Phenomenology
of social dynamics
Santo Fortunato
Outline
• Prologue
• Building a phenomenology:
1) elections
2) collective opinion shifts
• Outlook
“Measure what is measurable, and make
measurable what is not so…”
Physics
Society!
History
Social statistics: number of births,
deaths, crimes, suicides, etc.
From Newtonian mechanics of particles
to
statistical mechanics to describe gases
Sociophysics
From individuals that interact locally to
collective behaviour and organization.
Risky business!
People are not atoms: their
interactions are not reproducible!
Necessary condition: the size of the
social groups must be big (large scale
behaviour)
In this way, the phenomena won’t be
much affected by individual features
Interesting aspects for statistical
physicists:
• Large-scale regularities: scaling
• Universal features
• Microscopic origin of macroscopic
behaviour
Quantitative understanding!
Focus: opinion dynamics
• Opinion dynamics models explain if
and when consensus is formed or not
• Shall we content ourselves with such
a qualitative description?
• Is it possible to validate this
approach?
Building a phenomenology
of social dynamics
Quantitative characterization of
large
scale social phenomena
• Elections
• Collective opinion shifts
Elections
• Large scale social phenomenon
• Lots of available data
Elections
State elections in Brazil 1998 (Costa Filho et al.,
PRE, 1999)
v = # votes received
by a candidate
Focus: distribution of
v across all
candidates
1/v behavior
Elections in Brazil 2002
(Costa Filho et al., Physica A 2003)
1/v decay reproducible over the years
Indian elections (González et al.
IJMPC, 2004)
• 1/v decay occurs in different countries
• Is it universal?
The 1/v behaviour is not universal!
Problem: is it correct to put together
candidates of different parties?
Support for different parties wildly
fluctuates, in an unpredictable way !
If we model the competition of candidates
of the same party, the party does not play
any role!
Candidates are chosen based on some form
of contact between them and the voters:
model!
A new analysis (S.F. & C. Castellano,
Phys. Rev. Lett. 99, 138701, 2007)
Proportional elections with open lists
Examples:
Italy (1946-1992), Poland, Finland
Distribution of votes for candidates
within a party
P(v,Q,N)
N = total votes for party
Q = number of party
candidates
Scaling I
Only two independent variables!
P(v,Q,N)=P*(v,N/Q)= P*(v,v0)
Scaling II
Only one independent variable!
P(v,Q,N)=P*(v,N/Q)= F(vQ/N)!
The scaling function is universal!
The universal curve has a
lognormal shape!
F ( x) 
1
2 x
e
 (ln( x )   ) 2 / 2 2
  0.45
2
  0.91
Municipal elections display identical decay
Conclusion
of election analysis
Same behaviour in different
countries and years: the dynamics
must be elementary!
Collective opinion shifts
Studied by Michard and Bouchaud (2004)
Principle: imitation + social pressure lead
to collective effects with rapid variations
Examples: crowd panic, financial crashes,
economic crisis, boom of new products,
etc.
A model
Binary choices: Si=+1,-1
Three ingredients:
• each agent i has a personal opinion Φi,
real in ]-∞,+∞[, distribution R(Φ)
• public information: a field F(t) in ]-∞,+∞[
acting on all agents
• social pressure: agent i is affected by
“neighboring” agents, coupling Jij


1
Si (t )  sign i  F (t ) 
N


1
O
Si
N


j


J S j (t  1)


i
Field F varies from -∞ to +∞, which O(F)?
Random Field Ising Model at T=0
J. Sethna et al., Nature 410, 242 (2001)
For J larger than a critical Jc, O(F) has a
discontinuity at some Fc(J) (opinion swings)
For J <~ Jc
dO[ F ] 1  F  Fc ( J ) 

 G
,   Jc  J
3/ 2

dF
  

G(x) is universal, i.e. independent of R(Φ)
h
w
Characteristic relation between height h
and width w of the curve:
2 / 3
h~w
Assumption: collective opinion shifts
occur near criticality
Expectation/hope: recovering the peak
of G(x) from real data!
2 / 3
O
h~w
t
?
Birth rates in Europe
Drop in most European countries in the
period 1950-2000
Cell phones in Europe
Total number of cell phones in use in
various European countries in the last
decade
Other evidence?
•
•
•
•
Elections
Consumer behavior
Web user behavior
Web-based experiments
Outlook
• The distribution of the number of votes
received by candidates of the same
party in proportional elections is
universal!
• Collective opinion shifts are
characterized by a universal pattern of
variation for the speed of change
• Search for other regularities in data is
necessary to create a quantitative
phenomenology in social dynamics
http://www.arxiv.org/pdf/0710.3256