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Opinion Polarization by Learning from Social Feedback Sven Banisch & Eckehard Olbrich MPI for Mathematics in the Sciences (Leipzig) Opinion Dynamics and Collective Decision, Bremen 2017
Opinion Polarization by Learning from Social Feedback
Sven Banisch & Eckehard OlbrichMPI for Mathematics in the Sciences (Leipzig)
Opinion Dynamics and Collective Decision, Bremen 2017
Opinion Dynamics and Cultural Conflictin European Spaces
WESTERNNATIONALISM
Europeannationalism
White pride
The Golden One
Traditionalist Western Art
The Patriarchy
Smash Cultural Marxism
Unity Rosaries
Freedom of Fear
Be more Swedish
Holland& Barrett Sweden
Norse Art By Micke Johansson
Jack Donovan
Magnanimity
Omniphi
Génération Identitaire
PPDM X Straight Edge X Father Frost Mode X
Beauty
Identity Ireland
Mariusz Pudzianowski
This is Europa
The United Patriots Front
United Patriots Front
Basic Philosophical Re-Education by Blair Cottrell
Maxime Solemn
Right On
Justnationalistgirls
Daniel Friberg
Total War
Nordic Wear
MURDERSCENE
The Aristocrat
Architectural Revival
I'm white
Dennis Michael Lynch
Traditum Orbis Architecture
Imperium
The World Art Nouveau
The Occidental Sentinel
Masterpieces Drawing& Painting
Cultura Classica
Dark and fantastic arts
Counter-Currents PublishingRed Ice
Artaman: The Hyperborean Garden
Golden Century of World Fairs 1851-1951
Art Nouveau& Art Deco
Spells of Art, Gnōsis, and Ritual
The Artists of The Artists Rifles
Europe's Awakening
Anglo American Identity Movement
Women Painters ~
No More Brother Wars
A Handbook of Traditional LivingThe Traditionalist
Nordic Beauty
Real Crusades History
American White History Month 2
Teagan's SmileVoice of One Crying in the Wilderness
Damsel of the Faith
Theotokos Institute for Catholic Studies
A Gentleman's RowFight the New Drug
Institute of Classical Architecture& Art
Scala Regia
Veronica Partridge
The Warden Post
The Soul of the East
Outdoor Research
André Andersson Custom Knives
Smash Cultural Marxism
Refugees Not Welcome In Devon
Soutien au général Piquemal
Smash Freemasonry
Smash Marxismo Cultural
Fascism a misconception
World War II Day by Day
United Patriots Front Productions.
Support the Dover to calais truckers.The Return.
The Populist Party
The Hidden World
Maldon and Heybridge British National Party
Aryan Women in Wheat Fields
World Politics Review
BBC Politics
League of the South
The Beauty of European Girls& Women
Architecture of Ireland
Francis Terry and Associates
Stephen Mitford Goodson
Better Out Than In
The RAMZPAUL Show
Comrade Corbyn: Jeremy Exposed
Nordic Sisterhood
All Nationalist Association& Media
AZL
Labour25
The Conservative Revolution
Pissed Off White Americans
Reporting the anti-white filth on FB
Occidental Offensive
White People World Wide 1
Stop White South African Genocide
White History Month
Eesti Iseseisvuspartei - EIP
Honor USS Liberty Vets
Ukrainian Genocide Famine Foundation - USA
Preserve Our HeritageEuropa Identitaria
Kleinfontein
Orania
Raise awareness of South African farm murders by brutal torture
Smash Cultural Marxism II
Australia First Party Brisbane
American Freedom Party
Smash Usury
The Occidental Observer
I Am Proud To Be British
Remove all EU flags
Praying for South Africa
In Favor Of Traditional Gender Roles
A History of British America
Arktos
Christian Women Against Femen
Nationalism and Religion
The Return of Reason
White Girls who love White Guys II
Українська Естетика
Svoboda - Ukrainian political party
Red October
Traditionalist Youth Hour Podcast
Political Correctness Must Die
Fed Up White Person
BudweiserConservative Voices
Nordic gods The South Africa Project
Open Borders for Israel
Nordic Brotherhood
Censorbugbear Reports
Prosper in Israel
Heterosexual Awareness Month 3
Endecja Podlaskie
Political Correctness Gone Wild
Proud to be White does Not Mean Racist
Support Human Rights for Whites 2
Letters From White South Africa
Enough is Enough: Stop Homosexual Promotion.
This is Italy
European Independent Media Centre
Hellenic Victims of Communism - ĬȪȝĮIJĮ IJȠȣ ȀȠȝȝȠȣȞȚıȝȠȪ
Nationalists of the World Unite
This is Austria
This is Ireland
By The People For The People
Be Active Front USA 2
Traditional Britain Group
Aryan Hyperborean Heritage
Generation Identity London
BNPtv
British National Party
CasaPound Italia
This is Sweden
This is the Netherlands
This is Germany
▶ online and offline data▶ precision language processing▶ dynamic graph theory▶ media geography
▶ computational modelling ▶ game theory▶ conceptual spaces▶ divergent mindsets
Embedding into (latent) political space
argu
men
ts o
n a
set of issues
resulting positions
on the set of issues
argu
men
ts o
n a
set of issues
resulting positions
on the set of issues
argu
men
ts o
n a
set of issues
resulting positions
on the set of issues
Over the course of a discourse not all the issues playing a role are visible from the very beginning. New issues may arise, first-time issues may cease to be central, and sometimes very few controverse points turn out and become the key issues
A controversy, most often, involves a series of issues that are logically and cognitively linked. A proper spatial representation of such complexity should therefore take into account the
multi-dimensionality and interconnectedness of the points at stake.
We propose to model this by a network the nodes of which are key issues in a debate and the links weights for relations in between those.
Over the course of a discourse not all the issues playing a role are visible from the very beginning. New issues may arise, first-time issues may cease to be central, and sometimes very few controverse points turn out and become the key issues
across the participants and this has important consequences for the process of finding compromise. In a prolonged debate the importance of and relations between the dimensions of it are subject to cognitive negotiations as well.
on which final decisions are based. Importantly, the weights assigned to the different issues as well as the understanding about their mutual relatedness differ
multi-dimensionality and interconnectedness of the points at stake.
We propose to model this by a network the nodes of which are key issues in a debate and the links weights for relations in between those.
multi-dimensionality and interconnectedness of the points at stake.
We propose to model this by a network the nodes of which are key issues in a debate and the links weights for relations in between those.
multi-dimensionality and interconnectedness of the points at stake.
We propose to model this by a network the nodes of which are key issues in a debate and the links weights for relations in between those.
multi-dimensionality and interconnectedness of the points at stake.
We propose to model this by a network the nodes of which are key issues in a debate and the links weights for relations in between those.
For a debate to be fruitful the emergence of a common understanding of the structure underlying a controversy is necessary.
A controversy, most often, involves a series of issues that are logically and cognitively linked. A proper spatial representation of such complexity should therefore take into account the
H2020 – FETPROACT-2016 - 732942
odycceus.eu
Polarization: an important but also controversial issue
The Puzzle of Polarization
» If people tend to become alike in their beliefs, attitudes, and behavior when they interact, why do not all such differences eventually disappear? « (Axelrod, 1997)
» Since universal ultimate agreement is an ubiquitous outcome of a very broad class of mathematical models, we are naturally led to inquire what on earth one must assume in order to gene-rate the bimodal outcome of community cleavage studies. « (Abelson, 1964)
▶ These questions have inspired a lot of modelling work throug-hout decades: the field is now known as Opinion Dynamics
Terminology
-
)
mainly -
Mechanisms
Mechanisms → Outcomes
social influence + status homophily → consensus (static networks, traditional models, binary models)
social influence + opinion homophily → plurality with
Positive + negativ social influence → polarization (Bourdieu: cultural/aesthetic differentiation)
influence + opinion homophily → consensus Argument persuasion + opinion homophily → polarizationBiased assimilation + opinion homophily → polarization
Polarization Dynamics by Learning from Social Feedback Social feedback + status homophily → polarization
Ƒ or Ŷ social neighborhood
or non-confirming response depending on the current opinion in the neighborhood
Q(Ƒ) Q(Ŷ)
Rooted in Reinforcement Learning
→ → r = -1 i i
j
i = oi oj Ƒ = 1 Ŷ = -1
4.
Q(Ƒ) Q(Ŷ)
o
Micro- and Macrodynamics▶ Selected individual trajectories (spatial random graph)
Q(Ƒ) Q(Ŷ)
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0 20 40 60 80 100��
0
���
���
���
���
1
0 20 40 60 80 100 0 20 40 60 80 100
Agent 29 Agent 17 Agent 69
time time time
value
Q(1)4��
opinion change
time (every Nth step)
∆V =
V(Ƒ
)-V(Ŷ
)
Polarization Dynamics▶ Value difference ∆Q = Q(Ƒ)-Q(Ŷ) can be interpreted as
strength of support (interval in continuous models is usually interpreted this way)
Q(Ƒ) Q(Ŷ)
emergence of two opposing opinion groups
Micro- and Macrodynamics▶ Macroscopic polarization measures (DiMaggio et al. 1996)
Q(Ƒ) Q(Ŷ)
0 10 20 30 40 50 60 70 80 90 1000
0.2
0.4
0.6
0.8
1
time (every Nth step)
Mac
rosc
opic
Mea
sure
s
6XSSRUW�6WUHQJWK�ï�Support Strength 1DispersionBimodalityAverage OpinionDissimilarity
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Mathematical Characterizations
»solve«-
Q(Ƒ) Q(Ŷ)
Opinion Games I
→ oN → -oN
ε > 0 *i oN | *
i -oN
i *i
*i oN
→ !
Q(Ƒ) Q(Ŷ)
Opinion Games IIA B
A B A B = 1)→ » «→
Convergence of Q-LearningDynamical evolution of two agents A and B each linked
to a fixed community of opposed sign (kA = 10, kB = 2) ▶ Quick convergence to the payoffs of the associated opinion game
0 100 200 300 400 500 600 700 800 900 1000ï�
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0
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1
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2
time (every 10th step)
6 Q
i
6QB6QA6/A6/B
0 100 200 300 400 500 600 700 800 900 1000ï�
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Qi(o
i)
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/A��
/A(1)
A B
Cohesive Sets and Stable Play
1 and S
1 and S S1 S
Q(Ƒ) Q(Ŷ)
On Two-Island Graphs
▶
▶
On Two-Island Graphs▶ qM and qL probability that one agent is less
than 1/2-cohesive▶ There are M respectively L agents in the communities and probability that
none of them is less than 1/2-cohesive is
M = 10 | L = 10
M = 10 | L = 50
M = 50 | L = 100
M = 50 | L = 50
M = 100 | L = 100
M = 500 | L = 500
p
Pr[S
M a
nd S
L ½-c
ohes
ive]
NetworkRealizations
Theory
▶ Comparison of the theoretical results with an average over 100 network realizations
▶ Notice that for large system limit there is a sharp transition at p = 1/2
Stability of Polarization on Two-Island Graphs▶ Polarized initialization of the two-community network such that agents in
M maximally support 1 and agents in L support -1▶ 100 model realizations à
20000 × N steps▶ Combinatorial analysis of
cohesiveness provides reasona-ble approximation
▶ Loss of stability for smaller p in large systems due to finite-size fluctuations (learning rate)
p
Pr[ s
tabl
e po
lari
zatio
n ]
M = L = 10M = L = 50M = L = 100M = L = 500
Cohesiveness:
M = L = 10M = L = 50M = L = 100M = L = 500
Simulations:
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 10
0.2
0.4
0.6
0.8
1
modularity
pola
rizat
ion
| con
sens
us p
roba
bilit
y
Consensus Prob. N = 100Consensus Prob. N = 500Consensus Prob. N = 1000Polarization N = 100Polarization N = 500Polarization N = 1000
On Socio-Structural Conditions for Polarization▶ Polarization measure (Flache/Macy) and consensus probability as
a function of molularity in a stochastic block model (C = 10)▶ (Almost) linear relation between modularity and polarization
indicative ofmeaningful
communities
A Bigger Picture (Discussion)
» «
The Big Picture (Discussion)
Conclusion V(Ƒ) V(Ŷ)
Online Demonstrations▶ www.universecity.de/demos/OpinionValuesSmall.html
▶
▶
▶ In
