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Scaling in Social Systems

A one day EPSRC-funded workshop (at which yours truly presented) in Oxford at the Complex Agent-Based Dynamic Networks group (CABDyN) at the Said Business School (1st December 2011) had five interesting speakers all talking about the new social physics of cities and economies, focusing on regularities and irregularities in the structure and dynamics of these systems. Didier Sornette from ETH Zurich threw down the challenge telling us that scaling was boring and that all the action should be on departures from scaling – in the case of Zipf laws, departures from such regularity where the biggest cities, incomes, firm sizes and so on are substantially less or more than what Zipf’s Law might predict.

I kicked off the day with a talk on Scaling Laws for Cities, the pdf of which you can get if you click here and then Luis Bettencourt of Santa Fe talked about Scaling and Allometry with respect to what happens when cities get bigger. The essential insight from Bettencourt and West and their other collaborators is that big cities generate more than proportionate returns to scale – positive allometry or superlinearity for things like creative industries, patents, incomes and so on, linearity for local consumption at the individual level, and sublinearity for the use of physical resources such as roads and utilities. There are profound implications for bigness from these results and a lively debate ensured which involved ourselves at CASA where our own results are more controversial. It looks like cities by size do not scale superlinearly in the UK but here lies a puzzle – we need to factor out the effect of the primate city which is London and then look at residuals. Very positive suggestions from Luis Bettencourt on this from the meeting.

Didier Sornette from ETH went first after lunch talking about cascades arguing that there were distinct discontinuities caused by endogenous and exogenous factors – he presented a great classification of dynamics. Then came Tim Evans from Imperial on citations analysis which revealed the same kinds of issues related to defining the objects of interest – in this case papers – as we find in defining the size of cities. As you drill into these areas, definitional problems abound. The objects of interest in the social science are essentially blurred, ambiguous and fuzzy and this was widely recognized at the meeting.

Geoff West from Santa Fe summed up and posed twenty critical questions that pertain to how we might articulate the physics of social systems. These provided the essence of how we might tackle the future of this field and many open questions were posed. At some point, Felix Reed-Tsochas who runs the group at Oxford will post the pdfs I guess but the batting order for the day can be retrieved by clicking here.