biased_trust.nlogo

globals [biasSTD s alpha]

turtles-own [
  myjudg ; my judgment (signal + bias + noise)
  p ; my estimated probability of response 1
  myconf ; my confidence in my percept (always > 0.5)
  myconf2; my confidence after interaction
  myacc ; my accuracy
  mybiasty ; my bias type
  mybias ; my bias mean
  myslope ; slope of the confidence sigmoid function
  n ;; noise
  b ;; trial-level bias
  interact ;; interacting turtle
]

links-own [
  trust
]

patches-own []

to setup
  ca
  crt npopulation
  [
    set shape "Person"
    set color blue
    set heading 0
    set size 20 / npopulation
    set myslope random-float 1
    set mybiasty random 2
    ifelse mybiasty = 0
    [
      set color green
      set mybias (- bias)
      ]
    [
      set color red
      set mybias bias
      ]
    create-links-from other turtles
  ]
    layout-circle sort-on [color] turtles 8
    set alpha 0.01
    reset-ticks
end

to go
  repeat 1000 [
  tick
  set s (random-float 1) - 0.5
  ask turtles [
    make-private-decision
  ]
  ask turtles [
    update-trust
  ]
  if biased_advisor_sampling [
    ask turtles [
      sample-advisor]
    ask turtles [
      update-confidence]
    ask turtles [
      update-bias
      ]
    ]
  ]
end

to make-private-decision
  set n random-normal 0 noise ; noise
  set b random-normal mybias 1
  set myjudg (s + b + n) ;; my judgment = signal + bias + noise
  set p sigmoid myjudg myslope 0 1
  set myconf 0.5 + abs(p - 0.5)
  ifelse (myjudg > 0) = (s > 0)
  [set myacc 1]
  [set myacc 0]
end

to update-trust
  ask my-out-links [
    let outcome pcorr
    set trust (trust + (delta outcome trust))
    set thickness trust / 2
    ]
end

to sample-advisor
  let ids [] ; initialize ids to an empty list
  let weights [] ; initialize weights to an empty list
  ask other turtles [
    set ids lput who ids
    set weights lput [trust] of link [who] of myself who weights
    ]
  ;show ids
  ;show weights
  set interact turtle random-weighted ids weights ; choose interacting turtle by probability matching based on trust
end

to update-confidence
  let agree (myacc  = ([myacc] of interact)); agreement with interacting turtle
  ifelse agree
  [set myconf2 bayes myconf [myconf] of interact]
  [set myconf2 bayes myconf (1 - [myconf] of interact)]
end

to update-bias
  ;sign(sign([myjudg] of interact) * sign(myjudg)) * abs([myjudg] of interact - myjudg))
  let influence myconf2 - myconf
  set mybias (mybias + (sign myjudg) * sigmoid influence 10 -0.5 0.5)
end

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; delta learning rule
to-report delta [observed expected] ; delta rule
  report alpha * (observed - expected)
end

; probability that your partner is correct. For feedback cases this is real partner's accuracy; for no feedback cases this is estimated probability correct
to-report pcorr
  ifelse feedback
  [report [myacc] of end2] ;; with feedback
  [
    ifelse (([myacc] of end2) = ([myacc] of end1)); agreement
    [report ([myconf] of end1)]
    [report (1 - [myconf] of end1)]
    ] ;; with no feedback
  ;[
  ;  let p1 [myconf] of end2
  ;  let p2 [myconf] of end1
  ;  bayes p1  p2] ; with no feedback
end

; Bayes theorem given two probabilities
to-report bayes [p1 p2]
  report (p1 * p2) / ((p1 * p2) + ((1 - p1) * (1 - p2))) ;; with no feedback
end

; sigmoid function value with a given slope
to-report sigmoid [x slope lo hi]
  report lo + ((hi - lo) / (1 + e ^ (- slope * x)))
end

; report the bias of turtle at the end of a given link
to-report end2bias
  report [mybias] of end2
end

; select a value in values with probability distribution equal to weights
to-report random-weighted [values weights_raw]
     let weights [] ; normalised weights (add up to 1)
     foreach weights_raw [ ?1 -> set weights lput (?1 / sum weights_raw) weights ]
     let selector (random-float sum weights)
     let running-sum 0
     (foreach values weights [ [?1 ?2] ->
         set running-sum (running-sum + ?2)
         if (running-sum > selector) [
             report ?1
         ]
     ])
end

to-report sign [value]
  ifelse value > 0 [report 1]
  [ifelse value = 0 [report 0] [report -1]]
end

; make bias on each trial dependent on the previous trial interaction: if you interacted equally with everybody you should see convergence of bias to 0, but if you interact more with your bias population you expect to not converge


; if one person does not change where the final bias converge to?
@#$#@#$#@
GRAPHICS-WINDOW
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8
859
550
-1
-1
16.152
1
10
1
1
1
0
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1
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ticks
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SLIDER
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npopulation
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1
NIL
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BUTTON
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18
955
51
Setup
setup
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1
T
OBSERVER
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NIL
1

SWITCH
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189
110
feedback
feedback
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BUTTON
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Go
go
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T
OBSERVER
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SLIDER
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bias
bias
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1
NIL
HORIZONTAL

SLIDER
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noise
noise
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NIL
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PLOT
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25
1159
179
mean judgment
time
NIL
0.0
10.0
-10.0
10.0
true
false
"" ""
PENS
"red judgement" 1.0 0 -16777216 true "" "plot mean [myjudg] of turtles with [color = red]"
"green judgment" 1.0 0 -7500403 true "" "plot mean [myjudg] of turtles with [color = green]"
"pen-2" 1.0 0 -2674135 true "" "if ticks = 500 [\n  plot-pen-up\n  plotxy ticks plot-y-min\n  plot-pen-down\n  plotxy ticks plot-y-max\n]"

PLOT
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188
1159
337
mean bias
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NIL
0.0
10.0
-10.0
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true
false
"" ""
PENS
"red bias" 1.0 0 -16777216 true "" "plot mean [mybias] of turtles with [color = red]"
"green bias" 1.0 0 -7500403 true "" "plot mean [mybias] of turtles with [color = green]"
"pen-2" 1.0 0 -2674135 true "" "if ticks = 500 [\n  plot-pen-up\n  plotxy ticks plot-y-min\n  plot-pen-down\n  plotxy ticks plot-y-max\n]"

PLOT
1173
24
1340
178
mean confidence
NIL
NIL
0.0
10.0
0.0
1.0
true
false
"" ""
PENS
"red confidence " 1.0 0 -16777216 true "" "plot mean [myconf] of turtles with [color = red]"
"green confidence" 1.0 0 -7500403 true "" "plot mean [myconf] of turtles with [color = green]"
"pen-2" 1.0 0 -2674135 true "" "if ticks = 500 [\n  plot-pen-up\n  plotxy ticks plot-y-min\n  plot-pen-down\n  plotxy ticks plot-y-max\n]"

PLOT
1175
188
1341
338
bias STD
time
std bias
0.0
10.0
0.0
10.0
true
false
"" ""
PENS
"default" 1.0 0 -16777216 true "" "plot standard-deviation [mybias] of turtles"
"pen-1" 1.0 0 -2674135 true "" "if ticks = 500 [\n  plot-pen-up\n  plotxy ticks plot-y-min\n  plot-pen-down\n  plotxy ticks plot-y-max\n]"

SWITCH
20
237
255
270
biased_advisor_sampling
biased_advisor_sampling
0
1
-1000

@#$#@#$#@
## WHAT IS IT?

(a general understanding of what the model is trying to show or explain)

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## CREDITS AND REFERENCES

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@#$#@#$#@
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@#$#@#$#@
NetLogo 6.0.2
@#$#@#$#@
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@#$#@#$#@
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@#$#@#$#@
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