DECISION MAKING IN A CONDOMINIUM AN ISING-LIKE SOCIOPHYSICAL - - PowerPoint PPT Presentation

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DECISION MAKING IN A CONDOMINIUM AN ISING-LIKE SOCIOPHYSICAL - - PowerPoint PPT Presentation

Apr 07, 2023 6 likes •558 views

DECISION MAKING IN A CONDOMINIUM AN ISING-LIKE SOCIOPHYSICAL SYSTEM Mrta Jvor Tams Geszti Roland Etvs University IN MEMORIAM GEORGE MARX (1927 2002) 2 Purpose to show: how we can use a simple model of statistical

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DECISION MAKING IN A CONDOMINIUM – AN ISING-LIKE SOCIOPHYSICAL SYSTEM

Márta Jávor Tamás Geszti Roland Eötvös University

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IN MEMORIAM

GEORGE MARX (1927 – 2002)

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Purpose

  • to show:

how we can use a simple model of statistical physics – the Ising model – and a statistical method – Monte Carlo - to study a complex sociological system

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Sociophysics

adaptation of statistical physics methods to sociological systems

  • Serge Galam „father of sociophysics”:

COLLECTIVE DECISION TAKING is like MAGNETIC ORDERING

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Two men dissussing with one another are similar to two interacting spins

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Simple model of ferromagnetism

The game is to learn about human community from the Ising model.

Ernst Ising

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𝐹 = −

𝑗,𝑘

𝐾𝑗𝑘𝑇𝑗𝑇

𝑘 − 𝐼 𝑗

𝑇𝑗

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ISING MODEL

energy coupling coefficient external magnetic field magnetization spin

The coupling is SYMMETRICAL!

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Only two possibilities

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Without external magnetic field

𝐼 = 0 𝐹 = −

𝑗,𝑘

𝐾𝑗𝑘𝑇𝑗𝑇

𝑘

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Simulation method

  • MC – Monte Carlo method

(using computer-generated random numbers) – using the Metropolis algorithm

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Metropolis algorithm

  • run over all spins on a lattice, and for each

spin

– propose a change from the current state: flip

  • 1 to +1 or +1 to -1, and calculate the

acceptance probability – decide to accept or reject this change by using a random number between 0 and 1:

  • accept the change

if random number ≤ acceptance probability

  • reject the change

if random number › acceptance probability

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Acceptance probability:

if if

Evaluate energy change ∆E accompanying the flip;

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Decision

  • generate a random number: r ⋲ (0,1)

Accept change if r‹W, Reject

  • therwise
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EXCEL Visual Basic macro

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2D 25×25 lattice

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Neighbours

i-1;j i;j-1 i,j i;j+1 i+1;j

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Periodic boundary conditions

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Periodic boundary conditions

each cell has 4 neighbours 25×25 lattice

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MADRID

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MOSCOW

„BUBLIK”

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TORUS

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Random initial configuration

1 2 2 1 2 1 1 1 1 2 1 2 2 2 2 1 1 1 1 1 1 1 2 2 1 1 2 2 2 2 1 1 1 1 1 1 2 1 2 2 1 1 2 2 2 2 1 2 2 2 2 1 1 2 1 1 1 1 1 2 2 1 1 1 1 2 2 1 1 2 2 2 1 2 2 1 2 2 2 1 1 2 1 1 2 2 1 1 1 2 2 1 2 1 2 2 2 2 1 1 1 2 2 1 1 1 2 1 2 2 2 1 1 1 1 2 2 2 2 1 1 1 2 1 1 1 2 2 1 1 2 1 1 1 2 2 2 2 2 1 2 1 2 1 2 1 2 2 1 2 1 2 2 2 2 2 1 1 1 2 1 1 2 1 2 2 2 1 2 1 1 2 2 2 1 2 1 2 1 2 1 2 2 1 2 2 1 2 2 2 1 2 1 1 2 2 2 2 1 1 1 2 2 1 2 1 1 1 1 1 2 2 1 2 1 2 2 2 1 2 1 1 2 2 2 1 2 2 2 1 1 1 1 1 2 2 2 1 2 2 2 2 2 1 1 2 2 2 1 1 2 2 2 1 2 2 2 1 2 2 2 1 2 2 1 2 2 1 1 2 1 1 2 2 2 1 1 1 1 2 1 1 1 1 2 1 1 1 2 1 1 2 1 2 1 2 1 2 2 2 2 2 2 2 1 2 1 2 2 2 2 2 2 1 2 2 2 2 1 2 1 1 1 1 1 2 1 1 2 2 2 1 2 2 1 2 2 2 2 2 2 1 2 1 2 2 1 1 1 1 2 1 2 2 2 2 2 2 2 2 1 1 1 1 1 2 2 2 2 1 2 2 2 2 2 2 2 2 1 1 2 1 2 1 2 2 1 2 1 2 2 2 2 2 1 2 1 2 1 1 2 1 1 1 1 2 2 2 2 1 1 1 2 1 1 1 1 1 1 2 1 2 2 1 1 2 2 1 2 1 2 1 2 2 2 2 2 1 1 2 1 2 2 1 1 1 1 1 2 1 1 2 2 1 1 1 2 2 1 1 2 1 2 2 2 1 1 1 2 1 2 1 1 2 1 2 1 1 1 1 1 2 2 1 2 2 1 1 1 1 1 2 1 2 1 1 1 2 2 2 1 1 1 1 2 2 1 2 1 1 1 2 1 2 1 1 1 2 2 1 2 2 2 1 2 2 1 1 1 1 2 1 2 1 2 2 1 2 2 2 1 1 2 1 1 1 2 1 1 2 2 1 1 2 2 2 1 1 1 1 2 2 2 2 2 2 1 1 2 1 1 1 2 1 1 2 2 1 2 1 1 2 1 2 2 2 2 2 1 1 1 1 2 2 1 2 1 1 1 2 1 1 1 1 1 2 1 1 1 1 2 2 1 1 1 2 1 1 1 2 2 2 2 1 1

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EXCEL worksheet

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100-step iteration result

  • 1.0000
  • 0.5000

0.0000 0.5000 1.0000 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 kT/J

M/N

M/N

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Statistics – EXCEL worksheet

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M/N depending on parameters

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Decision in the condominium

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One example

  • There is a hole on the roof

– two possibilities:

  • to repair
  • not repair, resolve
  • therwise
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Factors influencing decision

  • psychology

– individual background – openness towards other people

  • Sociology

– connections between neighbours – knowledge about the problem to decide

  • effects from environment unrelated to

the decision

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J=0

Everybody having his/her

  • wn idea
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Discussion J≠0

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Types of coupling

J›0 J‹0 asymmetrical non-Ising! symmetrical

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Symmetrical coupling ; J›0

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magnetizations from seven 100-step simulations, as a function of kT/J

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magnetizations from seven 100-step simulations, as a function of kT/J

2.27

ONSAGER theory

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Analysis of model’s results about the decision

  • main parameter of the model is the

ratio

𝑄 = 𝑙𝑈 𝐾

  • if this parameter is low (T is low)

– the neighbours pay attention to each other

  • if this parameter is hight (T is high)

– the neighbours pay attention to many other things

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EXTERNAL MAGNETIC FIELD may correspond to:

  • a strong argument

in favour of some decision

  • r a dominant personality
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Magnetization ~ achieving majority („polarization”), even in the presence of strong noise („high temperature”)

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Beyond the physical model:

asymmetric coupling

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Beyond the physical model: asymmetric coupling

i-1;j i;j-1 i,j i;j+1 i+1;j

upper & left neighbours

J

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Beyond the physical model: asymmetric coupling

i-1;j i;j-1 i,j i;j+1 i+1;j

upper & left neighbours lower & right neighbours

J qJ

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Beyond the physical model: asymmetric coupling

i-1;j i;j-1 i,j i;j+1 i+1;j

upper & left neighbours lower & right neighbours

J qJ

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Beyond the physical model: asymmetric coupling

i-1;j i;j-1 i,j i;j+1 i+1;j

upper & left neighbours lower & right neighbours

J qJ

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Beyond the physical model: asymmetric coupling

i-1;j i;j-1 i,j i;j+1 i+1;j

upper & left neighbours lower & right neighbours

J qJ

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q=0.4 kT/J=1.5

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q=0.2 kT/J=1.0

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Conclusion:

symmetrical coupling: the decision is final asymmetrical coupling: the decision is temporary

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SUMMARY

  • Simple physical models may reveal a lot about

complex social problems

  • Some common physical features of the model

(e.g. symmetric coupling) should be given up to get closer to social reality

  • Numerical modeling using simple tools (excel)

provide good insight for high-school teaching

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Beyond the physical model: asymmetric coupling

i-1;j i;j-1 i,j i;j+1 i+1;j

upper & left neighbours lower & right neighbours

J qJ