Netlogo-Models/Bias and Information Exchange.nlogo at master

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	turtles-own [heads tails bias h? accuracy-list accuracy]

	directed-link-breed [active-links active-link]
	directed-link-breed [inactive-links inactive-link]
	links-own [ current-flow ]

	globals [T H]


	to setup
	clear-all

	set-default-shape turtles "person"
	create-biased-turtles
	create-turtles-prior
	create-links
	reset-ticks
	print (word "Heads:" H)
	print (word "Tails:" T)
	print (word "Total:" (H + T))
	format
	end

	to create-biased-turtles
	crt num_agents [
	setxy random-xcor random-ycor
	let b random-float (Agents_bias / 100)
	let sign random 2
	ifelse (sign = 0) [set bias b] [set bias (-1 * b)]
	set h? 0
	]
	end

	to create-turtles-prior
	ask turtles [
	;set agents' bias
	let r random 10
	set heads (r + 1)
	set tails (10 - r)
	set H (H + heads)
	set T (T + tails)
	]
	end

	to create-links
	ask turtles [
	let numberlinks random (Max_number_of_links + 1)
	let v 0
	while [v < numberlinks]
	[let l random num_agents
	if (([who] of self) != l)

	[create-active-link-to turtle l
	set v (v + 1)
	]]]
	end


	to go
	if (ticks > 80)
	[stop]
	ask turtles [
	;they flip the coin with their bias
	let x random-float 1
	ifelse ((x + bias) > (Coin_Bias / 100))
	[set tails (tails + 1)

	;the total number of Tails is recorded
	set T (T + 1)

	;whether the last flip was tails or head is recorded
	set h? 0
	]
	[set heads (heads + 1)

	set H (H + 1)

	set h? 1
	]]

	signal-result

	let total-accuracy compute-agents-accuracy


	print word "Heads:" H
	print word "Tails:" T
	let coinflips (H + T)
	print word "Total:" coinflips
	print (word "Total" " " "accuracy:" total-accuracy)

	tick
	end

	to signal-result
	let x 0
	while [(x + 1) <= num_agents]
	[
	ask turtles
	[if (in-link-neighbor? turtle x)
	[ifelse
	([h?] of turtle x = 1)
	[set heads (heads + 1)]
	[set tails (tails + 1)]

	]]
	set x (x + 1)
	]
	end

	to-report compute-agents-accuracy
	let v1 ((Coin_Bias / 100) - 0.05)
	let v2 ((Coin_Bias / 100) + 0.05)
	let z 0
	ask turtles
	[
	let x 0
	let y 0
	let w v1
	set accuracy-list n-values 0 [ ?1 -> ?1 ]
	while [w <= v2]
	[
	set x (stepwisefactorial3 (heads - 1) (tails - 1) (heads + tails - 1))
	set y (((w ^ (heads - 1)) * ((1 - w) ^ (tails - 1))) / x)
	set accuracy-list lput y accuracy-list
	set w (w + 0.01)
	]
	print accuracy-list
	set accuracy (sum accuracy-list)
	set z (z + accuracy)
	]
	report z
	end


	to-report factorial [n]

	if n = 0 [ report 1 ]
	report n * factorial (n - 1)

	end


	to-report stepwisefactorial3 [n1 n2 d]

	if (n1 = 0) [report stepwisefactorial2 (n2) (d)]
	if (n2 = 0) [report stepwisefactorial2 (n1) (d)]
	if (d = 0) [report (stepwisefactorial1 (n1) * stepwisefactorial1 (n2))]
	report ((((n1 * n2) / d)) * stepwisefactorial3 (n1 - 1) (n2 - 1) (d - 1))
	end

	to-report stepwisefactorial2 [n d]

	if (n = 0) [report (1 / (stepwisefactorial1 (d)))]
	if (d = 0) [report stepwisefactorial1 (n)]
	report ((n / d)* stepwisefactorial2 (n - 1) (d - 1))
	end

	to-report stepwisefactorial1 [d]
	if d = 0 [ report 1 ]
	report d * stepwisefactorial1 (d - 1)
	end

	to format
	let n 0
	while [n < 100][
	layout
	set n (n + 1)]
	end

	to layout
	;; the number 3 here is arbitrary; more repetitions slows down the
	;; model, but too few gives poor layouts
	repeat 3 [
	;; the more turtles we have to fit into the same amount of space,
	;; the smaller the inputs to layout-spring we'll need to use
	let factor sqrt count turtles
	;; numbers here are arbitrarily chosen for pleasing appearance
	layout-spring turtles links (1 / factor) (7 / factor) (16 / factor)
	display ;; for smooth animation
	]
	;; don't bump the edges of the world
	let x-offset max [xcor] of turtles + min [xcor] of turtles
	let y-offset max [ycor] of turtles + min [ycor] of turtles
	;; big jumps look funny, so only adjust a little each time
	set x-offset limit-magnitude x-offset 0.1
	set y-offset limit-magnitude y-offset 0.1
	ask turtles [ setxy (xcor - x-offset / 2) (ycor - y-offset / 2) ]
	end

	to-report limit-magnitude [number limit]
	if number > limit [ report limit ]
	if number < (- limit) [ report (- limit) ]
	report number
	end
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	BUTTON
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	PLOT
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	Agents' density function
	Heads bias prob
	Probability of bias
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	PENS
	"Turtle 1" 0.01 1 -2674135 true "if any? turtles with [who = 0]\n[\nlet x 0\nwhile [x <= 1]\n[plot-pen-up\nplotxy x 1\nplot-pen-down\nset x (x + 0.01)\n]]" "if any? turtles with [who = 0]\n[\nlet x 0\nlet y 0\nlet z 0\nlet he ([heads] of turtle 0)\nlet te ([tails] of turtle 0)\nplot-pen-reset\nwhile [x <= 1]\n[plot-pen-up\nset z (stepwisefactorial3 (he - 1) (te - 1) (he + te - 1))\nset y (((x ^ (he - 1)) * ((1 - x) ^ (te - 1))) / z)\nplotxy x y\nplot-pen-down\nplot-pen-up\nset x (x + 0.01)\n]]"
	"Turtle 2" 0.01 1 -13345367 true "if any? turtles with [who = 1]\n[\nlet x 0\nwhile [x <= 1]\n[plot-pen-up\nplotxy x 1\nplot-pen-down\nset x (x + 0.01)\n]]" "if any? turtles with [who = 1]\n[\nlet x 0\nlet y 0\nlet z 0\nlet he ([heads] of turtle 1)\nlet te ([tails] of turtle 1)\nplot-pen-reset\nwhile [x <= 1]\n[plot-pen-up\nset z (stepwisefactorial3 (he - 1) (te - 1) (he + te - 1))\nset y (((x ^ (he - 1)) * ((1 - x) ^ (te - 1))) / z)\nplotxy x y\nplot-pen-down\nplot-pen-up\nset x (x + 0.01)\n]]"
	"Turtle 3" 0.01 1 -1184463 true "if any? turtles with [who = 2]\n[\nlet x 0\nwhile [x <= 1]\n[plot-pen-up\nplotxy x 1\nplot-pen-down\nset x (x + 0.01)\n]]" "if any? turtles with [who = 2]\n[\nlet x 0\nlet y 0\nlet z 0\nlet he ([heads] of turtle 2)\nlet te ([tails] of turtle 2)\nplot-pen-reset\nwhile [x <= 1]\n[plot-pen-up\nset z (stepwisefactorial3 (he - 1) (te - 1) (he + te - 1))\nset y (((x ^ (he - 1)) * ((1 - x) ^ (te - 1))) / z)\nplotxy x y\nplot-pen-down\nplot-pen-up\nset x (x + 0.01)\n]]"
	"Turtle 4" 0.01 1 -13840069 true "if any? turtles with [who = 3]\n[\nlet x 0\nwhile [x <= 1]\n[plot-pen-up\nplotxy x 1\nplot-pen-down\nset x (x + 0.01)\n]]" "if any? turtles with [who = 3]\n[\nlet x 0\nlet y 0\nlet z 0\nlet he ([heads] of turtle 3)\nlet te ([tails] of turtle 3)\nplot-pen-reset\nwhile [x <= 1]\n[plot-pen-up\nset z (stepwisefactorial3 (he - 1) (te - 1) (he + te - 1))\nset y (((x ^ (he - 1)) * ((1 - x) ^ (te - 1))) / z)\nplotxy x y\nplot-pen-down\nplot-pen-up\nset x (x + 0.01)\n]]"
	"Turtle 5" 0.01 1 -3026479 true "if any? turtles with [who = 4]\n[\nlet x 0\nwhile [x <= 1]\n[plot-pen-up\nplotxy x 1\nplot-pen-down\nset x (x + 0.01)\n]]" "if any? turtles with [who = 4]\n[\nlet x 0\nlet y 0\nlet z 0\nlet he ([heads] of turtle 4)\nlet te ([tails] of turtle 4)\nplot-pen-reset\nwhile [x <= 1]\n[plot-pen-up\nset z (stepwisefactorial3 (he - 1) (te - 1) (he + te - 1))\nset y (((x ^ (he - 1)) * ((1 - x) ^ (te - 1))) / z)\nplotxy x y\nplot-pen-down\nplot-pen-up\nset x (x + 0.01)\n]]"
	"Turtle 6" 0.01 1 -5825686 true "if any? turtles with [who = 5]\n[\nlet x 0\nwhile [x <= 1]\n[plot-pen-up\nplotxy x 1\nplot-pen-down\nset x (x + 0.01)\n]]" "if any? turtles with [who = 5]\n[\nlet x 0\nlet y 0\nlet z 0\nlet he ([heads] of turtle 5)\nlet te ([tails] of turtle 5)\nplot-pen-reset\nwhile [x <= 1]\n[plot-pen-up\nset z (stepwisefactorial3 (he - 1) (te - 1) (he + te - 1))\nset y (((x ^ (he - 1)) * ((1 - x) ^ (te - 1))) / z)\nplotxy x y\nplot-pen-down\nplot-pen-up\nset x (x + 0.01)\n]]"
	"Turtle 7" 0.01 1 -9276814 true "if any? turtles with [who = 6]\n[\nlet x 0\nwhile [x <= 1]\n[plot-pen-up\nplotxy x 1\nplot-pen-down\nset x (x + 0.01)\n]]" "if any? turtles with [who = 6]\n[\nlet x 0\nlet y 0\nlet z 0\nlet he ([heads] of turtle 6)\nlet te ([tails] of turtle 6)\nplot-pen-reset\nwhile [x <= 1]\n[plot-pen-up\nset z (stepwisefactorial3 (he - 1) (te - 1) (he + te - 1))\nset y (((x ^ (he - 1)) * ((1 - x) ^ (te - 1))) / z)\nplotxy x y\nplot-pen-down\nplot-pen-up\nset x (x + 0.01)\n]]"
	"Turtle 8" 0.01 1 -817084 true "if any? turtles with [who = 7]\n[\nlet x 0\nwhile [x <= 1]\n[plot-pen-up\nplotxy x 1\nplot-pen-down\nset x (x + 0.01)\n]]" "if any? turtles with [who = 7]\n[\nlet x 0\nlet y 0\nlet z 0\nlet he ([heads] of turtle 7)\nlet te ([tails] of turtle 7)\nplot-pen-reset\nwhile [x <= 1]\n[plot-pen-up\nset z (stepwisefactorial3 (he - 1) (te - 1) (he + te - 1))\nset y (((x ^ (he - 1)) * ((1 - x) ^ (te - 1))) / z)\nplotxy x y\nplot-pen-down\nplot-pen-up\nset x (x + 0.01)\n]]"
	"Turtle 9" 0.01 1 -6459832 true "if any? turtles with [who = 8]\n[\nlet x 0\nwhile [x <= 1]\n[plot-pen-up\nplotxy x 1\nplot-pen-down\nset x (x + 0.01)\n]]" "if any? turtles with [who = 8]\n[\nlet x 0\nlet y 0\nlet z 0\nlet he ([heads] of turtle 8)\nlet te ([tails] of turtle 8)\nplot-pen-reset\nwhile [x <= 1]\n[plot-pen-up\nset z (stepwisefactorial3 (he - 1) (te - 1) (he + te - 1))\nset y (((x ^ (he - 1)) * ((1 - x) ^ (te - 1))) / z)\nplotxy x y\nplot-pen-down\nplot-pen-up\nset x (x + 0.01)\n]]"
	"Turtle 10" 0.01 1 -2064490 true "if any? turtles with [who = 9]\n[\nlet x 0\nwhile [x <= 1]\n[plot-pen-up\nplotxy x 1\nplot-pen-down\nset x (x + 0.01)\n]]" "if any? turtles with [who = 9]\n[\nlet x 0\nlet y 0\nlet z 0\nlet he ([heads] of turtle 9)\nlet te ([tails] of turtle 9)\nplot-pen-reset\nwhile [x <= 1]\n[plot-pen-up\nset z (stepwisefactorial3 (he - 1) (te - 1) (he + te - 1))\nset y (((x ^ (he - 1)) * ((1 - x) ^ (te - 1))) / z)\nplotxy x y\nplot-pen-down\nplot-pen-up\nset x (x + 0.01)\n]]"

	INPUTBOX
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	PENS
	"default" 1.0 0 -16777216 true "" "plot compute-agents-accuracy"

	@#$#@#$#@
	This model studies the effect of information sharing when agents are biased, and it shows that given a set of biased agents, information sharing washes the biases out.

	Picture a community of scientists all of whom want to gather evidence about a pattern in nature. For example, they may be interested in finding the exact numeric probability of a chance event type or whether two variables are statistically correlated or have a causal relationship. Since they are rational scientists, they proceed by experimenting and gathering information about the sort of phenomena they are studying, and later applying statistical machinery in order to make their inferences. Yet, we are well aware that scientific practice does not occur in isolation from psychological and sociological factors. Scientists are biased and the information they obtain in inquiry is polluted by their own prejudices and preferences. They are also selfish reputation seeking agents that are reluctant to share their information with other scientists unless they get something out of it. The present essay pretends to study how these factors interact. In particular, assuming the agents are scientists, in so far as they reason and analyze data according to our best normative theories, the central question is how restrictions to information exchange affects a community with individual biases. The hypothesis is that the greater the information exchange – i.e. the more each agent is aware of the data of the others –, the better the community does in finding patterns about the world. In other words, information exchange serves as a buffer to subjective biases.

	The model has an underlying sociology, which is captured by a network between the agents. Each agent is directly linked with a certain number of other agents. The connections between agents represent the information exchange. At each cycle of the simulation, each agent gathers some information about the world in a biased way – the bias is represented differently in both scenarios, more on this later. Then, after gathering the data and before the cycle ends, she shares the information she gathered during that cycle with the agents she is pointing to (notice that this needs not be a symmetric relation). The amount of connections that agents have is one of the variables to study, as it is clear that the more connections, the more each agent knows about the (possibly biased) information that the others gathered.

	In this scenario the community is interested in finding the objective probability of a chancy event type. In particular, they all share an exact copy of a probabilistic device – in this case a biased coin with two possible outcomes - and they want to find the probability of one of the outcomes. They do this by experimenting at each cycle, i.e. flipping the coin once, and updating their prior density function (a beta distribution) on the new information. But two caveats are introduced. First, the coin each scientist flips has, on top of its objective bias, a subjective bias that is contributed by the agent in turn. Suppose for example that the device has an even distribution, so that the objective probability of each of the outcomes (heads and tails) is the same: 0.5. Sometimes, simply because the scientist is impure in the sense that she is affected by psychological and sociological effects, she might be inclined to neglect or confuse the observation of one outcome over the other. Hence, although the device is fair, the scientist records observed data with certain bias (say 0.6 heads and 0.4 tails). Second, at the end of each cycle, powerful agents not only have the information they gathered, but they will also get the (biased) data from the scientists pointing to them. All the information, the result from theirs as well as the others experimentation, is incorporated into the Bayesian updating. The variable under study here is the amount of bias agents have.
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	Circle -16777216 true false 30 30 240
	Circle -7500403 true true 60 60 180
	Circle -16777216 true false 90 90 120
	Circle -7500403 true true 120 120 60

	tree
	false
	0
	Circle -7500403 true true 118 3 94
	Rectangle -6459832 true false 120 195 180 300
	Circle -7500403 true true 65 21 108
	Circle -7500403 true true 116 41 127
	Circle -7500403 true true 45 90 120
	Circle -7500403 true true 104 74 152

	triangle
	false
	0
	Polygon -7500403 true true 150 30 15 255 285 255

	triangle 2
	false
	0
	Polygon -7500403 true true 150 30 15 255 285 255
	Polygon -16777216 true false 151 99 225 223 75 224

	truck
	false
	0
	Rectangle -7500403 true true 4 45 195 187
	Polygon -7500403 true true 296 193 296 150 259 134 244 104 208 104 207 194
	Rectangle -1 true false 195 60 195 105
	Polygon -16777216 true false 238 112 252 141 219 141 218 112
	Circle -16777216 true false 234 174 42
	Rectangle -7500403 true true 181 185 214 194
	Circle -16777216 true false 144 174 42
	Circle -16777216 true false 24 174 42
	Circle -7500403 false true 24 174 42
	Circle -7500403 false true 144 174 42
	Circle -7500403 false true 234 174 42

	turtle
	true
	0
	Polygon -10899396 true false 215 204 240 233 246 254 228 266 215 252 193 210
	Polygon -10899396 true false 195 90 225 75 245 75 260 89 269 108 261 124 240 105 225 105 210 105
	Polygon -10899396 true false 105 90 75 75 55 75 40 89 31 108 39 124 60 105 75 105 90 105
	Polygon -10899396 true false 132 85 134 64 107 51 108 17 150 2 192 18 192 52 169 65 172 87
	Polygon -10899396 true false 85 204 60 233 54 254 72 266 85 252 107 210
	Polygon -7500403 true true 119 75 179 75 209 101 224 135 220 225 175 261 128 261 81 224 74 135 88 99

	wheel
	false
	0
	Circle -7500403 true true 3 3 294
	Circle -16777216 true false 30 30 240
	Line -7500403 true 150 285 150 15
	Line -7500403 true 15 150 285 150
	Circle -7500403 true true 120 120 60
	Line -7500403 true 216 40 79 269
	Line -7500403 true 40 84 269 221
	Line -7500403 true 40 216 269 79
	Line -7500403 true 84 40 221 269

	wolf
	false
	0
	Polygon -16777216 true false 253 133 245 131 245 133
	Polygon -7500403 true true 2 194 13 197 30 191 38 193 38 205 20 226 20 257 27 265 38 266 40 260 31 253 31 230 60 206 68 198 75 209 66 228 65 243 82 261 84 268 100 267 103 261 77 239 79 231 100 207 98 196 119 201 143 202 160 195 166 210 172 213 173 238 167 251 160 248 154 265 169 264 178 247 186 240 198 260 200 271 217 271 219 262 207 258 195 230 192 198 210 184 227 164 242 144 259 145 284 151 277 141 293 140 299 134 297 127 273 119 270 105
	Polygon -7500403 true true -1 195 14 180 36 166 40 153 53 140 82 131 134 133 159 126 188 115 227 108 236 102 238 98 268 86 269 92 281 87 269 103 269 113

	x
	false
	0
	Polygon -7500403 true true 270 75 225 30 30 225 75 270
	Polygon -7500403 true true 30 75 75 30 270 225 225 270
	@#$#@#$#@
	NetLogo 6.0.2
	@#$#@#$#@
	@#$#@#$#@
	@#$#@#$#@
	@#$#@#$#@
	@#$#@#$#@
	default
	0.0
	-0.2 0 0.0 1.0
	0.0 1 1.0 0.0
	0.2 0 0.0 1.0
	link direction
	true
	0
	Line -7500403 true 150 150 90 180
	Line -7500403 true 150 150 210 180
	@#$#@#$#@
	0
	@#$#@#$#@

IgnacioOQ/Netlogo-Models