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To build better theories of cities, companies, and other social institutions such as universities, requires that we understand the tradeoffs and complementarities that exist between their core functions, and that we understand bounds to their growth. Scaling theory has been a powerful tool for addressing such questions in diverse physical, biological and urban systems, revealing systematic quantitative regularities between size and function. Here we apply scaling theory to the social sciences, taking a synoptic view of an entire class of institutions. The United States higher education system serves as an ideal case study, since it includes over 5,800 institutions with shared broad objectives, but ranges in strategy from vocational training to the production of novel research, contains public, nonprofit and for-profit models, and spans sizes from 10 to roughly 100,000 enrolled students. We show that, like organisms, ecosystems and cities, universities and colleges scale in a surprisingly systematic fashion following simple power-law behavior. Comparing seven commonly accepted sectors of higher education organizations, we find distinct regimes of scaling between a school’s total enrollment and its expenditures, revenues, graduation rates and economic added value. Our results quantify how each sector leverages specific economies of scale to address distinct priorities. Taken together, the scaling of features within a sector along with the shifts in scaling across sectors implies that there are generic mechanisms and constraints shared by all sectors, which lead to tradeoffs between their different societal functions and roles. We highlight the strong complementarity between public and private research universities, and community and state colleges, that all display superlinear returns to scale. In contrast to the scaling of biological systems, our results highlight that much of the observed scaling behavior is modulated by the particular strategies of organizations rather than an immutable set of constraints. 

Abstract To what extent do simultaneous innovations occur and are independently from each other? In this paper we use a novel persistent keyword framework to systematically identify innovations in a large corpus containing academic papers in evolutionary medicine between 2007 and 2011. We examine whether innovative papers occurring simultaneously are independent from each other by evaluating the citation and co-authorship information gathered from the corpus metadata. We find that 19 out of 22 simultaneous innovative papers do, in fact, occur independently from each other. In particular, co-authors of simultaneous innovative papers are no more geographically concentrated than the co-authors of similar non-innovative papers in the field. Our result suggests producing innovative work draws from a collective knowledge pool, rather than from knowledge circulating in distinct localized collaboration networks. Therefore, new ideas can appear at multiple locations and with geographically dispersed co-authorship networks. Our findings support the perspective that simultaneous innovations are the outcome of collective behavior.