globals [ magnetization ] turtles-own [ opinion flip-rate temp-opinion ] ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;; AGENT INITIALIZATION ;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to initialize-hvm ;; turtle procedure ask turtles [ set opinion one-of n-values number-states [?] recolor set flip-rate random-float 1 ] set-magnetization end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;; UPDATE RULES ;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to go-ising ;; From Masuda, Gilbert, Redner 2010, it is unclear whether the voters ;; follow the traditional voting rules where one agent is picked at random, ;; that agent looks at a neighbor's opinions, then changes his opinion to ;; that neighbor's opinion. ;; ;; Instead, it seems more similar to the Ising model in that an agent is ;; chosen, then the agent flips his state. I implement this here. ;; ;; We have two ways of doing this. ;; A: 1. choose a random patch ;; 2. draw a random number, and if smaller than individual flip-rate, ;; flip ifelse simultaneous? [ ask turtles [if random-float 1 < flip-rate [flip]] ask turtles [ set opinion temp-opinion recolor ] set-magnetization tick ] [ ask one-of turtles [ if random-float 1 < flip-rate [ flip set opinion temp-opinion recolor ] ] set-magnetization tick ] end ;; GOING LIKE VOTER MODEL ;; to go-vote ifelse simultaneous? [ ask turtles [ if random-float 1 < flip-rate [ set temp-opinion one-of [opinion] of link-neighbors ] ] ask turtles [ set opinion temp-opinion recolor] set-magnetization tick ] [ ask one-of turtles [ if random-float 1 < flip-rate [ set opinion one-of [opinion] of link-neighbors recolor ] ] set-magnetization tick] end to go-majority ifelse simultaneous? [ ask turtles [ if random-float 1 < flip-rate [ set temp-opinion one-of modes [opinion] of link-neighbors] ] ask turtles [ set opinion temp-opinion recolor ] set-magnetization tick ] [ ask one-of turtles [ if random-float 1 < flip-rate [ set opinion one-of modes [opinion] of link-neighbors ;changed the not simulatneous one here from "of turtles" to this, did same thing for voter version recolor ] ] set-magnetization tick ] end to flip set temp-opinion random number-states if temp-opinion = opinion [ flip ] end to set-magnetization set magnetization mean [opinion] of turtles / number-states end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;; COLORING RULES ;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to recolor set color 102 + opinion * 7 / number-states end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;; NETWORK STRUCTURES ;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to setup-patch-lattice end to setup-lattice [len dim] __clear-all-and-reset-ticks crt len ^ dim ask turtles [ let id [who] of self let coordinates [] let temp 0 let target (turtle-set) foreach n-values dim [? + 1] [ set coordinates lput (id mod len ^ ? / len ^ (? - 1)) coordinates ;; set coordinates from who number set id id - (id mod len ^ ?) ] ;; we want to add one to each coordinate, then create links with those coordinates foreach n-values dim [?] [ let temp-coordinates replace-item ? coordinates (item ? coordinates + 1) ;; add 1 to one of the coordinates if item ? temp-coordinates >= len [ set temp-coordinates replace-item ? temp-coordinates 0 ] foreach n-values dim [?] [ set temp temp + item ? temp-coordinates * len ^ ? ;; retrieve the turtle number from coordinates ] set target (turtle-set target turtle temp) set temp 0 ] create-links-with target ] initialize-hvm end to setup-fully-connected __clear-all-and-reset-ticks crt N ask turtles [create-links-with other turtles] initialize-hvm end to setup-preferential __clear-all-and-reset-ticks create-initial-nodes repeat N - m0 [make-node-with preferential-group] initialize-hvm end to create-initial-nodes repeat m0 [ make-node-with one-of other turtles ]; with [not link-neighbor? self] ] ;;do we need this part? end ;; Idea: first create a function that takes two turtles as inputs and when executed, links the two ;; Next, repeat N times the following: create new node, link to m separate lottery winners to make-node [arg] crt arg end ;; used for creating a new node. ;; if TARGET is a single agent, link with that agent ;; if TARGET is a set of agents, link with all agents. to make-node-with [target] make-node 1 ask max-one-of turtles [who] ;; the last turtle added [ if target != nobody [ if is-agent? target [ create-link-with target [ set color gray ] move-to target ] if is-agentset? target [ create-links-with target[ set color gray ] move-to one-of target ] ;; position the new node near its partner fd 20 ] ] end to-report preferential-group ;; connect the turtle to m number of partners ;; start by creating one target let targets (turtle-set find-partner) repeat (m - 1) [ let next-node find-partner ;; add a target that is not already a target while [member? next-node targets] [set next-node find-partner ] set targets (turtle-set targets next-node) ] report targets end ;; This code is borrowed from Lottery Example (in the Code Examples ;; section of the Models Library). ;; The idea behind the code is a bit tricky to understand. ;; Basically we take the sum of the degrees (number of connections) ;; of the turtles, and that's how many "tickets" we have in our lottery. ;; Then we pick a random "ticket" (a random number). Then we step ;; through the turtles to figure out which node holds the winning ticket. to-report find-partner let total random-float sum [count link-neighbors] of turtles let partner nobody ask turtles [ let nc count link-neighbors ;; if there's no winner yet... if partner = nobody [ ifelse nc > total [ set partner self ] [ set total total - nc ] ] ] report partner end to-report limit-magnitude [number limit] if number > limit [ report limit ] if number < (- limit) [ report (- limit) ] report number end to setup-random __clear-all-and-reset-ticks crt N ask turtles [create-link-with one-of other turtles] end to setup-small-world __clear-all-and-reset-ticks crt N ask turtles [ set shape "circle" ] layout-circle (sort turtles) max-pxcor - 1 let c 0 while [c < count turtles] [ ask turtle c [create-link-with turtle ((c + 1) mod count turtles)] set c c + 1 ] initialize-hvm end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;; LAYOUT ;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 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) (7 / 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 resize-nodes ifelse all? turtles [size <= 1] [ ;; a node is a circle with diameter determined by ;; the SIZE variable; using SQRT makes the circle's ;; area proportional to its degree ask turtles [ set size sqrt count link-neighbors ] ] [ ask turtles [ set size 1 ] ] end @#$#@#$#@ GRAPHICS-WINDOW 255 10 788 564 20 20 12.76 1 10 1 1 1 0 1 1 1 -20 20 -20 20 1 1 1 ticks 30.0 BUTTON 10 30 112 63 Steup Lattice setup-lattice cube-length dimension NIL 1 T OBSERVER NIL NIL NIL NIL 1 SLIDER 10 385 182 418 dimension dimension 1 5 2 1 1 NIL HORIZONTAL SLIDER 10 420 182 453 cube-length cube-length 0 100 20 1 1 NIL HORIZONTAL SLIDER 10 455 182 488 N N 0 5000 828 1 1 NIL HORIZONTAL BUTTON 10 70 97 103 Mean Field setup-fully-connected NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 100 70 180 103 Random setup-random NIL 1 T OBSERVER NIL NIL NIL NIL 1 SLIDER 10 140 182 173 number-states number-states 0 10 5 1 1 NIL HORIZONTAL SWITCH 10 295 160 328 simultaneous? simultaneous? 1 1 -1000 SLIDER 10 525 182 558 m0 m0 0 5 2 1 1 NIL HORIZONTAL SLIDER 10 490 182 523 m m 0 5 1 1 1 NIL HORIZONTAL BUTTON 10 105 97 138 Scale Free setup-preferential NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 10 255 77 288 Layout layout T 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 10 215 70 248 Ising go-ising T 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 75 215 140 248 Voter go-vote\n T 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 145 215 220 248 Majority go-majority T 1 T OBSERVER NIL NIL NIL NIL 1 PLOT 810 10 1085 235 magnetization NIL NIL 0.0 10.0 0.0 1.0 true false "" "" PENS "default" 1.0 0 -16777216 true "" "plot magnetization" BUTTON 345 590 457 623 radial-central layout-radial turtles links max-one-of turtles [count link-neighbors] NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 255 590 337 623 Resize resize-nodes ask turtles [set shape \"circle\"] repeat 6 [ask turtles [set size size * 1.1]] NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 550 590 617 623 lattice ask turtles [move-to one-of patches with [not any? other turtles-here and abs pxcor < cube-length + 0.5 / 2 and abs pycor < cube-length + 0.5 / 2]] ask turtles [setxy (xcor * (max-pxcor - 1) / (cube-length - 0.5)) (ycor * (max-pycor - 1) / (cube-length - 0.5))] NIL 1 T OBSERVER NIL NIL NIL NIL 1 PLOT 1090 10 1365 235 distribution NIL NIL 0.0 10.0 0.0 1.0 true false "" "" PENS "default" 1.0 1 -16777216 true "" "histogram [opinion] of turtles" BUTTON 465 590 542 623 arrange ask turtles [setxy who mod cube-length (who - who mod cube-length) mod cube-length ^ 2 / cube-length setxy xcor - cube-length / 2 ycor - cube-length / 2 setxy xcor / cube-length * 2 * max-pxcor ycor / cube-length * 2 * max-pycor] NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 100 105 180 138 Small World setup-small-world NIL 1 T OBSERVER NIL NIL NIL NIL 1 TEXTBOX 10 15 160 33 Setup 12 0.0 1 TEXTBOX 10 200 160 218 Running the model 12 0.0 1 TEXTBOX 255 575 405 593 Additional visualization tools 12 0.0 1 TEXTBOX 15 370 165 388 Variables 12 0.0 1 @#$#@#$#@ ## WHAT IS IT? In _Heterogeneous Voter Models_ (2010), Masuda, Gilbert and Redner introduce a heterogeneous voter model where agents have their own intrinsic rate to change opinion, reflecting the heterogeneity of real people. This model simulates their findings by studying how people adjust their opinion between multiple choices. The model simulates three different mechanisms for opinion adjustment: Ising, Voter, and Majority. ## HOW IT WORKS In this model, each agent is assigned an initial opinion. Each agent is then linked with one or more other agents. As the simulation runs, the opinions of the agents change depending on one of three adjustment rules: Ising, Voter, or Majority. For Ising, an agent's opinion does not depend on other agents; it changes solely due to randomness. Under the Voter rule, an agent adjusts one’s opinion based on the decision of a randomly selected linked agent; however, this change only occurs randomly. The Majority version is similar to the Voter version; however, instead of choosing a random agent’s opinion to follow, the agent follows the most prevalent opinion among its linked agents. Like the Voter version, the change in the Majority version occurs randomly. To start, each agent is assigned an opinion represented by a number between 0 and the variable number-states. ## HOW TO USE IT To start, select one of five setup versions. These versions differ in how the agents are connected to one another. The options are Lattice, Mean Field, Random, Scale Free, and Small World. -Lattice: Creates cube-length^dimension agents and arranges and links them to represent a lattice. -Mean Field: Creates N agents and connects every agent to every other agent. -Random: Creates N agents. Each agent then randomly selects one other agent and makes a link with that agent. Though each agent may only select one target, it is possible for one agent to be the target of many other agents. -Scale Free: Arranges N agents into preferential groups determined by the m0 and m variables. -Small World: Creates N agents and arranges them in a circle. Each agent is linked with its adjacent agents. When using the Lattice, Random, or Scale Free setup, the Layout button may be pushed to assist in visualization. Push Layout again to stop the agent rearrangement. After selecting a setup and rearranging the layout if need be, you will see the agents are colored different shades of blue. Each shade of blue represents a different opinion. The number of possible opinions can be adjusted using the number-states slider. There are three ways to run the simulation. The three ways match the three mechanisms of opinion change. Press whichever one you want to observe. To stop the simulation, press the same button. If you want to see all agents move simultaneously, simply select the On option under the simultaneous? switcher. As the simulation runs, the distribution of opinions is tracked on the right side of the interface along with the magnetization. The magnetization is the average opinion of the agents normalized by the number of possible opinions. The buttons under the Additional visualization tools may be helpful for you to examine your results. The Resize button can be especially useful to easily see the agents and their opinions/colors. The sliders under the Variables header affect the various setup options. ## THINGS TO NOTICE Notice how the simulation differs between the Ising, Voter, and Majority options; especially how they differ with regards to the distribution of opinions. Notice the relation between linked agents and their shade of blue and how this differs between the three options. ## THINGS TO TRY Adjust the sliders under the Variables header to modify the various setups. ## EXTENDING THE MODEL All three options depend on random chance. When the simulation is setup, each agent is randomly assigned a flip-rate between 0 and 1. This determines whether or not an agent follows the opinion change rule or not. By modifying the flip rate, e.g. making it higher for certain agents and lower for others, one can see how the heterogeneous voter model would act in situations where the likelihood of an agent switching opinion depends on factors such as their social network or current opinion among many possible options. In the motivating paper by Masuda, Gilbert and Redner, the authors contrast the heterogeneous voter model with a partisan voter model where agents have innate and fixed preferences for certain opinions. This partisan voter model is a possible extension that would be useful to simulate and contrast to the current heterogeneous voter model. ## RELATED MODELS Axelrod Confident Voter Social Consensus Ising Potts Voter Turnout ## CREDITS AND REFERENCES Masuda, Naoki, N. Gilber, and S. Redner. 2010. "Heterogeneous Voter Models." _Physical Review E_ 82 010103(R) @#$#@#$#@ 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 true true 15 75 15 225 150 285 150 135 Line -16777216 false 150 285 150 135 Line -16777216 false 150 135 15 75 Line -16777216 false 150 135 285 75 bug true 0 Circle -7500403 true true 96 182 108 Circle -7500403 true true 110 127 80 Circle -7500403 true true 110 75 80 Line -7500403 true 150 100 80 30 Line -7500403 true 150 100 220 30 butterfly true 0 Polygon -7500403 true true 150 165 209 199 225 225 225 255 195 270 165 255 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