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This chapter commences with a review of the theory of models as cognitive tools/linguistic devices by which we order and organize experiences and observations. Within the context of the theory of models, we then turn to the question of scalability of composite indices, that is: Can properties of a society, such as composite indices, be scaled across time periods and levels of analysis – from the whole system to subunits thereof? Because societies are considered complex systems, indeed among the most complex, we address this question within the context of two general sets of equations of state for complex systems. The first complexity model is a nonlinear deterministic dynamics model defined by difference or differential equations. A second complexity model incorporates stochastic (uncertainty) elements into the model specifications, leading to the various classes of statistical models that we use in our daily research. As a case study of the use of composite social indicators, the U.S. Child and Youth Well-Being Index (CWI) and various empirical findings for the years 1975–2014 are reviewed. Using the CWI as an example, the question of whether the scalability of composite social indicators is more likely due to one of the complexity models or the other is addressed. We conclude that both complexity models appear to be applicable and useful for studying, interpreting, and scaling composite indicators.

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