u has bought p, up to time t
From now on product p is fixed. We drop p for notational convenience
t
x :=
t
t
(x1 , . . . , xn )
Main result
Fix a product p. If the past fades away, then
t
lim E[x ] = x
t!1
1
THE SYSTEM ALWAYS CONVERGES TO A UNIQUE LIMIT!
Main result
Fix a product p. If the past fades away, then
t
lim E[x ] = x
t!1
x
L := (I
1
1
= Lb.
AM )
1
(I
A)
The matrix L captures market effects
Corollaries
x
1
= Lb.
x1
i = 0.2
n
X
=
Lij bj
j=1
= 0.001 + 0.002 + . . . + 0.1 + . . . + 0.003
We can quantify the influence of each user
on every other user
Influence and distortion
The relative contribution of each u to the overall
sales distribution is an influence vector over
users:
:= f L
Define the market distortion as the ratio of the
market share of p* with/without the RS:
:= ( · b)/(f · b)
Some known precedents
If all ↵u = ↵ , then turns out to be exactly the
vector of personalized pageranks [HKJ2003]
Consider a coalitional game where each user
either joins the coalition for p* or sits out. Then the
Shapley value of user u is u bu
EXPERIMENTS
Experiments
How do influence and distortion play out in real
social networks and RS?
Public datasets drawn from Google+, Twitter,
Slashdot, Yelp and Facebook.
Set all 𝛼 to be 0.2, which is abnormally large, to
see how much we can distort the market.
Convergence
Does the RS distort the
market?
“Real” social networks dampen influence pretty
heavily, with 𝝙 always measured in the range 1 ±
0.002
On the other hand, planting an oligarchy (where
everyone follows a few superstars) results in high
𝝙
Influence
In these “real” social networks, it was difficult to
build large influence.
This holds even under “nonlinear” experiments
where items were recommended with heavier
probability than uniform sampling.
Influencers
Although in real-world graphs there are users
whose influence is 10,000 times that of an
average user, their global effect on the
market is tiny
Summary
Fairly general model of RS with a view to studying
market influence.
Closed form for equilibrium, influence and market
distortion.
Experiments suggest that “real” social networks
dampen the influence of RS.
Future research
We view this as a proof of concept. Try to
extend approach to more realistic models
Thanks