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Web Science and Technologies
University of Koblenz–Landau, Germany
Fairness on the Web:Alternatives to the Power Law
Jérôme Kunegis, Julia PreusseUniversity of Koblenz–Landau
WebSci 2012, June 24Evanston, IL
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Fairness
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The Pareto Principle
“20% of people own 80% of land.”
(In 1910s Italy)
(Pareto, 1919)
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UNFAIR
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8.9% of bands make up 91.1% of plays on Last.fm.
14.6% of user groups account for 75.4% of group memberships on Flickr.
17.4% of movies receive 82.6% of ratings on MovieLens.
17.7% of profiles receive 82.3% of ratings on Czech dating site Libimseti.cz.
19.7% of all cats receive 80.3% of all friendships on Catster.com.
20.3% of all users receive 79.7% of “friend” and “foe” links on Slashdot.
21.3% of users receive 78.7% of wall posts on Facebook.
22.9% of users make up 77.1% of all “@” mentions on Twitter.
23.1% of projects make up 76.9% of project memberships on Github.
27.3% of users receive 72.7% of replies on Digg.
27.6% of all hamsters receive 72.4% of all friendships on Hamsterster.com.
35.7% of all Twitter users receive 64.3% of all follows.
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Degree distribution
C(n) » n¡°
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TODO
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Which distribution is fairer?
Flickr friendships OR Digg replies
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Lorenz Curve – Gini Coefficient
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Flickr Digg
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Perfect Power Laws
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High entropy
Low entropy
Entropy
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@kunegis
@noshir
@beyonce
@barabasi
@ststaab
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Entropy
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max He = ln jVj
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Normalized Entropy
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Gini vs Entropy
½ = ¡0.71p < 0.001
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Generality
Interpretation
Runtime
Coverage
Power Law
Power-law
Many (!)
Slow
d(u) ≥ dmin
Gini
All networks
Economy
Fast
All
Norm. Entropy
All networks
Physical
Fast
All
Comparison
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Thank YouJérôme Kunegis @kunegisJulia Preusse
WeST – Institute for Web Science and TechnologiesUniversity of Koblenz–Landau, Germany
konect.uni-koblenz.de
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ReferencesPareto, V. Manuale di economia politica con una introduzione alla scienza sociale (Manual of political economy). Milano : Societa Editrice Libraria, 1919.
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Edge distribution Degree distribution
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