The Society Model

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The Index of Balkanized Affiliation

Note: in order to run the simulation referred to in this slide, go here, to the Java Applet version. You will be directed to download the latest version of the Java plug-in.

We now return to the problem of finding a measure of balkanization that we can use to compare societies. If we associate each agent with one or more communities based on her affiliations, then we can measure the overlap or separation between the various communities. We formalize this notion below with the Index of Balkanized Affiliation, BA.

We define a community of type t, M(t), as the set of agents with an affiliation of type t. Recall that an agent has an affiliation to type t if knowledge of type t is available to him. We want our index to reflect how disjoint these communities M(t) are. The form we use is:

where T is the total number of knowledge types. BA has a maximum of 1 when communities are completely disjoint and no agent bears affiliation to more than one type. As the number of affiliations each agent has grows, the number of communities she belongs to increases, and consequently BA falls. BA has a minimum of 0 when every agent has affiliations to all types and hence belongs to every community.

Below, the index of balkanized affiliation is displayed for the society to the left. Two other measures are included: BC, the Index of Balkanized Communication, is a measure of balkanization that focuses on the connections that exist between agents and Average Similarity is just the average similarity between the agents. While these measures provide additional information about a society, they are not essential to the main findings and so we focus on BA throughout this tutorial. For a more thorough explanation of these additional measures please see the technical appendix.

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