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Other Measures of Balkanization and Similarity
The Index of Balkanized Affiliation is not the only way to measure the fragmentation of a society. Van Alstyne and Brynjolfsson provide three other measures that focus on different aspects of a society.
The Index of Balkanized Communication, BC, measures the fragmentation of communications paths between agents. Namely, let lij represent the total number of links in the shortest path connecting agent i with agent j. If there is no such path, define lij to be the total number of agents, N. BC is the average value of these distances divided by the maximum distance, N.
BC increases to its maximum value of 1 when each agent is a single disconnected island. The minimum value, which approaches zero for a large population, is reached when all agents are directly connected to each other.
The Average Similarity, Sij, measures the average degree to which all pairs of agents have access to the same information. The knowledge that each agent has access to can be represented in a knowledge vector, with each component representing a particular type of knowledge. We can roughly define the similarity between two agents as the cosine of the angle between their knowledge vectors. The similarity can be computed by dividing the dot product of the knowledge vectors by the product of their magnitudes. Averaging this value over all pairs of agents gives the Average Similarity.
The Index of Balkanized Information, BI, is another measure introduced by Van Alstyne and Brynjolfsson. This index measures the degree to which knowledge bases are fragmented. However, we do not include this index in our simulation because of the strict assumptions on which it relies.
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