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BRADFORD Sakodas Model of Social Interaction 6-25-14

by John Hamilton Bradford (Submitted: 06/26/2014)

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## WHAT IS IT?

This is based on Sakoda's 1971 paper "The Checkerboard Model of Social Interaction" in "The Journal of Mathematical Sociology"- the same edition in which Schelling's model of segregation was first published.

In this model, there are n groups, each with 2 attitudes: an "in-group" attitude towards its members, and an "out-group" attitude towards everybody else. currently, these attitudes can take on one of 3 values (+1, 0, and -1). On each turn, each agent decides to move one patch or remain in place, based on which patch location has the highest value. The value of each patch is determined by the following algorithm:

Patch_value = Sum (Vj / (Dj ^ (1/w))), where Vj is either +1, 0, or -1 (i.e. the 'value' for other turtle j), D is distance to that turtle, and "w" is the parameter "Importance of Far Away Agents". Basically, the potential patch location calculates this *for every other turtle* and then sums them to get the overall or total value for that patch. Then, the turtle picks the patch with the highest value and moves to it.

This model extends Sadoka's original model in several ways. First, you can choose more than two groups now. Second, you can choose the population level you want (in the original, there are only 6 agents per 2 groups).

## HOW IT WORKS

This is a simple model. Most of the work is done in the report procedure. There is also an output box which lists the groups and their ingroup and out-group attitudes.

## HOW TO USE IT

See what patterns emerge when groups of different preferences interact. For instance, a group that likes its own members but dislikes other groups, interacting with a second group that dislikes its own group members but likes other groups. This sort of dynamic captures hierarchical social processes. For example, the rich prefer to mingle with other rich people, while the poor would also rather mingle with the rich.

## EXTENDING THE MODEL

1. In this model, the preferences within each group are homogenous. This can be extended and made more realistic by making preferences somewhat heterogenous, but to count as a group, there should be less variation within the group than between groups regarding group preferences. Groups might also be modeled as tags or labels attached by outside groups.
2. The attitude values are discrete. They could also be modeled as continuous, say, using a random-float ranging from -1 to +1.
3. It would also be nice if the user could set up the group preferences explicitly choose the preferences of the groups they want to see interact. Right now, the group attitudes are randomly generated.

## CREDITS AND REFERENCES

Sakoda, J.M. (1971). The checkerboard model of social interaction. Journal of Mathematical Sociology 1(1). 119-132.
Elsenbroich, Corinna and Nigel Gilbert (2014) Modeling Norms. Chapter 8.

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