Challenges for complexity measures: A perspective from social dynamics and collective social computation.

We review an empirically grounded approach to studying the emergence of collective properties from individual interactions in social dynamics. When individual decision-making rules, strategies, can be extracted from the time-series data, these can be used to construct adaptive social circuits. Social circuits provide a compact description of collective effects by mapping rules at the individual level to statistical properties of aggregates. This defines a simple form of social computation. We consider the properties that complexity measures would need to have to best capture regularities at different level of analysis, from individual rules to circuits to population statistics. One obvious benefit of using the properties and structure of biological and social systems to guide the development of complexity measures is that it is more likely to produce measures that can be applied to data. Principled but pragmatic measures would allow for a rigorous investigation of the relationship between adaptive features at the micro, meso, and macro scales, a long standing goal of evolutionary theory. A second benefit is that empirically grounded complexity measures would facilitate quantitative comparisons of strategies, circuits, and aggregate properties across social systems.