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Human Behavior, Dynamics of

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Encyclopedia of Complexity and Systems Science

Definition of the Subject

Dynamics of human behavior (abbreviations DHB, HB, HD) deals with the effects of multiple causal forces in human behavior, including networkinteractions, groups, social movements, and historical transitions, among many other concerns. Description of movement and change distinguishes kinematicsfrom statics, while dynamics considers causes of movement and change. Pearl [95] summarizes issuesof causality with two fundamental questions: (1) What empirical evidence is required for legitimate inference of cause‐effect relationships? (2)Given that we are willing to accept causal information about a phenomenon, what inferences can we draw from such information, and how? Policy issuesentail beliefs about causation and open a second framework for evaluating beliefs about causality [28,112]. HB dynamics is a field replete with newdiscoveries—and applications of methods derived from problems and principles that apply across disciplines. Insights transfer across...

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Abbreviations

Connectivity-k (k‑connected, k‑cohesive , structural co hesion, cohesive.blocks):

refer to the Menger (1927) theorem for structure/traversal isomorphism in graph theory , as explained in the text, where k‑components are the largest possible expansion (maximal group) that preserve structural k‑cohesion. Computation is provided by cohesive.blocks in the igraph R package.

Scale-free network :

where the probability that a node i in the network connects with k other nodes is inversely proportional to the number of k's links (see: power law), more generally, \( { p_{i} (k) \sim k^{-\gamma} } \), with \( { \lambda =1 } \) for scale-free.

Nonindependence:

is characteristic of complex phenomena with built-in interdependencies, where distributions of attributes or relations should not be not directly subject to statistical inference using the null hypothesis of independence, as in structural measures sampled from networks, and autocorrelated time series or autocorrelated spatial distributions.

Sufficient statistic:

a sufficient statistic for a statistical model is one that captures the information relevant to statistical inference within the context of the model, including the size and composition of the units of study. Let \( { X_{1},\dots, X_{M} } \) be a random sample, governed by the density or probability mass function \( { f(x\vert \theta) } \). The statistic T(x) is sufficient for θ if the conditional distribution of x, given \( { T(x)=t } \), is independent of θ. Equivalently, the functional form of \( { f_{\theta \vert x}(x) } \) does not involve θ, and the Fisher–Neyman factorization theorem may be used to help spot sufficient statistics. The likelihood ratio test can often be reduced to a sufficient statistic of the data for hypothesis testing. The minimum variance unbiased estimator of a parameter θ can be characterized in parameter estimation by sufficient statistics and the Rao–Blackwell Theorem. See Scharf Statistical Signal Processing [107]. A sufficient unit is one for which a random sample of aggregate statistics are sufficient.

Aggregate (“sufficient unit”) equation modeling:

assumes that causality can be found with quantitative equation models that use sufficient statistics , which implies that the aggregate units studied have cohesive mass or entitivity for causal interactions to act on their aggregate characteristics. See Sect. “Aggregate (“Sufficient Unit”) Equation‐based Modeling”.

NP-complete:

(NPC) algorithms require an order of non‐deterministic polynomial time (NP) but are exceptionally difficult: if a deterministic polynomial time solution can be found for any of them, it would provide a solution to every other problem in NP and empty out the class of NPC.

Dictator game:

where the first player proposes a split of some endowment and the second, entirely passive, receives the remainder. Not formally a game at all (as the term is used in game theory , where every player's outcome must depend on the actions of others), it is used in decision theory to test the homo economicus model of individual behavior, where selfishness would dictate allocation entirely to oneself. Henrich et al. [50] discovered in a 15‐society cross cultural study that people do allocate a share of the endowment to others. Skyrms [113] gives the dynamics of an evolutionary game theory variant.

Concentration indices:

such as the Laakso–Taagepera Index \( { 1/\Sigma _{i}p_{i} } \), where p i is an effective proportion weighting for each unit, are used for problems such as “what are the effective numbers of political parties self‐weighted by their membership (for polities: by their population or area)”, e. g., US party proportions {.49, .49, .02} would have an effective number of 2.08 while France with 101 parties (each weighted by its number of members) might have effective party number of 22.1.

Power law:

is a Pareto distribution where probability \( { p(x) \sim x^{-\alpha} } \), as for example: “multifractals have tails that follow a power law” (p. 209 in [75]) in how the frequency of similar units at different scales varies with the scale; see multifractal. Power laws tend to become ubiquitous when what is studied involves dimensional constraints. Power-law growth is expressed as \( { N = K/(t_{0}-t)^{k} } \) where K is an initial constant, t is calendrical time, and t 0 is the calendrical singularity date at which \( { K/(t_{0}-t)=K/0 } \), where division by zero produces dynamical instability as \( { K/(t_{0}-t)\to \infty } \).

Fractal:

is a pattern or object (e. g. geometrical) whose parts echo the whole, only scaled down, i. e., scale invariant; invariant at any scale of magnification or reduction. Fractal prices occur when positive and negative changes in prices (daily, weekly, monthly, yearly) follow a power law. “To improve almost any fractal model it is a good idea to replace it with a multifractal one” (p. 209 in [75]). A multifractal (with root and generator) is a composite pattern that begins with an initial root (e. g., a straight line) that is successively replaced with a generator (e. g., a zagged line) that replaces every instance of the initial element. See power law.

Causality :

is a relation holding between two variables such that manipulation of one of the variables (the potential cause) is reliably associated with variation in the other (the response), for some configuration of the values of other potential causes of the response. Estimation includes classical structural equations approaches [74], the treatment effects framework [102,103], the directed acyclic graph (DAG) probabilistic approach [95], and the settable system probabilistic approach that unifies all three [141]. Another aspect of causation is probabilistic evaluation and decision theory, in which case the effect of evidence in revising beliefs about causation can be studied in a Bayesian framework [28,112]. Probability of causation is not causation of probability, although there are probabilistic causative models.

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Acknowledgment

As a Santa Fe Institute external faculty member, the author greatly appreciates SFI support andthe benefits of interactions with scores of SFI researchers, visitors, and staff. Special thanks to JeroenBruggeman for sharing his prepublication book manuscript and the cross‐fertilization of ideas presented inSect. “ Cooperation, Connectivity-k and“Critical Mass” in Collective Action”, to Henry Wright for detailed commentary andsuggestions, Eric Smith for comments on the coalescence of the argument, Peter Turchin for sharing historicaldata, and to Bruggeman, Turchin, Art Griffin, Charles Stanish, and Emily Erikson for suggestions on thediscussions of their findings, to Lilyan Brudner‐White for many editorial suggestions, and to D. Eric Smithand many other colleagues at SFI for discussions.

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  1. University of California, Irvine, USA

    Douglas R. White

  2. Santa Fe Institute, Santa Fe, USA

    Douglas R. White

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  1. Douglas R. White
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  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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© 2009 Springer-Verlag

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White, D.R. (2009). Human Behavior, Dynamics of. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_272

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