breed [believers believer] breed [disbelievers disbeliever] breed [recovers recover] globals [infected_per infected_mean infected_list ] turtles-own [ Beliefs ; B = 1 if believes; B = -1 if doesn't believe; Strength ; strength of belief varies from 0 to 1 Compliance ; binary; 1 if complies/enforces norm, and 0 otherwise. Enforcement ; 1 if enforces norm; -1 if enforces deviance. Enforcement_Need ; Wi = 1-(Bi/Ni)SumCj / 2 ;; is just the proportion of i's neighbors whose behavior does not conform with it's Beliefs B Enforcement_Need_2 ;; same # but divided by 2; as used in the article. N_Neighbors Convert ] ;; CODE: ;; BELIEVERS = arrow, DISBELIEVERS = default shape ;; COMPLIANCE = RED, DEVIANCE = BLUE ;; ENFORCEMENT = HEADING TO THE RIGHT (90) ; NO ENFORCEMENT = HEADING TO THE LEFT (270) ;; Basic MODEL of ED: 1. agents observe neighbors compliance and enforcement. 2. Each agent then makes two decisions: ;; (i) whether to comply with the norm, and (ii) whether to enforce the norm. to setup __clear-all-and-reset-ticks let IB initial_believers let ID population - IB ;if Condition = "Local Random" OR Condition = "Global" [ create-believers IB [ set size 1 set color red setxy random-pxcor random-pycor while [any? other turtles-here] [ let empty_patch one-of patches with [any? turtles-here = false] move-to empty_patch ] ] if Condition = "Local Clustered" [ let a 20 let b 12 let p patch 20 12 let d (list believers) foreach d [ ask ? [move-to p set p patch-at-heading-and-distance 45 1] ] ] ask believers[ set Beliefs 1 set Strength 1 ;; by default all true believers initially comply! set compliance 1 set convert 0 set shape "arrow" set heading 90 ; NO INITIAL ENFORCEMENT ] create-disbelievers ID [ set size 1 set color blue ; BLUE COLOR BECAUSE NOT COMPLYING WITH setxy random-pxcor random-pycor while [any? other turtles-here] [ let empty_patch one-of patches with [any? turtles-here = false] move-to empty_patch ] set Beliefs -1 set Strength random-float 0.38 set convert 0 set compliance -1 set heading 90 ; NO INITIAL ENFORCEMENT ] ask turtles [setup-map] end to START! ED update-plots end to setup-map if Condition = "Global" [set N_Neighbors Other Turtles] if Condition = "Local Clustered" OR Condition = "Local Random" [ set N_Neighbors turtle-set turtles-on neighbors if small_worlds? = true [ small-worlds ] ] end to ED ask turtles [ if small_worlds? = true AND Continuous-Rewiring? = true AND Condition != "Global" [ small-worlds ] let Ni_list (list N_Neighbors) let Ni count N_Neighbors if Ni = 0 [set Ni 1] let Bi [Beliefs] of self let NCi count N_Neighbors with [Compliance = Bi] set Enforcement_Need 1 - (NCi / Ni) set Enforcement_Need_2 Enforcement_Need / 2 ; output-print Enforcement_Need_2 COMPLY? ENFORCE? ] end TO COMPLY? ;; disbeliever complies if the proportion of neighbors enforcing compliance is greater than the strength of disbeliever's belief; let S [strength] of self let Bi [Beliefs] of self let Ej count N_Neighbors with [Enforcement = -1 * Bi] ;; neighbors enforcing opposite belief let Ni count N_Neighbors if Ni = 0 [set Ni 1] ifelse (Ej / Ni) > S [set compliance -1 * Bi] [set compliance Bi] if Compliance = 1 [set color red] if Compliance = -1 [set color blue] end to ENFORCE? let S [strength] of self let Bi [Beliefs] of self let Ci [Compliance] of self let Ej count N_Neighbors with [Enforcement = -1 * Bi] ;; neighbors enforcing opposite belief let Ni count N_Neighbors if Ni = 0 [set Ni 1] let Wi Enforcement_Need_2 ifelse (Ej / Ni) > (S + K) AND Bi != Ci [set Enforcement -1 * Bi] ; Enforcement is opposite of belief if: ; a) the proportion of enforcement against belief is greater than the strength of belief plus the cost of enforcement, AND ; b) agent already complies against agent's own belief; violates one's own belief already. ;; THIS MEANS THAT AGENTS CANNOT ENFORCE COMPLIANCE UNLESS THEY HAVE ALREADY COMPLIED. [ ifelse S * Wi > K AND Bi = Ci [set Enforcement Bi] [set Enforcement 0] ] if enforcement = 1 [set heading 270] ;; to better visualize enforcement if conversion? = true [CV] end to CV let a conversion / 10000 ; 1 will equal .0001 - the learning parameter set in the article if Enforcement != Beliefs [ set convert convert - (a * Enforcement * Beliefs) if convert > Strength AND Beliefs != compliance [ hatch-believers 1 [ set color red set Beliefs 1 set compliance 1 set convert 0 set shape "arrow" set heading 90 ];; NOTICE THAT I AM NOT RESETTING THE STRENGTH OF THEIR CONVICTIONS. THESE NEW CONVERTS ARE A LESS CONVINCED GROUP OF BELIEVERS THAN THE ORIGINAL! die ;; THE ORIGINAL DISBELIVER DIES ] ] end to small-worlds let a self let N_list [] let h turtle-set turtles-on neighbors let g turtle-set N_Neighbors ; ask N_Neighbors [set color yellow] ask N_Neighbors [ ;; whether to rewire it or not? ifelse (random-float 1) < rewiring-probability [ let b (turtle-set a h g) ; a = self, original turtle; N_neighbors list here includes this turtle replacing itself with another random turtle let c one-of turtles while [member? c b = true] [set c one-of turtles] ; keeps changing the turtle until it isn't itself or a neighbor ask a [set N_list fput c N_list] ; set N_list replace-item (? - 1) N_list c ;show N_list ask c [set color brown] ] [ask a [set N_list fput myself N_list]] ;;myself or self? ] ;; must be ? - 1 to replace the correct turtle ask a [set N_Neighbors turtle-set N_list] ; must go back and ask original turtle to do this! end to-report prcnt_comply let comply count turtles with [compliance = 1] let Ni count turtles if Ni = 0 [set Ni Ni + 1] report (comply / Ni) * 100 end to-report prcnt_enforce let enforce count turtles with [enforcement = 1] let Ni count turtles if Ni = 0 [set Ni Ni + 1] report (enforce / Ni) * 100 end to-report prcnt_believe let B count believers let Ni count turtles if Ni = 0 [set Ni Ni + 1] report (B / Ni) * 100 end to-report false_comply ;; proportion of disbelievers who falsely comply let D count disbelievers if D = 0 [set D D + 1] let F count disbelievers with [Compliance = 1] report (F / D) * 100 end to-report false_enforce let D count disbelievers if D = 0 [set D D + 1] let F count disbelievers with [Enforcement = 1] report (F / D) * 100 end @#$#@#$#@ GRAPHICS-WINDOW 142 10 592 316 -1 -1 11.0 1 10 1 1 1 0 1 1 1 0 39 0 24 0 0 1 ticks 30.0 BUTTON 2 10 65 43 NIL setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 65 10 120 43 NIL START! T 1 T OBSERVER NIL NIL NIL NIL 1 SLIDER 1 44 141 77 population population 10 1000 1000 10 1 NIL HORIZONTAL SLIDER -3 78 141 111 Initial_Believers Initial_Believers 0 population 10 5 1 NIL HORIZONTAL PLOT 598 10 1140 233 Percentage of Agents that Comply and Enforce NIL NIL 0.0 10.0 0.0 100.0 true true "" "" PENS "% Comply" 1.0 0 -2674135 true "" "plot prcnt_comply" "% Enforce" 1.0 0 -16777216 true "" "plot prcnt_enforce" "% Believe" 1.0 0 -7500403 true "" "plot prcnt_believe" "% False Compliance" 1.0 0 -955883 true "" "plot false_comply" "% False Enforce" 1.0 0 -6459832 true "" "plot false_enforce" TEXTBOX 217 325 663 403 Believers = Arrow, Disbelievers = Default\nCompliance with Believers = RED, Deviance from Believers = BLUE\nEnforcement = Heading to Left (270) <-- ; No Enforcement = Heading to Right (90) -->\nBy default, all true believers initially comply; S = 1. \nBrown agents are those connected via \"Small Worlds\" linking. 11 0.0 1 MONITOR 789 233 933 278 Average Links per Node (count links) / population 2 1 11 SLIDER -2 112 146 145 Influence_Range Influence_Range 1 20 10 1 1 NIL HORIZONTAL SLIDER -2 145 146 178 K K 0 .5 0.125 .005 1 NIL HORIZONTAL MONITOR 597 234 788 279 Mean Conviction of Disbelievers mean [strength] of disbelievers 2 1 11 CHOOSER 0 180 138 225 Condition Condition "Global" "Local Clustered" "Local Random" 2 MONITOR 596 280 758 325 % of False Compliance false_comply 2 1 11 MONITOR 759 280 909 325 % of False Enforcement false_enforce 2 1 11 SLIDER 1 275 139 308 Conversion Conversion 0 10 10 1 1 NIL HORIZONTAL SWITCH 1 243 138 276 Conversion? Conversion? 1 1 -1000 SWITCH 5 329 159 362 small_worlds? small_worlds? 0 1 -1000 SLIDER 5 363 198 396 rewiring-probability rewiring-probability 0 .5 0.01 .01 1 NIL HORIZONTAL SWITCH 5 396 180 429 Continuous-Rewiring? Continuous-Rewiring? 0 1 -1000 @#$#@#$#@ ## WHAT IS IT? This model is derived from and inspired by: Centola, Damon, Robb Willer, and Michael Macy. “The Emperor’s Dilemma: A Computational Model of Self‐Enforcing Norms.” American Journal of Sociology 110, no. 4 (January 1, 2005): 1009–1040. The basic idea is to test under what conditions people will not only comply with norms they privately disbelieve (i.e. 'FALSE COMPLIANCE'), but also when they will actively enforce them (i.e. 'FALSE ENFORCEMENT'). EMPEROR'S DILEMMA ROUTINE: 1. agents observe neighbors compliance and enforcement. 2. Each agent then makes two decisions: (i) whether to comply with the norm, and (ii) whether to enforce the norm. ## HOW IT WORKS Below are the main agent variables: Beliefs: B = 1 if believes; B = -1 if doesn't believe. Strength (of Belief): varies from 0 to 1 Compliance: 1 if agent complies with the norm, and 0 the agent does not comply. Enforcement: 1 if agent enforces norm, -1 if enforces deviance, and 0 if agent doesn't enforce at all. First, agents must decide whether to comply with the norm. In this model, a disbeliever complies if the proportion of neighbors enforcing compliance is greater than the strength of disbeliever's belief. For example, if the strength of disbelief is .5, but 60% of an agent's neighbors are enforcing compliance, then this agent will also comply. Thus, this depends on the question of enforcement, given next. Second, agents make a decision to enforce based on whether those around them are complying with their private norms. In this model, the "Need to Enforce" is inversely related to the proportion of neighbors complying with their private beliefs! This is a somewhat strange assumption. In practice, it means that an isolated individual constituting an extreme minority is more likely to impose his or her beliefs on others when nobody else believes them. A more plausible approach is that groups are more likely to enforce norms on minorities, but that will wait for another model. Because of this assumption, enforcement drops whenever full compliance is achieved, causing the system to swing back towards non-compliance. Note that the parameter "K" refers to the Cost of Enforcement. "Rewiring probability" here is the same as that used in "Small Worlds" algorithm, but instead of rewiring links, it asks each neighbor and randomly assigns one of these neighbors to an agentset N_Neighbors if probability is below "rewiring probability". The "Small Worlds" parameter will set up small-worlds links. At the limit, where re-wiring probability = 1, small-worlds is the same as the global condition. ## Other Assumptions - No hypocritical enforcement; Agents can only enforce compliance if they also complied, and can only enforce deviance if they have deviated. - Initial condition is that agents conform to their own private beliefs and no one enforces anything. - In the article, strength of belief, S, of disblievers ranges 0 < S <= .38 The mean of their conviction is 0.19. ## THINGS TO TRY Change the "Conversion" setting. Conversions allow the beliefs of agents to change according to a stochastic process. The parameter K (cost of enforcement) was fixed in the article cited above. It turns out that the interesting results do not obtain when the cost is varied. There are several conditions in which this model can be run: - Global: Each agent can interact with any other agent. - Local: Each agent can interact only with its N closest neighbors, where N is set by "Influence_Range." There are two local conditions: i) Clustered, or ii) Random. These refer to whether the BELIEVERS are initially clustered or randomly distributed. The interesting finding of this article is that cascades of false compliance and false enforcement will only be generated if the BELIEVERS (i.e. zealots) are initially clustered together, and agents can only interact locally (i.e. they lack global or outside information). ## CREDITS AND REFERENCES Centola, Damon, Robb Willer, and Michael Macy. “The Emperor’s Dilemma: A Computational Model of Self‐Enforcing Norms.” American Journal of Sociology 110, no. 4 (January 1, 2005): 1009–1040. @#$#@#$#@ default true 0 Polygon -7500403 true true 150 5 40 250 150 205 260 250 airplane true 0 Polygon -7500403 true true 150 0 135 15 120 60 120 105 15 165 15 195 120 180 135 240 105 270 120 285 150 270 180 285 210 270 165 240 180 180 285 195 285 165 180 105 180 60 165 15 arrow true 0 Polygon -7500403 true true 150 0 0 150 105 150 105 293 195 293 195 150 300 150 box false 0 Polygon -7500403 true true 150 285 285 225 285 75 150 135 Polygon -7500403 true true 150 135 15 75 150 15 285 75 Polygon -7500403 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