Caciques Funcionando

7/28/2019 Caciques Funcionando

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Phase transitions in

social hierarchies with a

distribution of resources(caciques y cabezones)

Marcelo del Castillo-Mussot, Gerardo

G. Naumis, Gerardo Vzquez, Luis

Prez

Instituto de Fsica, UNAM. Mxico D.F.,


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Introduction

Our interests: energy and societySocial hierarchies

Bonabeau model of social hierachies.

The role of resources.Conclusions


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Hierarchies in animals

C. Darwin, 1859, animal fitness: key to evolution

Our abilities has planted:

humans at the center of the universe.

Plato differentiated two distinct souls,

Man, with two souls: one, capable of reason.

Non-human animals, only brute mortal soul.


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Many animals held territories.

Entry into foreign areas causes fighting.Thus animals are forced to spread out.

Surplus animals may be expelled, or may stay on as non-breeders.

Gregarious animals develop hierarchies.

Dominant animals often have first choices.

Lowest members of the hierarchy suffer food shortages,

This limits their reproduction rate.

Example: hens exhibit this type of hierarchy: the pecking order.

Inside species, there are social hierarchies


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Class formation in historic times did not take place through gradual

differentiation in pacific economic competition, but was the result of

violent conquest and subjugation." (Franz Oppenheimer).

Sociological consensus:


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Social stratification is relatively rigid; social position determined

by ancestors. (example: slavery)

Everybody wants to rise (of course!!): role of education and productivity.


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Bonabeau Model

Territory: a square lattice with NsitesMagents are placed at random:

E. Bonabeau, G. Theraulaz, J.L. Deneubourg, Physica A 217, 1157 (1995).

Mp

N


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Agents chose at random one of the 4 neighbouring sites and try to move there:

1) Site empty: stay there.

2) Site not empty: FIGHT


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Figths are decided at random.

h(i) is the history (or fitness) of agent i, and his probability of winning is:

( ( ) ( ))

1

1 e h j h iq

If the agresor wins, he and the defensor interchange places.

For the winner h(i) h(i)+1, and the looser h(i) h(i)-1. is a parameter

ORDER PARAMETER (DEGREE OF HIERARCHY)

22q q

Enhanced phase transition: D. Stauffer, Int. J. Mod. Phys. C 16, 8 (2003).


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Our modifed rules of movement

At the beginning, a value is assigned to each site of the lattice atrandom, following a certain distribution (natural resources) or with acertain geometry (MxicoUSA border)

An agent always moves to the richest site in the neighbourhood.

Special cases arise when two or more sites have similar values.Rule: decide at random among rich sites.

If the original site has the same value of the richest neighbour, jumpin order to recover Bonabeau model when all sites are rich or poor.


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Results

Diffusivity

Valuable sites per capita

2

1

1lim

Ni

t i

xD

N t

1

1 N

i

i

m mN


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Percolat ion o f r ich sites: order parameter and d if fus iv i ty


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Ampl i f icat ion o f the di f fus iv i ty


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Wealth or money per capita: percolation


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Non-Percolat ion o f r ich sites: order parameter and d if fus iv i ty


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Distribution of valuable sites per capita: non-percolation of rich sites


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Caciqu es y c abezon es


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Cacique phase: lackof global information and glassy behavior


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CONCLUSIONS

The introduction of valuable sites enhance hierarchies even at low populations

(except at high populations and high concentration of rich sites).

If there are few valuable sites, there is a high inequality due to local power: caciques.

The system can be trapped in a cacique phase, as in a glass, due to lack of global

information about the available resources.

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Caciques Funcionando