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view/download model file: 2D Majority Game.nlogo
WHAT IS IT?
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This model presents a basic two-dimensional majority or plurality voting model. It is, in fact, nearly identical to the 1D version except that the agents live on a torus (so there are still no 'edge effects'). As before, the agents can only be one of two types: red or blue. In each step, agents change their state based upon the majority (or plurality) of their neighbors' states.
HOW TO USE IT
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Clicking SETUP fills the world with agents (one per patch) each with a randomly chosen color.
Clicking GO makes the turtles look at their neighbors and decide what color to become. All the agents look and change simultaneously, that is, the model employs synchronous updating. Clicking STEP runs GO just once.
The RADIUS slider allows the user to set how far away the agents will look to collect information about other users' states. In two dimensions, radius is a bit tricky. The radius includes all cells that can be reached from the home cell by moving vertically, horizontally, or diagonally for up to that many spaces. For example, if you set RADIUS to 1, each agent will look out to the eight cells surrounding it (plus the cell that itself is on). If you set RADIUS to 3, then it will include all spaces that can be reached in 3 "steps"; left 3, up 3, north-east 3, 2 to the right and one NE, etc. For more info about radius, see "Neighborhoods Example" in the Code Examples folder.
The USE-PLURALITY toggle switch allows the user to specifiy whether the decision rule is a "majority" rule or a "plurality" rule. If the USE-PLURALITY switch is on then each agent will convert to whichever color is most prominent among its neighbors.
If USE-PLURALITY is off, then the decision is based upon majority rule. The PERCENT-NEEDED slider determines the quorum, i.e. how many neighbors of a color are necessary make an agent change its color. At the lowest level (50%) the models runs a strict majority and at the maximum level (100%) unanimity is required.
The NUMBER_NEEDED monitor box lets the user know how many agents of a single color are required to convert each agent, given the provided RADIUS and PERCENT-NEEDED. Note that the actual number must be strictly greater than the number in this box (can you look at the code and answer why?).
THINGS TO NOTICE
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The colors start off very scattered. Notice that they form clusters after you run the model. While the model is running, change the radius. Notice how that changes the cluster size (cluster size = the number of contiguous agents of the same color) and SHAPE. Why does the overall cluster shape change like that?
QUESTIONS
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1) What is the difference between a 50% majority rule and the plurality rule in this model?
2) Under each rule, what happens when an agent has equal numbers of neighbors with each color?
3) What does increasing the radius do to the model's performance and why?
THINGS TO TRY
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Notice the ratio of reds:blues after you click SETUP. Do you think this will have an effect on the final ratio. Why might it not matter (what could be more important)? With the radius set to 3 or higher, record which color has a greater initial number and which color has more after the model has settled down. Is there a correlation?
CREDITS AND REFERENCES
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To refer to this model please use: Bramson, A and Scott Page (2005). NetLogo 2D Majority Game model. "http://bramson.net/academ/scottsnetlogo/2D Majority Game.html". Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI.