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## NetLogo User Community Models

## WHAT IS IT?

This is a model of the development of Social Capital or bonding within groups of 2 to 20 people. It shows how Social Capital grows or decays from a starting position which is based on the initial levels of attraction within the group. Growth or decay is then dependent on 2 factors:

1. the quality of relationship between connected individuals which is a function of their behaviour towards each other, and

2. the number of connections between individuals which is a function of the changing attractiveness of the group and the desire and capacity of individuals to maintain relationships.

## HOW IT WORKS

At the outset, a group is created with the number of People in the group given as an input. The number of people connected, the number of connections and the initial level of Social Capital for each connection is determined by the input level of Attraction. The group is represented visually as a social network of people and their connections.

At each tick, the 2 people at the ends of every connection interact. The number of interactions for each pair is determined by the Social Capital of the connection, the more the pair are bonded, the more they interact.

One will act and the other will react. The acting person decides whether to act in a 'good' or 'bad' way by checking which behaviour will give them the greater reward with the current probabilities of a counter-reaction by the second person. The second person will then react or not with that probability.

The resultant rewards for both people from the interaction are combined to calculate the net effect on the Social Capital within the relationship. If the net reward is positive, Social Capital rises and, if the net reward is negative, Social Capital falls. This process is based on a Game Theory approach using a reward matrix and the reaction probabilities.

The Social Capital of the group is then determined by combining the Social Capital of every pair to calculate the Average Weighted Degree of the network. AWD is a standard network metric which reflects of the number of connections each person has and the strength, or level of Social Capital for each pair, for each of their connections.

Once every pair has interacted, individuals decide whether to make new connections or sever existing connections based on the perceived benefits of Social Capital shared with connected others and inherent levels of attraction within the group. The level of attraction sets a threshold for Social Capital which determines whether connections will be made or severed. The threshold is a function of a constant within the inequalities. This represents a 'cost/benefit' decision making process, whether it is worth making the effort to make or maintain connections. New connections are coloured red.

The maximum Social Capital for an individual is limited by the individual's ability to expend Emotional Capital, Cognitive Capital and Physical Capital on interacting with others and maintaining relationships. This is calculated using an approach based on the theories of Robin Dunbar and the so-called 'Dunbar Number'.

Following set-up, the model will run and display the group as a network and Social Capital as a plot. The level of social capital in each connection is reflected in the thickness of the connection. The importance of each person to the group is reflected in the size of the person.

## HOW TO USE IT

To set up the initial group network, set the number of People and the initial level of Attraction.

Set the level of Reaction to Pro Behaviour. This is the percentage of 'good' actions which will result in a favourable reaction. The higher the level, the more 'good' behaviour will be reinforced.

Set the level of Reaction to Anti Behaviour. What this does is to reduce the degree to which reaction to 'bad' behaviour is itself reduced as Social Capital rises. The result is that, the higher this input, the more reaction there will be to 'bad' behaviour and the less 'bad' behaviour there will be.

The Go-forever button will set the group into action. Social Capital will rise or fall and connections will be made or lost. The Social Capital of each pair is reflected by the thickness of the connection between them. The importance of each person to the group is reflected in their size.

While the model is running, interventions can be made by altering the Attraction and Reaction sliders to see what effect that has on the direction of change in Social Capital and the final outcome.

The first set of monitors show the maximum possible Social Capital, the maximum possible number of connections, and the actual Social Capital achieved by the group.

The second set of monitors show the actual number of people with connections and the actual number of connections.

The third set of monitors shows the maximum possible SocialCapital of those people who are connected and the actual Social Capital of those people who are connected. This may be different than the first set if people have become disconnected from the group and have not reconnected.

The final monitor shows the time which has passed before the group reaches its settled state.

## THINGS TO NOTICE

There is at least one 'tipping point' for a combination of input settings at which a group of any size larger than 3 will always survive in some form with a small level of Social Capital but a single point of reduction in any of the variable input settings of Attraction or Reaction will guarantee that the group will disintegrate. With settings of Attraction 6.3, Reaction to Pro-Behaviour 53% and Reaction to Anti-Behaviour 1.26, a group of any size larger than 3 will always just survive. Reduce any of the settings by 1 point and it will always fail.

For groups of 2 or 3, the same settings will sometimes result in survival and sometimes failure. This is because levels of Attraction are randomly set up to the maximum and there is insufficient 'averaging' effect with small numbers of connections.

## THINGS TO TRY

(suggested things for the user to try to do (move sliders, switches, etc.) with the model)

## EXTENDING THE MODEL

(suggested things to add or change in the Code tab to make the model more complicated, detailed, accurate, etc.)

## NETLOGO FEATURES

(interesting or unusual features of NetLogo that the model uses, particularly in the Code tab; or where workarounds were needed for missing features)

## RELATED MODELS

(models in the NetLogo Models Library and elsewhere which are of related interest)

## CREDITS AND REFERENCES

(a reference to the model's URL on the web if it has one, as well as any other necessary credits, citations, and links)