A Simple Model of Increasing Access
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A More Sophisticated Graph
The results from the previous slide will vary from society to society. Fixing channel count at 3, we observed 200 different societies over the full range of access, and averaged the Indices of Balkanized Affiliation. The results are graphed below.
As you can see, the rationality bound changes the effect that access has on Balkanization. This graph has several characteristic features:
Access < Channel Count:
For very low access, Balkanization is high. Up until the channel count, Balkanization tends to decrease with access. The reason for this is simple. While access is very low, agents are not using all of their channels, because they only have the ability to connect to their very closest neighbors. As access increases, agents can simply increase their number of connections. Thus, in this range, the channel count is irrelevant and the graph acts just as it did in the case without rationality bound. The Balkanization coefficient begins at 1, because for zero access all agents are isolated so no agent has more than one affiliation.
Access > Channel Count:
As access exceeds channel count, agents can no longer increase their number of connections. Thus, increasing access now has the sole effect of giving agents more potential partners to select from. Since agents prefer similar partners, increasing access allows them to find more and more partners of the same type to form connections to. Thus, the number of affiliations per agent will decrease and Balkanization increases. For our particular society, with universal access, all agents connect only to those of the same type, so the Index of Balkanized Affiliation reaches a maximum of one.
To add some perspective to this graph, remember that channel count for a real person may be as high as a few thousand, while full access on the planet would correspond to a number in the billions. Thus, the initial decreasing part of the graph is much smaller than the later increasing part. When we observe a graph of this type from now on, we will generally be interested in its behavior after the initial drop.
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