Simple models for complex systems toys or tools? (part I) Katarzyna Sznajd-Weron Institute of Theoretical Physics University of Wrocław

Lessons from simple models Computational philosophy: lessons from simple models (October 11-13, 2007, Niels Bohr Institute) This meeting celebrates the 20 year anniversary of selforganized criticality and the approach to science personified by one of its inventors the late Per Bak. Organizers: Dante Chialvo, Maya Paczuski and Kim Sneppen (c) 2011 Katarzyna Sznajd-Weron 2

Simple models Easier to deal with Do not attempt many detailed predictions Help to understand universal features Pose fundamental questions related to cooperativity self-organization communication regulation and functionality How do complicated systems keep any organization? Simple rules complex behaviour? (c) 2011 Complex Katarzyna Sznajd-Weronsystem simple behavior? 3

Agenda: Physics and Sociology Schelling Segregation Model A short historical perspective Can we treat people like particles? - social psychology Sociology public opinion Simple models of opinion dynamics Types of social response Introducing noise Updating scheme is important! (c) 2011 Katarzyna Sznajd-Weron 5

Thomas Schelling An American economist (14 April 1921) Nobel Prize in Economic Sciences (2005) for "having enhanced our understanding of conflict and cooperation through game-theory analysis. Checkerboard model of residential segregation (c) 2011 Katarzyna Sznajd-Weron 6

An Interview with One day I was flying home from Chicago, and I did not have anything to read. I wondered what to do ( ) So, I drew a line on a sheet of paper, put down ( ) X s and O s, and said now suppose I thought that these were black and whites, and both had ideas about neighbors. I started moving them around ( ) xo o x x o x o x o xoo ox (c) 2011 Katarzyna Sznajd-Weron 8

Dynamic Model of Segregation. The spatial structure of the model is a 2D grid. There are B (blue) agents and R (red) agents who are initially located on the grid at random. Agents may be happy or unhappy. Agent are unhappy if the proportion of other agents of its color in its neighborhood is below a certain threshold. In each iteration one unhappy agent is randomly selected to move to a random empty cell in the lattice (c) 2011 Katarzyna Sznajd-Weron Schelling, Thomas C. (1971) Dynamic Models of Segregation. Journal of Mathematical Sociology 1:143-186. 11

Lesson from this simple model Mild preferences total segregation Simple agent s rules can create complex global patterns or emergent behavior A milestone in the study of emergent global phenomena based on local social interactions Agent based modeling Schelling, Thomas C. (1971) Dynamic Models of Segregation. Journal of Mathematical Sociology 1:143-186. (c) 2011 Katarzyna Sznajd-Weron 13

What about Ising model? ( ) long time ago I discovered, somebody told me that, there were some physical models, I think something in crystal formation. Somebody was referring to ISING model, which was a well-known model of, I think, crystal formation [cytat z wywiadu przeprowadzonego 06.03.2001 przez N. Emrah Aydinon] (c) 2011 Katarzyna Sznajd-Weron 14

A historical perspective Philip Ball The physical modeling of society: a historical perspective, Physica A (2002) English philosopher Thomas Hobbes (1588 1679) - The first person to try to deduce what the mechanical model of the universe meant for human society Leviathan, 1642: a model the collective Commonwealth theoretical framework - preferences of individuals and the nature of the interactions between them (c) 2011 Katarzyna Sznajd-Weron 18

Social physics Introduced by Adolphe Quetelet in 1835 Essay on Social Physics: Man and the Development of his Faculties Project of a social physics and concept of the "average man Average man - characterized by the mean values of measured variables that follow a normal distribution Goal - to understand the statistical laws underlying such phenomena as crime rates, marriage rates or suicide rates. (c) 2011 Katarzyna Sznajd-Weron 19

Average man and crime rates France (from 1827) statistical data about crimes Number of crimes is constant (each year) Quetelet behavior is driven by forces independent of the free will Everybody has a free will!!! What about sociology? (c) 2009 Katarzyna Sznajd-Weron 22

Social physics Sociology French political philosopher Auguste Comte Comte defined social physics as the study of the laws of society (1842) He discovered that Quetelet had appropriated the term 'social physics' prior to him He invented the term 'sociologie' (sociology) He disagreed with Quetelet's collection of statistics. (c) 2011 Katarzyna Sznajd-Weron 23

Physics becomes statistical Maxwell - Kinetic theory of gases (1859) He indicated in 1873, the experiences of social physicists lent him confidence that this statistical approach could extract order from the microscopic chaos The molecules are like so many individuals, having the most various states of motion, and the properties of gases only remain unaltered because the number of these molecules Statistics, entering physics through the agency of social science, soon came to dominate it (c) 2011 Katarzyna Sznajd-Weron 24

Sociophysics was born XXXVI Winter School Exotic Statistical Physics (2000) Serge Galam father and mother of sociophysics Galam, Gefen i Shapir (1982 ) new field sociophysics You can learn more from 25

Can we treat people like particles? Social psychology situation more important than individual traits Social influence (Latane, 1981) Informational influence (Sherif 1935) Normative influence (Asch 1956) Conformity: obedience to authority, peer pressure, social validation (c) 2011 Katarzyna Sznajd-Weron 28

Conformity Conformity - the main mechanism of collective actions. Informational: when in doubt, imitate Normative: when in Rome, do as the Romans do. Aversion to standing out in the crowd (c) 2011 Katarzyna Sznajd-Weron 29

Sherif experiment (1935) Informational Influence Participants observed a stationary point of light in a dark room Asked to judge how much the light source moved (autokinetic effect) Participants took part in groups, heard each other s judgments (c) 2011 Katarzyna Sznajd-Weron 30

The power of social validation Milgram, Bickman & Berkowitz, 1969 Results of experiments: 1 4%, 4-5 80% Robert B. Cialdini: Social Validation the fundamental way of decision making (c) 2011 Katarzyna Sznajd-Weron 32

conformity conformity (%) The size of the group is important Conformity (social validation) Group size a threshold of 4-5 persons (Latane, 1981) 80 60 40 40% 30% 20 Milgram et al (1969) 0 0 5 10 15 the size of the group (c) 2011 Katarzyna Sznajd-Weron 20% 10% Asch (1956) 0% 1 2 3 4 5 6 7 8 9 10 The size of the group 34

Unanimity is the key! The presence of a social supporter reduced the total number of yielding responses from 32% to 5.5%! Participants were far more independent when they were opposed by a seven person majority and had a partner than when they were opposed by a three-person majority and did not have a partner. (c) 2011 Katarzyna Sznajd-Weron 36

Opinion opinion - verbalized attitude (Trommsdorff 1998), measured in surveys discrete opinions: Ising spins Potts variables Continues opinions? not in surveys private attitude public opinion (c) 2011 Katarzyna Sznajd-Weron 37

Opinion and attitude Attitude - is a hypothetical construct that represents an individual's like or dislike for an item; learned predisposition to respond towards a given object (Fishbein/Ajzen 1975) Attitude based on cognition rational thinking Attitude based on emotions values we subscribe Opinion - verbalized attitude (Trommsdorff 1998), measured in surveys (c) 2011 Katarzyna Sznajd-Weron 38

individual collective action The hunger protest took place in May-June 2004 in several prisons in Poland. It started in Wołów (reason: overcrowding in cells) Within a week several prisons joined the protest (2320 prisoners in 10 prisons) (c) 2011 Katarzyna Sznajd-Weron 41

Protests in Egypt and Tunisia In Egypt protests started on Tuesday, January 25 2011 - first on such a large scale since the 1970s The reason? Sociologists claim that it was a domino effect Egyptian revolution has been inspired by the successful revolution in Tunisia In Tunisia - Suicide of a young man who could not find a job and was barred from selling fruit without a permit (c) 2011 Katarzyna Sznajd-Weron 42

Interesting variables: exit (relaxation) time to reach final state as a function of the system size density of interfaces (active bonds) versus the relative number of pairs of neighboring spins with opposite signs exit probability the probability that the system, initially in a disordered configuration with a fraction p of positive spins, reaches a state with all spins of the same sign survival probability fraction of runs surviving at time t, i.e. not having reached full order 1- CDF of exit times (c) 2011 Katarzyna Sznajd-Weron 44

Voter model on the lattice Exactly solvable in any dimension (Frachebourg & Krapivsky, 1996) The only stable states are the fully ordered ones! d=1 -> consensus, reached by a finite system after a time τ(n) ~ N^2 d=2 -> consensus, reached by a finite system after a time τ(n) ~ N log N (c) 2011 Katarzyna Sznajd-Weron 46

Remember - Unanimity is the key! The presence of a social supporter reduced the total number of yielding responses from 32% to 5.5%! Participants were far more independent when they were opposed by a seven person majority and had a partner than when they were opposed by a three-person majority and did not have a partner. (c) 2011 Katarzyna Sznajd-Weron 50

agreement preexposure disagreement Responses to social influence (Nail et. al. 2000) postexposure agreement disagreement conformity independence congruence anticonformity P.R.Nail, G.MacDonald, D.A.Levy Psychological Bulletin vol. 126, pp. 454-470 (2000) (c) 2011 Katarzyna Sznajd-Weron 60

Conformity and anticonformity They are similar in the sense that both acknowledge the group norm The level of anticonformity depends on the society (asserting uniqueness) Contrarians (Galam, 2002) p 1 p 2 (c) 2011 Katarzyna Sznajd-Weron 62

Lesson from this model Model with conformers and anticonformers For small values of anticonformity (<p*) spontaneous reorientations occur complete repolarizations The mean reorganization time for p=p* is minimal No need to introduce an external field nor a strong leader to obtain social repolarizations (c) 2011 Katarzyna Sznajd-Weron 69

Updating matters K. Sznajd-Weron, S. Krupa, Phys. Rev. E 74, 031109 (2006) random sequential updating parallel updating c-parallel updating (randomly chosen fraction c of spins is updated synchronously) Bartosz Skorupa, PhD student Dr Sylwia Krupa (c) 2011 Katarzyna Sznajd-Weron 71

Summary Simple models are used by computational sociologists Problem with social data (not a science?) The goal is to understand the system Social influence interactions between individuals Several types of social responce Unexpected behaviour complex systems Dynamics and updating scheme is important! (c) 2011 Katarzyna Sznajd-Weron 80