## "Social influence."

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## WHAT IS IT?

The simulation in this model tries to show the effect of social influence in a group of people, that is a complete connected graph: studying the initial median of people’ opinions and its difference with on the go median, it is possible to observe how people influence each other, creating none, one or several patches of opinions.

## HOW IT WORKS

According to Deffuant and Hegselmann-Krause models, when people meet each other they change their own opinion towards another: a new opinion depending on mu for Deffuant, the avarage opinion of other people in radius vision for Hegselmann-Krause.

## HOW TO USE IT

Before running the procedure, the user has to choose how many agents he wants to create and the distribution of opinions, with its relative parameter (“power-law-exponent” or “lambda-exponent”). “Setup” button actually creates people.
Pressing “go” the user can observe the evolving system and the median of the distribution of opinions: changing “epsilon” and “mu” is useful to create or destroy patches of opinions and setting the speed of achievement of consensus.
Slider “vision” changes the radius of every people in which others agents are chosen to modify opinions.
The two different opinion models can be chosen from “OpinionModel” button.

## THINGS TO NOTICE

The color of the agents is set equal to their opinion: for this reason the probability distributions of opinions are normalized on [0,140] instead of [0,1].

An extended value of “vision” drastically reduces the continuous refresh of agents’ movement on the world.

## THINGS TO TRY

The user should try both models: beginning from a low “epsilon”, he could increase its value to observe fast achievement of consensus. With Hegselmann-Krause model, moreover, he should not observe any difference in changing “mu”.

## EXTENDING THE MODEL

The effect of social influence in this model is studied on complete connected graph: the user could change this situation creating a random graph, or a Watts-Strogatz one or Barabasi one.

# PROCEDURES

```extensions [array]

breed [people person]

globals [
med0
med
]

people-own[opinion]

to setup
;; (for this model to work with NetLogo's new plotting features,
;; __clear-all-and-reset-ticks should be replaced with clear-all at
;; the beginning of your setup procedure and reset-ticks at the end
;; of the procedure.)
__clear-all-and-reset-ticks
setup-people
tick
do-plots
end

to setup-people
create-people number
set shape "person"
setxy random-xcor random-ycor
setup-opinion
set color opinion
]
set med0 median [opinion] of people
end

to setup-opinion
if (distribution = "power-law")[
if (power-law-exponent <= 0) [
user-message ( word "Error: the power law exponent must be greater than 0" )
stop
]
set opinion 140 * random-float 1.0 ^ (1 / (1 + power-law-exponent))
]
if (distribution = "exponential")[
if (lambda-exponent = 0)[
user-message ( word "Error: the lambda exponent must be different from 0" )
stop
]
set opinion (-1 / lambda-exponent) * ln(1 - (random-float 1.0) * (1 - e ^ (- 140 * lambda-exponent)))
]
end

to go
move-people
set med median [opinion] of people
tick
do-plots
end

to move-people
right random 360
forward 1
]
end

to change-opinion
if(OpinionModel = "Deffuant")[Deffuant]
if(OpinionModel = "Hegselmann-Krause")[Hegselmann-Krause]
ifelse show-opinion?
[set label opinion]
[set label ""]
end

to Deffuant
if (any? other people in-radius vision)[
let othe one-of other people in-radius vision
if (abs ([opinion] of self - [opinion] of othe) < epsilon) [
let increment opinion - [opinion] of othe
set opinion opinion - mu * increment
ask othe [set opinion opinion + mu * increment]
]
]
set color opinion
end

to Hegselmann-Krause
if (any? other people in-radius vision)[
let vectorOthers ([opinion] of other people in-radius vision)
let vectorOpinion filter [abs(? - [opinion] of self) < epsilon] vectorOthers
if (length vectorOpinion != 0) [
set opinion mean vectorOpinion
set color opinion
]
]
end

to do-plots
set-current-plot "Medians"
set-current-plot-pen "Initial-median"
plot med0
set-current-plot-pen "On-the-go-median"
plot med
end
```