On the Dynamics of Social Conflicts

On the Dynamics of Social Conflicts
Looking for the Black Swan
Andrea Tosin∗
Istituto per le Applicazioni del Calcolo “M. Picone”
Consiglio Nazionale delle Ricerche
Rome, Italy
a.tosin@iac.cnr.it
http://www.iac.cnr.it/~tosin
Mathematical Models and Methods for Planet Earth
Rome, May 27–29, 2103
∗
Joint work with: N. Bellomo (Polytechnic University of Turin, Italy), M. A. Herrero (Universidad Complutense, Madrid, Spain), G.
Ajmone Marsan (OECD, Paris, France)
Andrea Tosin, IAC-CNR (Rome, Italy)
On the Dynamics of Social Conflicts, Looking for the Black Swan
1/7
Complexity Features of Social Systems
Living → active entities
Andrea Tosin, IAC-CNR (Rome, Italy)
On the Dynamics of Social Conflicts, Looking for the Black Swan
2/7
Complexity Features of Social Systems
Living → active entities
Behavioral strategies, bounded rationality → randomness of human
behaviors
Andrea Tosin, IAC-CNR (Rome, Italy)
On the Dynamics of Social Conflicts, Looking for the Black Swan
2/7
Complexity Features of Social Systems
Living → active entities
Behavioral strategies, bounded rationality → randomness of human
behaviors
Heterogeneous distribution of strategies
Andrea Tosin, IAC-CNR (Rome, Italy)
On the Dynamics of Social Conflicts, Looking for the Black Swan
2/7
Complexity Features of Social Systems
Living → active entities
Behavioral strategies, bounded rationality → randomness of human
behaviors
Heterogeneous distribution of strategies
Behavioral strategies can change in time
Andrea Tosin, IAC-CNR (Rome, Italy)
On the Dynamics of Social Conflicts, Looking for the Black Swan
2/7
Complexity Features of Social Systems
Living → active entities
Behavioral strategies, bounded rationality → randomness of human
behaviors
Heterogeneous distribution of strategies
Behavioral strategies can change in time
Self-organized collective behavior can emerge spontaneously:
A Black Swan is a highly improbable event with three
principal characteristics: It is unpredictable; it carries a massive
impact; and, after the fact, we concoct an explanation that
makes it appear less random, and more predictable, than it was.
[N. N. Taleb. The Black Swan: The Impact of the Highly Improbable, Random House, New
York City, 2007]
Andrea Tosin, IAC-CNR (Rome, Italy)
On the Dynamics of Social Conflicts, Looking for the Black Swan
2/7
Methods of the Generalized Kinetic Theory for Active Particles
v1
u1
Andrea Tosin, IAC-CNR (Rome, Italy)
Politica
l
vr
opinion
vm
ui
un
Social classes
On the Dynamics of Social Conflicts, Looking for the Black Swan
3/7
Methods of the Generalized Kinetic Theory for Active Particles
v1
u1
Politica
l
vr
opinion
vm
ui
un
Social classes
Social classes: (poor) u1 = −1, . . . , ui , . . . , un = 1 (wealthy)
Andrea Tosin, IAC-CNR (Rome, Italy)
On the Dynamics of Social Conflicts, Looking for the Black Swan
3/7
Methods of the Generalized Kinetic Theory for Active Particles
v1
u1
Politica
l
vr
opinion
vm
ui
un
Social classes
Social classes: (poor) u1 = −1, . . . , ui , . . . , un = 1 (wealthy)
Political opinion: (dissensus) v1 = −1, . . . , vr , . . . , vm = 1 (consensus)
Andrea Tosin, IAC-CNR (Rome, Italy)
On the Dynamics of Social Conflicts, Looking for the Black Swan
3/7
Methods of the Generalized Kinetic Theory for Active Particles
v1
u1
Politica
l
vr
opinion
vm
ui
un
Social classes
Social classes: (poor) u1 = −1, . . . , ui , . . . , un = 1 (wealthy)
Political opinion: (dissensus) v1 = −1, . . . , vr , . . . , vm = 1 (consensus)
Distribution function: fir (t) = # pepole in ui with opinion vr at time t
dfir
=
dt
Andrea Tosin, IAC-CNR (Rome, Italy)
On the Dynamics of Social Conflicts, Looking for the Black Swan
3/7
Methods of the Generalized Kinetic Theory for Active Particles
v1
u1
Politica
l
vr
opinion
vm
ui
un
Social classes
Social classes: (poor) u1 = −1, . . . , ui , . . . , un = 1 (wealthy)
Political opinion: (dissensus) v1 = −1, . . . , vr , . . . , vm = 1 (consensus)
Distribution function: fir (t) = # pepole in ui with opinion vr at time t
m
n
X
X
dfir
=
dt
pq pq
ηhk
Ahk (i, r)fhp fkq
p, q=1 h, k=1
|
{z
Gain
}
pq
Ahk (i, r):=P((uh , vp )→(ui , vr )|(uk , vq ))
Andrea Tosin, IAC-CNR (Rome, Italy)
On the Dynamics of Social Conflicts, Looking for the Black Swan
3/7
Methods of the Generalized Kinetic Theory for Active Particles
v1
u1
Politica
l
vr
opinion
vm
ui
un
Social classes
Social classes: (poor) u1 = −1, . . . , ui , . . . , un = 1 (wealthy)
Political opinion: (dissensus) v1 = −1, . . . , vr , . . . , vm = 1 (consensus)
Distribution function: fir (t) = # pepole in ui with opinion vr at time t
m
n
X
X
dfir
=
dt
pq pq
ηhk
Ahk (i, r)fhp fkq
− fir
p, q=1 h, k=1
|
m X
n
X
rq q
ηik
fk
q=1 k=1
{z
Gain
}
|
{z
Loss
}
pq
Ahk (i, r):=P((uh , vp )→(ui , vr )|(uk , vq ))
Andrea Tosin, IAC-CNR (Rome, Italy)
On the Dynamics of Social Conflicts, Looking for the Black Swan
3/7
Stochastic Games: Cooperation/Competition + Self-Conviction
Social dynamics: cooperation vs. competition
9
competition
h-1 h
k k+1
γ0=3
γ0=7
8
7
1
n
6
γ
class distance ≤ γ
5
4
cooperation
h h+1
k-1 k
3
2
1
1
n
class distance > γ
Andrea Tosin, IAC-CNR (Rome, Italy)
0
-1 -0.8 -0.6 -0.4 -0.2
0
S
0.2 0.4 0.6 0.8
On the Dynamics of Social Conflicts, Looking for the Black Swan
1
4/7
Stochastic Games: Cooperation/Competition + Self-Conviction
Social dynamics: cooperation vs. competition
9
competition
h-1 h
k k+1
γ0=3
γ0=7
8
7
1
n
6
γ
class distance ≤ γ
5
4
cooperation
h h+1
k-1 k
3
2
1
1
n
0
-1 -0.8 -0.6 -0.4 -0.2
class distance > γ
0
S
0.2 0.4 0.6 0.8
1
Opinion dynamics: self-conviction
Andrea Tosin, IAC-CNR (Rome, Italy)
On the Dynamics of Social Conflicts, Looking for the Black Swan
4/7
Stochastic Games: Cooperation/Competition + Self-Conviction
Social dynamics: cooperation vs. competition
9
competition
h-1 h
k k+1
γ0=3
γ0=7
8
7
1
n
6
γ
class distance ≤ γ
5
4
cooperation
h h+1
k-1 k
3
2
1
1
n
0
-1 -0.8 -0.6 -0.4 -0.2
class distance > γ
0
S
0.2 0.4 0.6 0.8
1
Opinion dynamics: self-conviction
Poor individuals in poor society → distrust
Andrea Tosin, IAC-CNR (Rome, Italy)
On the Dynamics of Social Conflicts, Looking for the Black Swan
4/7
Stochastic Games: Cooperation/Competition + Self-Conviction
Social dynamics: cooperation vs. competition
9
competition
h-1 h
k k+1
γ0=3
γ0=7
8
7
1
n
6
γ
class distance ≤ γ
5
4
cooperation
h h+1
k-1 k
3
2
1
1
n
0
-1 -0.8 -0.6 -0.4 -0.2
class distance > γ
0
S
0.2 0.4 0.6 0.8
1
Opinion dynamics: self-conviction
Poor individuals in poor society → distrust
Wealthy individuals in a wealthy society → trust
Andrea Tosin, IAC-CNR (Rome, Italy)
On the Dynamics of Social Conflicts, Looking for the Black Swan
4/7
Stochastic Games: Cooperation/Competition + Self-Conviction
Social dynamics: cooperation vs. competition
9
competition
h-1 h
k k+1
γ0=3
γ0=7
8
7
1
n
6
γ
class distance ≤ γ
5
4
cooperation
h h+1
k-1 k
3
2
1
1
n
0
-1 -0.8 -0.6 -0.4 -0.2
class distance > γ
0
S
0.2 0.4 0.6 0.8
1
Opinion dynamics: self-conviction
Poor individuals in poor society → distrust
Wealthy individuals in a wealthy society → trust
Poor individuals in a wealthy society
→ most uncertain behavior
Wealthy individuals in a poor society
Andrea Tosin, IAC-CNR (Rome, Italy)
On the Dynamics of Social Conflicts, Looking for the Black Swan
4/7
Case Studies
Initial conditions
0.05
0.05
0
-1 -0.75
-0.5-0.25
0 0.25
0.5 0.75
Social classes
1
1
0.75
0.5
0.25
0
-0.25 Political
-0.5
opinion
-0.75
-1
Society “neutral” on average
Mean wealth: 0
Andrea Tosin, IAC-CNR (Rome, Italy)
0
-1 -0.75
-0.5-0.25
0 0.25
0.5 0.75
Social classes
1
1
0.75
0.5
0.25
0
-0.25 Political
-0.5
opinion
-0.75
-1
Society poor on average
Mean wealth: −0.4
On the Dynamics of Social Conflicts, Looking for the Black Swan
5/7
Case Studies
Society which is “economically neutral” on average
γ=3
cooperative
0.15
γ=7
competitive
0.35
0.3
0.25
0.1
0.2
0.15
0.05
0.1
0
-1 -0.75
-0.5-0.25
0 0.25
0.5 0.75
Social classes
Andrea Tosin, IAC-CNR (Rome, Italy)
1
1
0.75
0.5
0.25
0
-0.25 Political
-0.5
opinion
-0.75
-1
0.05
0
-1 -0.75
-0.5-0.25
0 0.25
0.5 0.75
Social classes
1
1
0.75
0.5
0.25
0
-0.25 Political
-0.5
opinion
-0.75
-1
On the Dynamics of Social Conflicts, Looking for the Black Swan
5/7
Case Studies
Society which is poor on average
γ=3
cooperative
0.25
0.2
0.15
constant γ
0.1
0.05
0
-1 -0.75
-0.5-0.25
0 0.25
0.5
Social classes
0.75 1
1
0.75
0.5
0.25
0
-0.25 Political
-0.5
opinion
-0.75
-1
0.4
0.35
0.3
0.25
0.2
variable γ
0.15
0.1
0.05
0
-1 -0.75
-0.5-0.25
0 0.25
0.5
Social classes
Andrea Tosin, IAC-CNR (Rome, Italy)
0.75 1
1
0.75
0.5
0.25
0
-0.25 Political
-0.5
opinion
-0.75
-1
γ=7
competitive
0.55
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-1 -0.75
-0.5-0.25
0 0.25
0.5
Social classes
0.65
0.6
0.55
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-1 -0.75
-0.5-0.25
0 0.25
0.5
Social classes
0.75 1
1
0.75
0.5
0.25
0
-0.25 Political
-0.5
opinion
-0.75
-1
0.75 1
1
0.75
0.5
0.25
0
-0.25 Political
-0.5
opinion
-0.75
-1
On the Dynamics of Social Conflicts, Looking for the Black Swan
5/7
What About Black Swans?
Andrea Tosin, IAC-CNR (Rome, Italy)
On the Dynamics of Social Conflicts, Looking for the Black Swan
6/7
What About Black Swans?
A Black Swan is a highly improbable event with
three principal characteristics: It is unpredictable;
it carries a massive impact; and, after the fact, we
concoct an explanation that makes it appear less
random, and more predictable, than it was.
Andrea Tosin, IAC-CNR (Rome, Italy)
On the Dynamics of Social Conflicts, Looking for the Black Swan
6/7
What About Black Swans?
A Black Swan is a highly improbable event with
three principal characteristics: It is unpredictable;
it carries a massive impact; and, after the fact, we
concoct an explanation that makes it appear less
random, and more predictable, than it was.
Need for macroscopically detectable indicators of sudden changes
Identify early-warning signals preceding radicalization
Andrea Tosin, IAC-CNR (Rome, Italy)
On the Dynamics of Social Conflicts, Looking for the Black Swan
6/7
What About Black Swans?
A Black Swan is a highly improbable event with
three principal characteristics: It is unpredictable;
it carries a massive impact; and, after the fact, we
concoct an explanation that makes it appear less
random, and more predictable, than it was.
Need for macroscopically detectable indicators of sudden changes
Identify early-warning signals preceding radicalization
Example
Let f̃ be a phenomenologically guessed/expected asymptotic distribution:
dBS (t) := kf̃ − f (t)kRn×m
Andrea Tosin, IAC-CNR (Rome, Italy)
On the Dynamics of Social Conflicts, Looking for the Black Swan
6/7
What About Black Swans?
A Black Swan is a highly improbable event with
three principal characteristics: It is unpredictable;
it carries a massive impact; and, after the fact, we
concoct an explanation that makes it appear less
random, and more predictable, than it was.
Need for macroscopically detectable indicators of sudden changes
Identify early-warning signals preceding radicalization
Example
Let f̃ be a phenomenologically guessed/expected asymptotic distribution:
e.g.
dBS (t) := kf̃ − f (t)kRn×m = max
1≤r≤m
Andrea Tosin, IAC-CNR (Rome, Italy)
n
X
|f˜ir − fir (t)|.
i=1
On the Dynamics of Social Conflicts, Looking for the Black Swan
6/7
What About Black Swans?
0.8
γ =3
γ =7
0.7
0.6
dBS
0.5
0.4
0.3
0.2
0.1
0
Tmax
0
t
Andrea Tosin, IAC-CNR (Rome, Italy)
On the Dynamics of Social Conflicts, Looking for the Black Swan
6/7
What About Black Swans?
0.8
γ =3
γ =7
0.7
0.6
dBS
0.5
0.4
0.3
0.2
tipping points
0.1
0
Tmax
0
t
Andrea Tosin, IAC-CNR (Rome, Italy)
On the Dynamics of Social Conflicts, Looking for the Black Swan
6/7
Bibliography
G. Ajmone Marsan, N. Bellomo, and A. Tosin.
Complex Systems and Society – Modeling and Simulation.
SpringerBriefs in Mathematics. Springer, 2013.
N. Bellomo, M. A. Herrero, and A. Tosin.
On the dynamics of social conflicts looking for the Black Swan.
Kinet. Relat. Models, 6(3):459–479, 2013.
Andrea Tosin, IAC-CNR (Rome, Italy)
On the Dynamics of Social Conflicts, Looking for the Black Swan
7/7

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