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Direct attempts to model social capital dynamics with "currency" metaphors ("like" counts, whuffie) are not credible imo.
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I tried to work on this from learning theory: is there a social capital production function? whats its intrinsic dimensionality?
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I think 2^S is a upper bound in that model, there could be lower dimension that preseve the stucture; types within social group
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or is your argument that to accumulate social capital some "uinque snowflake" characteristic is needed in individual?