wcss2012 - consensus by segregation - the formation of local consensus within context switching...

Consensus by segregation - the formation of localconsensus within context switching dynamics

Davide Nunes, Luis Antunes

GUESS / LabMAg / University of Lisbon, Portugal{davide.nunes, xarax}@di.fc.ul.pt

September 7, 2012

WCSS 2012

Outline

1 Introduction

2 Multi-context ModelsConsensusContext PermeabilityOn Context SwitchingA Model of Context Segregation

3 Model of Experiments

4 Preliminary Model analysisContext Tolerance AnalysisSwitching mechanism trends

5 Conclusion and Future Work

Introduction Multi-context Models Model of Experiments Preliminary Model analysis Conclusion and Future Work

On Social Spaces

In real world scenarios, agents interact in multiple complex socialrelations with other agents and/or institutions.

Social Space

Provides Structure, fundamental for the construction ofplausible interaction scenarios

Shape the interaction processes

Highly contextual

Davide Nunes, Luis Antunes (GUESS) WCSS2012 3 / 22


Problems of current modeeling approaches

To collapse the complexity of social relations into a singlerelation depicted in a bi-dimensional space or a single socialnetwork is overly simplistic.

It may jeopardise the quality of simulation results andundermine the confidence in the derived conclusions and theirapplicability.



Multiple context Models

Social relations may be of different kind and quality,possessing different topologies and social dynamics.

We model social spaces with multiple concurrent socialnetworks [3, 1, 2].These networks represent abstract social relations.

Research Context

We focus on the study of dynamic consequences of the topologicalstructures underlying social simulation scenarios.





We model social spaces with multiple concurrent socialnetworks [3, 1, 2].

These networks represent abstract social relations.

Research Context






We model social spaces with multiple concurrent socialnetworks [3, 1, 2].These networks represent abstract social relations.

Research Context




Consensus

Consensus Game

The agent society is trying to achieve arbitrary globalconsensus

The agents must choose between two possible choices

In each iteration of the game:1 each agent selects an available neighbour2 an agent observes the choice adopted by the neighbour3 the agent decides to switch its choice if the newly observed

choice represents the majority



Consensus

Consensus Game



In each iteration of the game:

1 each agent selects an available neighbour2 an agent observes the choice adopted by the neighbour3 the agent decides to switch its choice if the newly observed




Consensus

Consensus Game



In each iteration of the game:1 each agent selects an available neighbour

2 an agent observes the choice adopted by the neighbour3 the agent decides to switch its choice if the newly observed




Consensus

Consensus Game



In each iteration of the game:1 each agent selects an available neighbour2 an agent observes the choice adopted by the neighbour

3 the agent decides to switch its choice if the newly observedchoice represents the majority



Consensus

Consensus Game



In each iteration of the game:1 each agent selects an available neighbour2 an agent observes the choice adopted by the neighbour3 the agent decides to switch its choice if the newly observed




Consensus

The emergence of conventions

Consensus games can be regarded as a process of abstractconvention emergence.

Problem - Self Reinforcing Substructures

Daniel Villatoro, “Social Norms for Self-Policing Multi-agentSystems and Virtual Societies”

groups of nodes that, given the appropriate configuration ofagent preferences and network topology, do maintain subconventions

present in network models like BA scale-free networks

modelling social spaces with a single network containing thesestructures prevents the convergence to global consensus

This phenomenon was also confirmed in all our previous work[1, 2, 3]



Context Permeability

Context Permeability

Our previous work on context permeability [3, 1] explored anagent-based model in which agents interact in multiple socialnetworks at the same time playing the consensus game.

This provided some basis for the exploration of thepermeability phenomena.

Social Permeability

Social Contexts can overlap providing a context permeabilityphenomena.

This social world feature is of extreme importance for thedissemination of phenomena, and societal adaptiveness.



On Context Switching

The context switching model

We explore the previous idea of context permeability in whatregards to the temporal dynamics of multiple social contexts.

In this model agents interact in one context at the time.

Agents switch their context after each interaction based on aswitching probability ζ.

Temporal Context Permeability

some contexts can overlap providing permeability throughoutdifferent temporal instances



On Context Switching

Example of Context Switching

Figure : Example of context switching [2] considering two contexts forsocial agent denoted by the number 1. In this case, these contexts arecreated by two distinct physical spaces. Common nodes in bothneighbourhoods (like agent 2) represent an acquaintance of actor 1 inboth of them. The dashed circle represents the scope of each context.



A Model of Context Segregation


We extend the previous context switching model with asegregation mechanism.

We add a new parameter of social tolerance µ.

Questions

Does the formation of local consensus groups foster a fasterconvergence to global consensus?

What are the dynamics to be expected from strategic contextswitching by a segregation process?




Context Segregation Example

c

a

d

b

c

a

d

b

t + 1 - switching by segregation

Context 1Tolerance: 0.5

Time: t

Context 2Tolerance: 0.5

Time: t

Figure : At the end of the simulation iteration t, agent a has to decidewhether to switch context or not. The current context for agent a has atolerance of µC1 = 0.5. As the ratio of neighbours with an oppositechoice is above the tolerance threshold, the agent will become active incontext 2 at time t + 1.



Model of Experiments

Each experiment consists of 30 runs in which 300 agentsinteract until 3000 cycles pass, or total consensus is reached.

Our goal is to analyse the influence of the new parameter (thecontext tolerance µCi

) in the speed of convergence to globalconsensus measured in terms of the number of encountersnecessary.

tolerance parameter span from 0 to 1 in intervals of 0.05.

switching probability parameter ζCivaried between three

values that were found to be interesting for the contextswitching mechanism [2].



Preliminary Model analysis

We have analysed the response surfaces for the toleranceparameter span

We conducted different experiments varying the switchingprobability to observe the interplay between these twoparameters.

We vary the network topologies experimenting with bothhomogeneous and heterogeneous social contexts.



Context Tolerance Analysis

Homogeneous Social Contexts: scale-free networks

Tole

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0.0

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Tolerance for Context 20.0

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0.60.8

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ncounters 10000

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(a) (ζC1 , ζC2) = (0.25, 0.25)

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ncounters 10000

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(b) (ζC1 , ζC2) = (0.5, 0.5)

Tole

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ncounters

15000

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0.0 0.2 0.4 0.6 0.8 1.0

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(c) (ζC1 , ζC2) = (0.75, 0.75)



Context Tolerance Analysis

Heterogeneous Social Contexts: scale-free + k-regularnetworks

Tole

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xt 1

0.0

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(d) (ζC1 , ζC2) = (0.5, 0.5)and k = 10

Tole

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ncounters 5000

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(e) (ζC1 , ζC2) = (0.5, 0.5)and k = 30

Tole

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ncounters 5000

10000

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(f) (ζC1 , ζC2) = (0.5, 0.5)and k = 50


Global switching mechanism trends:homogeneous scale-free networks I

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0 50 100Simulation Steps

Num

ber

of A

gent

s S

witc

hing

Switching Method

●●●

●●●

●●●

No Switching

Switching by Probability

Switching by Tolerance

(g) (ζC1 , ζC2) = (0.25, 0.75)

Global switching mechanism trends:homogeneous scale-free networks II

50

100

150

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0 50 100 150Simulation Steps

Num

ber

of A

gent

s S

witc

hing

Switching Method

●●●

●●●

●●●

No Switching

Switching by Probability

Switching by Tolerance

(h) (ζC1 , ζC2) = (0.75, 0.75)


Conclusion

Summary

Contexts are important for dissemination phenomena instructured societies.

Social segregation allows for convergence speed-up of suchprocesses.

The formation of initial local consensus groups is deeplyconnected to the convergence to global consensus.

Future Work

The construction of an integrated model of multiple socialcontexts.

Model validation with real case studies.

Exploration of different kinds of context dynamics.



References I

L Antunes, J Balsa, P Urbano, and H Coelho.Exploring context permeability in multiple social networks.In Proceedings of the World Congress on Social Simulation,2008.

Luis Antunes, Davide Nunes, Helder Coelho, Joao Balsa, andPaulo Urbano.Context Switching versus Context Permeability in MultipleSocial Networks.In Progress in Artificial Intelligence, volume 5816 of LectureNotes in Computer Science, pages 547–559, 2009.

Luis Antunes, Paulo Urbano, and Helder Coelho.Context Permeability.Sciences-New York, 2006.



References II

Sean Luke, Claudio Cioffi-Revilla, Liviu Panait, Keith Sullivan,and Gabriel Balan.MASON: A Multiagent Simulation Environment.Simulation, 81(7):517–527, 2005.

Davide Nunes and Luis Antunes.Parallel execution of social simulation models in a gridenvironment.Proceedings of the 13th International Workshop onMulti-Agent Based Simulation, MABS 2012, 2012.


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