Phenomenology of social dynamics

Santo Fortunato

Outline

• Prologue• Building a phenomenology: 1) elections 2) collective opinion shifts• Outlook

Physics

Society!

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 scalebehaviour)

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 phenomenologyof social dynamics

• Elections • Collective opinion shifts

Quantitative characterization of largescale social phenomena

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 wildlyfluctuates!

• Position of parties is more or less known on relevant issues

• Party is selected depending on the issues• Candidate to be voted is chosen depending

on the existence of some form of direct/indirect contact with the voter → model!

A new analysis (S.F. & C. Castellano, physics/0612140)

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 partyQ = number of party

candidates

Scaling I

P(v,Q,N)=P*(v,N/Q)= P*(v,v0)

Only two independent variables!

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!

22/2))(ln(

2

1)(

xe

xxF

91.0

45.02

Municipal elections display identical decay

Same behaviour in different countries and years: the dynamics must be

elementary!

Conclusion of election analysis

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

• 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

Binary choices: Si=+1,-1

Three ingredients:

j

jii tSJN

tFsigntS )1(1

)()(

Random Field Ising Model at T=0

J. Sethna et al., Nature 410, 242 (2001)

Field F varies from -∞ to +∞, which O(F)?

i

iSN

O1

For J larger than a critical Jc, O(F) has a discontinuity at some Fc(J) (opinion swings)

For J <~ Jc

JJJFF

GdF

FdOc

c

,

)(1][2/3

G(x) is universal, i.e. independent of R(Φ)

Characteristic relation between height h and width w of the curve:

3/2~ wh

h

w

Assumption: collective opinion shifts occur near criticality

Expectation/hope: recovering the peakof G(x) from real data!

?~ 3/2wh

t

O

Birth rates in Europe

Drop in most European countries in theperiod 1950-2000

Cell phones in Europe

Total number of cell phones in use in various European countries in the last decade

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 “physical” phenomenology in social dynamics