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## WHAT IS IT?
The qvoter model with independence [3] is a model of opinion dynamics in which each agent verbalizes an opinion on a twopoint scale, such as yes/no or for/against. There are two types of social responses in the model, conformity and independence.
## HOW IT WORKS
We consider a population of agents on a network of size N. In this implementation we use WattsStrogatz network, which is described by two parameters: k (the average degree of the node) and beta (probablity of rewiring). Each agent can be in one of two states +1 or 1 (e.g. opinion for or against a given issue), which is marked in green or red, respectively. There are two parameters of the model: q (the size of the influence group) and p (probability of independent behavior). Time evolution of the systems is given by the following ALGORITHM:
## HOW TO USE IT NETWORK PARAMETERS
The model is implemented on the WattsStrogatz network, therefore first choose parameters of the network:
* N  number of agents
MODEL PARAMETERS
Choose parameters of the model:
* q  size of the influence group INITIAL CONDITIONS
The last thing to choose is the initial fraction of agents with positive opinion, with is given by parameter:
* density_of_greens  the fraction of greens (positive opinions) at the beginning of simulations; greens are randomly distributed over the whole system.
After choosing values of all parameters click:
Algorithm can be also observed in the stepbystep section by clicking one by one the following buttons:
## THINGS TO NOTICE
The society described by the model can be in one of two qualitatively different phases:
If we change only the independence parameter p, and keep all others fixed, we can see observe phase transition between these phases. The character of this transition depends on parameter q (size of the influence group).
For q < 6, depending on p system will be in one of these states. Disagreement is observed for p > p*, above critical point p<sup>*</sup>. In the case of agreement, for p < p*, system randomly chooses the dominating opinion. In the case of systems of finite size (as the one that we can observe here) the majority opinion may change in time  system switches between two states symmetric with respect to c = 0.5 and in the result on the histogram there are clearly two peaks.
For q >= 6 there is such a range of p, p*<sub>low</sub> < p < p*<sub>high</sub> that both qualitatively different states  agreement and disagreement coexist. The state of the system depends on the initial conditions, what we call hysteresis. However, again for the finite systems there are possible switches between these states, what can be noticed on the histogram. If the system evolves long enough, three peaks occur.
## THINGS TO TRY
* What happens for low / high probability of independence? How the histogram changes?
* How frequency of switches vary with the size of the network?
* Hysteresis  dependence on the initial conditions
* Coexistence of agreement and disagreement
Note that in order to observe meaningful histograms the system needs some time to evolve. We recommend to wait at least 100 000 ticks, however 1 000 000 would be even better.
## EXTENDING THE MODEL
One can extend the model by replacing independence with anticonformity or including both of these nonconformity behaviors at once. Another extension is regarding the underlaying structure, one can implement the model on other random networks such as ErdosRenyi or BarabasiAlbert.
## HOW TO CITE
The model was implemented in NetLogo to support the following publication
If you mention the original model, we ask you to cite [3]. If you mention this implementation of the model in a publication, we ask that you include the citations below:
Katarzyna SznajdWeron, Arkadiusz Jedrzejewski, Barbara Kaminska (2023), "Towards understanding of the social hysteresisinsights from agentbased modeling", submitted to Perspectives on Psychological Science
## ACKNOWLEDGEMENT
This model was created as part of the project funded by the National Science Center (NCN, Poland) through grant no. 2019/35/B/HS6/02530
## CREDITS AND REFERENCES
[1] Asch, S. E. (1955). Opinions and social pressure. Scientific American, 193(5), 31–35.
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