Manybody interactions in sociophysics and their role in coalition forming

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Many-body interactions in sociophysics and their
role in coalition forming

• Marcelo del Castillo-Mussot, Gerardo G. Naumis,
  Fernando Samaniego Steta, Gerardo J. Vazquez
• Institute of Physics, National University of
  Mexico (UNAM)
• Physica A, 379, 226 (2006)
• Chapter in book on Networks (NOVA PUBLISHERS)

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MOTIVATIONS

• Coalitions or blocks (family, clans, political
  parties, parlament, wars, etc)
• Important geopolitical event
• IRAQ WAR - which countries sent troops ?

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Coalition Members ( according to US White House )

• .
• Forty-nine countries are publicly committed to
  the Coalition, including
• Afghanistan Albania Angola Australia
  Azerbaijan
• Bulgaria Colombia Costa Rica Czech Republic
  Denmark Dominican Republic El Salvador
  Eritrea Estonia Ethiopia Georgia Honduras
  Hungary Iceland Italy Japan Kuwait Latvia
  Lithuania Macedonia Marshall Islands
  Micronesia Mongolia Netherlands Nicaragua
  Palau Panama Philippines Poland Portugal
  Romania Rwanda Singapore Slovakia Solomon
  Islands South Korea Spain Tonga Turkey
  Uganda Ukraine United Kingdom United States
  Uzbekistan

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Map of invading coalition
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US 27 countries (August 2003)
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Iraq troop numbers (March 2004)
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Bilateral Relationships
For every pair of agents i , j (people,
countries, political parties, etc.) we can
associate a pairwise propensity Jij as
positive (friends) or negative (enemies). Energy
E ij _ J ij si sj Where every si
can take the values 1 or - 1. ? the
product si sj is 1 or - 1.
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Bilateral Relationships

• The system is more stable when the energy E ij
  is minimum
• J ij positive ? Ferromagnetic si
  sj
  (friends)
• J ij negative ? Antiferromagnetic si
  ? sj (enemies)

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Bilateral Relationships

• E _ ? J ij si sj si sj
• J ij represents the afinity between i and
  j
• ( history, religion, political afinity,
  governments, etc).
• si is the intensity or force of the
  agent
• So we have to minimize the energy !

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Alignments prediction
PREVIOUS STUDIES 1. WORLD WAR II (Europe, 17
countries) Axelrod and Bennett, The complexity of
cooperation, Princeton (1997) 2. DESMEMBERING
OF FORMER YUGOSLAVIA Florian and Galam, Eur.
Phys. Journal B 16 (2000)
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Ising model

• Magnetic system.
• Each spin can take the values 1..
• B interacts with all spins.

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The Galam Model (G Model)

• This model considers the local and global
  interactions.
• All the agents are connected between them.
• Economical or military pressures over any agent
  i, are taked into account by
• The Hamiltonian of this model is the following one

where
For the coalition A
for the coalition B
When there is no a priori preference
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The Three-body Interactions

• The three-body interactions are not taken into
  account in the previous models.
• Simplified model of the Iraq War started in 2003
• IRAQ (Q)
• ISRAEL (I)
• MUSLIMS (M)
• U. S. A. (U)

The parameters are chosen according to the
following relation
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Considering the three-body interactions
E(3) H(3) - ? ? J ijk si sj sk si sI s
k J ijk relates i , j and kGeneral
case H H (2) ? H (3) is the
two-body Hamiltonian with a correction that
considers the three-body interactions
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where
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Aplying the model to our example...

• The numerical values for the parameters where

The case where M and I are neutrals is favorable
when
So a have to accomplish the following relation
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THE POTTS MODEL
Coalition A
Coalition B
Neutral agent
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Considering the three-body interactions...

• In this case, he perturbative term is

• Where we have to consider the energy costs due to
  the natural conflicts.

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CONCLUSIONS

• The three-body interactions can not be omitted
  (as in nuclear and particle physics).
• We can include neutral agents (Potts model).
• IMPORTANT THE INPUT DATA MUST BE REASONABLE!
• FUTURE
• MODELS OF 4, 5, 6 BODIES
• COHESION and DAMAGE EFFECTS