Abstract
Laws describe; theories explain. This chapter introduces the reader to laws of social complexity. These are formal descriptive relations that exist among components and variables of complex social systems. The approach in this chapter is to divide the study of laws of social complexity into two classes: structural laws and distributional laws. Structural laws of social complexity describe how social complexity depends on organizational architecture. The two fundamental patterns of structural architecture in structural laws of social complexity are serial and parallel, which correspond to conjunctive and disjunctive events in the performance of social systems and processes. The most complex social systems are ultimately based on these fundamental patterns. By contrast, distributional laws of social complexity describe how social complexity depends on nonequilibrium dynamics. The fundamental pattern of nonequilibrium dynamics in social complexity is the power law, which assumes various forms in different social systems and processes. Some of the most intriguing complex social phenomena (language, conflict, wealth, urbanization) are based on power laws and nonequilibrium dynamics.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The correct aphorism should be that a chain is weaker than its weakest link, which is an even worse condition than being as weak as the weakest link.
- 2.
Popular culture is silent about an analog of the serial chain metaphor for the case of a parallel structure. If it existed, it should say: a parallelized system is stronger than its strongest component.
- 3.
We will examine collective action theory more closely in the next chapter.
- 4.
Using the Stevens level of measurement as a classification criterion is useful for distinguishing formally different mathematical forms that are analyzed through different statistical and mathematical methods (discrete vs. continuous). The same classification might be less useful in physical power laws, where ranks and ordinal variables are not as common as they are in social science.
- 5.
For example, Bak (1996), Jensen (1998), and Barabasi (2002) misname these functions repeatedly—c.d.f., p.d.f., and complementary c.d.f.—as if they were synonymous, whereas each function refers to the probability of a different event: \(\mathbf {Pr}(X \le x), \mathbf {Pr}(x < X \le x + dx)\), and \(\mathbf {Pr}(X >x)\), respectively. The obvious but important point is simply that probability functions that refer to different events should be named differently and consistently.
- 6.
Note that Type II (absolute frequency) and Type III (relative frequency) yield the same slope b, although the functions on the left side are not mathematically identical.
- 7.
Also, strictly speaking, the event “\(X \ge x\)” makes more sense than “\(X > x\)” when X is a discrete (count) variable. This is because \(0.99999\dots \) is not computable and 0 is mathematically impossible, so 1 is the base count for social processes such as events, riots, wars, and other social count processes.
- 8.
The basic point is that care must be taken to specify which type of power law model is being discussed or presented; this should not have to be deciphered from poorly labeled plots or misnamed equations.
- 9.
“Binning” refers to the procedure of classifying values into equal and finite intervals, which creates problems when the distribution of the underlying population is unknown. It is unnecessary in power law analysis that uses raw data. The direct construction of the histogram of normalized cumulative frequencies is often feasible and always preferable because no binning is necessary. However, sometimes binning is unavoidable when using official statistics such as provided by government agencies.
- 10.
The exact value of the exponent b is of great theoretical relevance, as explained below in Sect. 6.4.2.1, so reporting the standard error of b is another good practice.
- 11.
However, recall that the standard error of estimates contains essentially the same information.
- 12.
Other important and insightful theoretical extensions of the power law functions discussed in this chapter consist of the gradient \(\nabla f\) associated with several of the functions. For instance, the field \(\mathbf {E}_b = - \nabla f(x; a, b)\) associated with the power law exponent has intrinsic interest for its social interpretation and relation to criticality, metastability, and other complexity concepts. Theoretical and empirical implications of these and other advanced extensions lie beyond the scope of this introductory textbook.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Cioffi-Revilla, C. (2017). Social Complexity II: Laws. In: Introduction to Computational Social Science. Texts in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-319-50131-4_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-50131-4_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-50130-7
Online ISBN: 978-3-319-50131-4
eBook Packages: Computer ScienceComputer Science (R0)