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Heterogeneous Voter - Network

by Daniel Diermeier (Submitted: 06/01/2015)

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## 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)

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