globals [uncertainty-colours uncert-of-extremists]

turtles-own [uncertainty opinion]

;;;;;;;;;;;;;;;;;;;;;;;;;
;;; global procedures ;;;
;;;;;;;;;;;;;;;;;;;;;;;;;

to setup
  ;; note that parameter names have suffixes of the paramter name in the paper

  clear-all
  
  ;; later used in colouring the plots
  set uncertainty-colours [red orange yellow green lime turquoise]
  set uncert-of-extremists 0.05
  
  ;; calculations as to the size of the various sub-populations
  let num-extremists round num-of-agents * prop-of-extremists
  let num-moderates num-of-agents - num-extremists
  let num-upper-extremists num-extremists / 2
  let num-lower-extremists num-extremists - num-upper-extremists
  
  ;; create moderates with random opinions
  create-turtles num-moderates [
    set uncertainty uncert-of-moderates
    set opinion (random-float 2) - 1
  ]
  
  ;; create upper then lower extremists
  create-turtles num-upper-extremists [
    set uncertainty uncert-of-extremists
    set opinion 0.99
  ]
  create-turtles num-lower-extremists [
    set uncertainty uncert-of-extremists
    set opinion -0.99
  ]
  
  ;; put tutles in intial position
  ask turtles [initialise-agent-display]
  reset-ticks
end

to go
  ;; if time is done stop simulation
  if ticks  > max-time * num-of-agents [stop]
  
  ;; pick two random agents let one influence the other
  ;; a simplification of the original paper since in that paper
  ;; agents simultaneously influence each other

  ask one-of turtles [
    ;; each agent is influenced by one other random one
    be-influenced-from one-of other turtles
  ]

  ;; only bother plotting every once in a while: when, on average, all have interacted once
  if (ticks mod num-of-agents) = 0 [ ask turtles [plot-agent] ]
  tick
end

;;;;;;;;;;;;;;;;;;;;;;;;
;;; agent procedures ;;;
;;;;;;;;;;;;;;;;;;;;;;;;

to be-influenced-from [oth]
  ;; only influenced if difference between opinion and other's opinion is less than
  ;; my uncertainty...
  if abs (opinion - [opinion] of oth) < uncertainty [
    ;; ...in which case shift my opinion and uncertainty towards other's
    set opinion 0.95 * opinion + 0.05 * [opinion] of oth
    set uncertainty (1 - speed-uncertainty-change) * uncertainty 
                    + speed-uncertainty-change * [uncertainty] of oth
  ]
end

;;;
;;; all the rest are to do with the display of agents
;;;

to initialise-agent-display
  ;; what each turtle does in setup
  hide-turtle
  penup
  colour-agent
  position-agent 0
  pendown
end

to position-agent [tck]
  ;; move the turtle to the position corresponding to its opinion and the time
  ;; values need scaling to fit exactly on current world
  setxy 
    (max-pxcor - min-pxcor) * (ceiling (tck / num-of-agents)) / max-time + min-pxcor
    0.5 * (opinion + 1) * (max-pycor - min-pycor) + min-pycor
end

to colour-agent
  ;; make the turtles (and hence their lines) a colour corresponding to their uncertainty
  ;; from 0 up to the max (the initial uncertainty of moderates) using the list of colours
  ;; set up as a global variable
  let pos round (0.49 + 5 * uncertainty / uncert-of-moderates)
  if pos > length uncertainty-colours [set pos length uncertainty-colours]
  set color item round (0.49 + 5 * uncertainty / uncert-of-moderates) uncertainty-colours
end

to plot-agent
  ;; once simulation is going, plotting involves (re)colouring each agent and moving it to its new position
  colour-agent
  position-agent ticks 
end
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@#$#@#$#@
## WHAT IS IT?

This is an example model, used as part of the "2-day Introduction to Agent-Based Modelling". 

It graphically shows a mutual influence process.


## HOW IT WORKS

Each simulation tick two agents are drawn at random and one influences the other.  

The influence of one agent on another depends on the uncertainty of the one being influenced.  Only if the difference in their opinions is within the uncertainty level is an agent influenced, in which case its opinion is mixed with a 5% proportion of the other and a 95% of their own (the % with which the uncertainty is mixed is set using a slider).

The simulation is initialised with a certain proportion of "extremists" who equally occupy the top and bottom of the range of opinions and who have a low uncertainty (0.05), and a broad "swathe" of moderates with random opinions but low initial uncertainty (set by a slider).

Agents all have different levels of:
* agreement on an issue, represented by a number -1 to 1
* uncertainty about their opinion, represented by a number from 0 to 2

Each iteration: one (randomly picked) agent is randomly paired with another
That other influences their opinion and uncertainty, but only if the other’s opinion is sufficiently close to their own (difference is less than their uncertainty)


## HOW TO USE IT

Set the population size, the proportion of extremists, the initial uncertainties of moderates and extremists, and the maximum number of time units the simulation will go for.  

The max-time is the length of the x-axis.

Press "setup" to intialise with these parameters, then press go to run.

## THINGS TO NOTICE

See if you can guess the outcomes with different parameter settings before you run it.  Under what settings does one get a big central group?  When does one get a split with one group tending towards one extreme and another to the other?  When does almost all moderates get pulled towards an extreme.

## THINGS TO TRY

Play with the settings, run the simulations, see how many qualitatively different kinds of outcome there are and under what conditions they tend to occur.

## EXTENDING THE MODEL

* What might one add to help understand what is happening in the simulation?
* What happens if you change the interaction rule: "be-influenced-from"? 
* How might you change the simulation so that everybody is influenced exactly once per simulation tick rather than one agent every tick?


## NETLOGO FEATURES

Note use of hidden turtles drawing lines to make a trace of the evolving opinion values.

We did not bother to define different breeds for moderates and extremists, since once the simulation has been initialised they interact and behave in the same way.

## RELATED MODELS

This is a distant relative of the model described in the paper: 

Guillaume Deffuant, Frédéric Amblard, Gérard Weisbuch and Thierry Faure (2002) How can extremism prevail? A study based on the relative agreement interaction model. Journal of Artificial Societies and Social Simulation 5(4)1. <http://jasss.soc.surrey.ac.uk/5/4/1.html> 

In that simulation the extent of influence is determined by the "overlap" of uncertainty regions and agents mutually influence each other each time they are paired.

## CREDITS AND REFERENCES

Originally written by Bruce Edmonds for Day 3 of "Introduction to Social Simulation" Course, 29th April 2012 and then further simplified for the "2-Day Introduction to Agent-Based Modelling" 28th Feb/1st March 2013
http://cfpm.org/simulationcourse
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