Behavioral and Brain Sciences

Target Article

Mapping collective behavior in the big-data era

R. Alexander Bentleya1, Michael J. O'Briena2 and William A. Brocka3

a1 Department of Archaeology and Anthropology, University of Bristol, Bristol BS8 1UU, United Kingdom. r.a.bentley@bristol.ac.uk http://www.alex-bentley.com

a2 Department of Anthropology, University of Missouri, Columbia, MO 65211 obrienm@missouri.edu http://cladistics.coas.missouri.edu

a3 Department of Economics, University of Missouri, Columbia, MO 65211; and Department of Economics, University of Wisconsin, Madison, WI 53706 wbrock@scc.wisc.edu http://www.ssc.wisc.edu/~wbrock/

Abstract

The behavioral sciences have flourished by studying how traditional and/or rational behavior has been governed throughout most of human history by relatively well-informed individual and social learning. In the online age, however, social phenomena can occur with unprecedented scale and unpredictability, and individuals have access to social connections never before possible. Similarly, behavioral scientists now have access to “big data” sets – those from Twitter and Facebook, for example – that did not exist a few years ago. Studies of human dynamics based on these data sets are novel and exciting but, if not placed in context, can foster the misconception that mass-scale online behavior is all we need to understand, for example, how humans make decisions. To overcome that misconception, we draw on the field of discrete-choice theory to create a multiscale comparative “map” that, like a principal-components representation, captures the essence of decision making along two axes: (1) an east–west dimension that represents the degree to which an agent makes a decision independently versus one that is socially influenced, and (2) a north–south dimension that represents the degree to which there is transparency in the payoffs and risks associated with the decisions agents make. We divide the map into quadrants, each of which features a signature behavioral pattern. When taken together, the map and its signatures provide an easily understood empirical framework for evaluating how modern collective behavior may be changing in the digital age, including whether behavior is becoming more individualistic, as people seek out exactly what they want, or more social, as people become more inextricably linked, even “herdlike,” in their decision making. We believe the map will lead to many new testable hypotheses concerning human behavior as well as to similar applications throughout the social sciences.

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Keywords

  • agents;
  • copying;
  • decision making;
  • discrete-choice theory;
  • innovation;
  • networks;
  • technological change

R. Alexander Bentley is Professor and Head of the Department of Archaeology and Anthropology, University of Bristol. He is the author, along with Michael J. O'Brien and Mark Earls, of I'll Have What She's Having: Mapping Social Behavior (MIT Press, 2011). Much of his recent research, published in PLoS ONE, European Business Review, Frontiers in Psychology, Mind and Society, and Current Zoology, addresses the spread of information, especially in the online age. He also uses isotopic analysis of prehistoric skeletons to study social organization in Neolithic Europe and Southeast Asia. Recent publications appear in Antiquity and Proceedings of the National Academy of Sciences, USA.

Michael J. O'Brien is Professor of Anthropology and Dean of the College of Arts and Science, University of Missouri. His recent research takes three directions: (1) the dynamics of information flow in modern societies, in collaboration with R. Alexan der Bentley and William A. Brock; (2) the role of agriculture in human niche construction, in collaboration with Kevin N. Laland (Univers ity of St Andrews); and (3) the first thousand or so years of human occupatio n of North America, in collaboration primarily with Mark Collard and Briggs Buchanan (Simon Fraser University). Recent publications appear in Current Anthropology, Journal of Archaeological Method and Theory, PLoS ONE, Journal of Archaeological Science, and Frontiers in Psychology.

William A. Brock is Vilas Research Professor Emeritus, University of Wisconsin, Madison, and Research Professor, Universit y of Missouri. He is a Fellow of the Econometric Society (since 1974), and was a Sherman Fairchild Distinguished Scholar, California Institute of Technology, in 1978, and a Guggenheim Fellow in 1987. He has been a Fellow of the American Academy of Arts and Sciences since 1992, a member of the National Academy of Sciences, USA, since 1998, and a Distinguished Fellow, American Economic Association, in 2004. Brock received the honorary degree of Doctor Honoris Causa from the University of Amsterdam in January 2009.

List of Figures and Tables

Figure 1.

Figure 1. Summary of the four-quadrant map for understanding different domains of human decision making, based on whether a decision is made independently or socially and the transparency of options and payoffs. The characteristics in the bubbles are intended to convey likely possibilities, not certitudes.

Figure 2.

Figure 2. (a) Generalized distributions characterizing the different map quadrants: normal (Gaussian) in the northwest, negative binomial in the southwest, log-normal in the northeast, and power law in the southeast. Each plot shows popularity of a choice on the x-axis versus cumulative probability of having at least that popularity on the y-axis. The left, boxed insets show the non-cumulative fraction of choices on the y-axis that have the popularity indicated on the x-axis; the right, unboxed insets show the same cumulative distributions but with double-logarithmic axes. (b) Representative timelines for the popularity of different options, for each quadrant. Note that the different lines plotted for the northwest quadrant represent different payoffs, such that curves with a lower y-intercept at asymptote represent lower payoff/cost decisions than those with higher intercepts. For the northeast quadrant, the curves (after Kandler & Laland 2009) represent innovations adopted at different rates and subsequently declining in popularity to levels commensurate with their real-world utility.

Figure 3.

Figure 3. Distribution and turnover of keywords among all the articles citing a certain seminal article (Barabási & Albert 1999): (a) Timelines of relative frequencies (number of keyword appearances divided by total number of words for the year), using the top five keywords of 2005 (logarithmic y-axes); (b) cumulative frequency distributions of all keywords. Open circles show distribution for 2001 and filled circles for 2005.

Figure 4.

Figure 4. Distribution of the popularity of boys' names in the United States: left, for the year 2009; right, top 1,000 boys' names through the twentieth century, as visualized by babynamewizard.com.

Figure 5.

Figure 5. Gaussian distributions of social ties per person as examples of behavior in the northwest. Open circles show hunter–gatherer gift-exchange partners, gray circles show school friends, and black circles show Facebook friends. The main figure shows cumulative distributions of social ties per person; the unboxed inset shows the same distribution on double logarithmic axes (compare to Figure 2, northwest inset); and the boxed inset shows the probability distribution. Data for the hunter–gatherer gift-exchange partners are from Apicella et al. (2012); for school friends from Amaral et al. (2000); and for Facebook friends from Lewis et al. (2008; see also Lewis et al. 2011).

Figure 6.

Figure 6. Charitable giving in the United States: left, past 30 years, at the national level; right, relative growth of several categories of charitable giving in the United States, over a 40-year period (popularity is expressed as the fraction of the total giving for that year, on a logarithmic scale). Data from Giving USA Foundation (2007).

Figure 7.

Figure 7. Wealth among pastorialists, with a cumulative probability distribution plot comparing published ethnographic data from the Somali (Lewis 1961) with gray circles, the Ariaal (Fratkin 1989) with white circles, and Karomojong (Dyson-Hudson 1966) with filled black circles.

Figure 8.

Figure 8. A representation of how social-network structure (or lack thereof) fits onto the map (schema adapted from Lieberman et al. 2005). In each quadrant, circles represent agents, and shades represent their choices. In the east, arrows represent social influences through which agents make most of their choices, whereas in the west, agents make choices independently.

1. Introduction

The 1960s' term “future shock” (Toffler 1970) seems ever more relevant today in a popular culture that seems to change faster and faster, where global connectivity seems to spread changes daily through copying the behavior of others as well as through random events. Humans evolved in a world of few but important choices, whereas many of us now live in a consumer world of almost countless, interchangeable ones. Digital media now record many of these choices. Doubling every two years, the digital universe has grown to two trillion gigabytes, and the “digital shadow” of every Internet user (the information created about the person) is already much larger than the amount of information that each individual creates (Gantz & Reinsel 2011).

These digital shadows are the subjects of “big data” research, which optimists see as an outstandingly large sample of real behavior that is revolutionizing social science (Aral & Walker 2012; Golder & Macy 2011; Onnela & Reed-Tsochas 2010; Ormerod 2012; Wu & Huberman 2007). With all its potential in both the academic and commercial world, the effect of big data on the behavioral sciences is already apparent in the ubiquity of online surveys and psychology experiments that outsource projects to a distributed network of people (e.g., Rand 2012; Sela & Berger 2012; Twenge et al. 2012). With a public already overloaded by surveys (Hill & Alexander 2006; Sumecki et al. 2011), and an ever-increasing gap between individual experience and collective decision making (Baron 2007; Plous 1993), the larger promise of big-data research appears to be as a form of mass ethnography – a record of what people actually say and decide in their daily lives. As the Internet becomes accessible by mobile phone in the developing world, big data also offer a powerful means of answering the call to study behavior in non-Western societies (e.g., Henrich et al. 2010).

But there is a downside to big-data research. Without clear objectives and a unifying framework, behavioral scientists may ask whether it is useful, for example, to infer from millions of Facebook pages or Twitter feeds that “men are more influential than women … [and] that influential people with influential friends help spread” information (Aral & Walker 2012) or that “people awaken later on weekends” (Golder & Macy 2011). Big-data research runs the risk of merely reinforcing the most convenient “as if” assumptions about human behavior that currently divide the behavioral sciences (e.g., Gintis 2007; 2009; Laland & Brown 2011; Mesoudi 2011; Mesoudi et al. 2006; Rendell et al. 2011). Such assumptions are often chosen to fit the purpose, either (a) at the economic end of the social-science spectrum, where individual decision rules are optimized for the environment and maximize reproductive success or some utility function (Gintis 2007), or (b) at the cultural-historical end, where choices are programmed by broader social influences, “culture” (Davis & Fu 2004), “norms” (Postmes et al. 2001), or “habitus” (Bordieu 1990).

The degree of social influence on decision making is an empirical question that underlies what big data mean and how they can be used. As an example of the importance of this issue, consider the ubiquitous reliance on crowdsourcing in behavioral studies, business, and politics (Horton et al. 2011) – what Wegner (1995) termed “transactive memory” and now commonly called the “wisdom of crowds” (Couzin et al. 2011; Lorenz et al. 2011; Surowiecki 2004): Ask a question of a group of diverse, independent people, and the errors in their answers statistically cancel, yielding useful information. Wikipedia is founded on this assumption, of course, even though copying of text is essential to its growth (Masucci et al. 2011).

The wisdom-of-crowds effect is lost, however, if agents are not thinking independently (Bentley & O'Brien 2011; Salganik et al. 2006). There are numerous indications that online behavior may be getting more herdlike, more confused, or even more “stupid” (Carr 2008; Onnela & Reed-Tsochas 2010; Sparrow et al. 2011). In economies replete with online communication and a constant barrage of information – often to the point of overload (Hemp 2009) – crucial human decision making might be becoming more herdlike in contexts such as voting (Arawatari 2009) and forming opinions about climate change (Ingram & Stern 2007), mating (Lenton et al. 2008; 2009), music (Salganik et al. 2006), and finances (Allen & Wilson 2003). Herdlike behavior could be worrisome, say, for those in the public-health and medical sectors (e.g., Bates et al. 2006; Benotsch et al. 2004; Zun et al. 2004).

How does one take advantage of big data, with its huge sample sizes and natural contexts, and still address the degree and nature of social influence among the contexts being studied? We introduce here a simple map of the different types and domains of human behavioral innovation – translated as “decision making” – that can be characterized directly from population-scale data. We view the map as analogous to a coarse-grained tool much like a Google map. We illustrate the “zoom” feature of the tool by using one major theory of human decision making: discrete-choice analysis (see McFadden [2001] and his references to creators of the theory [e.g., Kahneman, Tversky, and Luce]). We chose discrete-choice theory as an expository vehicle because it is related to many other theories of human decision making, both individually and in groups, such as replicator dynamics (Krakauer 2011), Bayesian updating and information theory (Krakauer 2011), and statistical mechanics (Durlauf 1999), as well as to empirical problems associated with measuring “social capital” (Durlauf 2002). We argue that our conceptual tool – a “reduced form” parameterization of the large research area of discrete-choice approaches to decision making – is useful in helping social scientists navigate these large areas of science just as the Google map tool is useful in navigating geographical areas at various levels of resolution.

2. The map

In the simplest of terms, the map (Figure 1) graphs two analytical dimensions: (1) the extent to which a decision is made independently or socially, and (2) the transparency or opaqueness of the decision in terms of payoff. The western edge of the map represents completely independent decision making, where agents use no information from others in making decisions, and the eastern edge represents pure social decision making, where agents' decisions are based on copying, verbal instruction, imitation, or other similar social process (Caldwell & Whiten 2002; Heyes 1994). The north–south dimension of the map represents a continuum from omniscience to ignorance, or – more formally – the extent to which there is a transparent correspondence between an individual's decision and the consequences (costs and payoffs) of that decision. The farther north we go on the map, the more attuned agents' decisions will be with the landscape of costs and payoffs. As we move south, agents are less and less able to discern differences in potential payoffs among the choices available to them.

Figure 1.

Figure 1.

Summary of the four-quadrant map for understanding different domains of human decision making, based on whether a decision is made independently or socially and the transparency of options and payoffs. The characteristics in the bubbles are intended to convey likely possibilities, not certitudes.

Low resolution version High resolution version

The map is considerably more than a qualitative description, as it is grounded in established discrete-choice approaches to decision making. If we start with the full version, which we simplify below, we have the equation



where there are N t possible choices at date t, and denote: (1) the probability that choice k is made at date t; (2) the “intensity of choice,” which is inversely related to a standard-deviation measure of decision noise in choice and is positively related to a measure of transparency (clarity) of choice; and (3) the deterministic payoff of choice k at date t. The deterministic payoff is a function, , of a list of covariates, x kt , that influence choice at date t. denotes the fraction of people in a relevant peer or reference group that choose option k, and J t denotes a strength of social-influence parameter that the fraction of people, , in an individual's peer group (sometimes called “reference group”) has on the person (agent) under study. Subscripts appear on variables because their values may change over time, depending on the dynamical history of the system.

The map allows us to operate with only two parameters extracted from Equation (1) above: J t and b t . The east–west dimension of the map represents J t – the extent to which a decision is made independently or socially. The western edge, representing completely independent learning, corresponds to J t  = 0 in mathematical notation. Conversely, the eastern edge, pure social decision making, corresponds to J t  = ∞. In between the extremes is a sliding scale in the balance between the two. This is a flexible measure in terms of the agents represented. The midpoint could represent, for example, a population of half social learners and half individual learners, or each individual giving a 50% weight to his or her own experience and a likewise amount to that of others. Location along the east–west dimension may not always affect the equilibrium toward which each behavior evolves, but it will certainly affect the dynamics by which that equilibrium is approached.

The north–south dimension of the map represents b t  – the extent to which there is a transparent correspondence between an individual's decision and the consequences of that decision. The farther north we go on the map, the more attuned agents' decisions will be with the landscape, which we can represent by the function U(...) of costs and payoffs. At the extreme northern end are behaviors where there is an immediately detectable impact of getting a decision right or wrong. It corresponds to b t  = ∞. As we move south, behavioral evolution can begin to create an unconstrained set of possible solutions, meaning there are fewer and fewer reasons for one solution to be preferred over another. The farthest south one can go corresponds to total indifference, which is where b t  = 0, and the probability of any particular choice among N t possible choices approaches zero (because 1/N t goes to zero as N t goes to infinity). Choices in the southern extreme of the map need not be trivial, as this end also represents cases where people are poorly informed about their choices and perhaps overwhelmed by decision fatigue – for example, when the number of choices, N t , is very large, or when agents are otherwise unable to discern differences in potential payoffs among the choices available to them (Baumeister & Tierney 2011; Sela & Berger 2012). As the number of options grows, a natural way to try to minimize the cognitive cost of choosing among them would be to simply copy the choices of more-experienced choosers.

In terms of J t and b t , we now have a four-quadrant map on which the extreme northwest is (J t , b t ) = (0,∞), the extreme southwest is (J t , b t ) = (0, 0), the extreme northeast is (J t , b t ) = (∞, ∞), and the extreme southeast is (J t , b t ) = (∞, 0). In addition to characterizing the quadrants in terms of J t and b t , we can characterize them in terms of empirical signatures amenable to big-data analysis.1 Our estimations are displayed in Figure 2. The default assumption for many social scientists is the normal distribution – shown in the northwest quadrant in Figure 2a – but there are others, including the negative-binomial distribution, which typifies the southwest quadrant, as well as highly right-skewed, “long-tailed” distribution, which is consistent with phenomena on the eastern half of the map (Fig. 2a).2 Figure 2b shows the same distributions plotted as cumulative functions, which accommodate different forms that data might take (cumulative distributions are especially useful for smaller data-sets so that histogram binning is not an issue).

Figure 2.

Figure 2.

(a) Generalized distributions characterizing the different map quadrants: normal (Gaussian) in the northwest, negative binomial in the southwest, log-normal in the northeast, and power law in the southeast. Each plot shows popularity of a choice on the x-axis versus cumulative probability of having at least that popularity on the y-axis. The left, boxed insets show the non-cumulative fraction of choices on the y-axis that have the popularity indicated on the x-axis; the right, unboxed insets show the same cumulative distributions but with double-logarithmic axes. (b) Representative timelines for the popularity of different options, for each quadrant. Note that the different lines plotted for the northwest quadrant represent different payoffs, such that curves with a lower y-intercept at asymptote represent lower payoff/cost decisions than those with higher intercepts. For the northeast quadrant, the curves (after Kandler & Laland 2009) represent innovations adopted at different rates and subsequently declining in popularity to levels commensurate with their real-world utility.

Low resolution version High resolution version

In general, the farther south on the map we go, the noisier and less predictable the time series are for the different options. In the northwest, the time series are essentially flat, except when a new discovery is made and adopted according to a rapidly rising r-curve (Fig. 2a, northwest). In the (b t , J t ) discrete-choice setting, this would correspond to adding a new option, call it N t +1, to the original N t options, where the payoff of the new option is larger than that of any of the original options. Given that b t is large in the northwest, we would expect rapid movement toward the new and superior option. Indeed, as b t becomes very large (approaching infinity), all choice jumps as fast as possible to the new option. In the northeast, these behaviors are adopted through social diffusion, which takes the shape of an S-curve, but over the long term, the result is similarly flat timelines (Fig. 2a, northeast). In the northeast, the system can get stuck on inferior alternatives if the social influence to conform to a previously popular choice is strong enough relative to the gain to switching even when the intensity of choice is large (Brock & Durlauf 2001b). In contrast to the north, timelines in the south show turnover in the most popular behavior, either dominated by random noise (Fig. 2a, southwest) or stochastic processes (Fig. 2a, southeast). Turnover in the composition of long-tailed distributions is a fairly new discussion (e.g., Batty 2006; Evans & Giometto 2011), as much of the work in the past century has considered the static form of these distributions.

The map requires a few simplifying assumptions to prevent it from morphing into something so large that it loses its usefulness for generating potentially fruitful research hypotheses. First, it treats the various competencies of agents (intelligence, however measured; education, motor, and cognitive skills; and so on) as real but too fine-grained to be visible at the scale of data aggregated across a population and/or time. Second, agents are not assumed to know what is best for them in terms of long-term satisfaction, fitness, or survival (even rational agents, who are very good at sampling the environment, are not omniscient). Third, we blur the distinction between learning and decision making. Technically, they are separate actions, but this distinction draws too fine a line around our interest in what ultimately influences an agent's decision and how clearly the agent can distinguish among potential payoffs. Fourth, although the map represents a continuous space of b t and J t , we divide it into quadrants for ease of discussion and application to example datasets. Importantly, our characterizations are based on extreme positions of agents within each quadrant. As agents move away from extremes, the characterizations are relaxed.

2.1. Northwest: Independent decision making with transparent payoffs

The northwest quadrant contains agents who make decisions independently and who know the impact their decisions will have on them. The extreme northwest corner is where rational-actor approaches and economic assumptions (Becker 1976; 1991) – for example, that individuals will always choose the option that provides the best benefit/cost ratio – most obviously and directly apply. Although we cite Becker (1976), especially his Treatise on The Family (Becker 1991), as examples of research work on the northwest, we also note Becker's (1962) article in which he shows that many predictions of economic rational-actor theory that would appear in the northwest quadrant (e.g., downward-sloping demand curves) still hold when agents are irrational and simply choose their purchases at random, subject to budget constraints – a behavior found in the southwest quadrant. This is the continuous-choice analog of b t  = 0 in a discrete-choice model.

We put Kahneman-type bounded-rationality theories (e.g., Kahneman 2003) in the northwest because they emphasize actual cognitive costs of information processing and other forces that are rational responses to economizing on information-processing costs and other types of costs in dealing with decision making in a complex world. One of many examples of empirical patterns in the northwest is the “ideal-free distribution,” which predicts the pattern of how exclusive resources are allocated over time through individual agents seeking the best resource patches (e.g., Winterhalder et al. 2010). Reward-driven trial and error and bounded rationality contribute to powerful hill-climbing algorithms that form the mechanism delivering the fitness-maximizing behaviors predicted by models of microeconomics and human behavioral ecology (e.g., Dennett 1995; Mesoudi 2008; Nettle 2009; Winterhalder & Smith 2000).

It is precisely these algorithms that also begin to move individuals out of the extreme northwest corner and into other areas of the map. This is why we state repeatedly that although we categorize each quadrant with a certain kind of behavior, they represent extremes. An example of a type of dynamic-choice mechanism that fits in the northwest quadrant, but toward the center of the map, is replicator dynamics,



where U k is the payoff to choice k (called “fitness” of choice k in the evolutionary-dynamics literature), P k is the fraction of agents making choice k, and b measures the speed of the system in reaching the highest fitness peak, that is, the best choice (Krakauer 2011; see also Mesoudi 2011). Here, b t plays a role similar to what it does in the discrete-choice model: It measures the “intensity” of adjustment of the replicator dynamics toward the highest fitness choice. It is easy to introduce social effects into the replicator dynamics by adding the term JP k to each U k .

2.1.1. Patterns in the northwest

In the northwest quadrant, the popularity of variables tends to be normally (Gaussian) distributed as a result of cost/benefit constraints underlying them.3 In terms of resource access, the northwest is exemplified by the “ideal-free distribution,” which predicts the static, short-tailed distribution of resource access per agent through time, as individual agents seek the best resource patches (e.g., Winterhalder et al. 2010). In terms of behavior, the northwest implies that the maximal behavior should become the most popular option and remain so until circumstances change or a better solution becomes available. As the new behavior is selected, choices in the northwest will thus have either a stable popularity over time (stabilizing selection) or a rapidly rising r-curve (Fig. 2b, northwest). The sizes of human tools and equipment – handaxes, pots of a certain function, televisions – are normally distributed and located in the northwest quadrant because humans select tools to fit the constraints of the purpose (Basalla 1989). The same is true of the market price of a product or service (Nagle & Holden 2002), daily caloric intake (Nestle & Nesheim 2012), culturally specific offers in the Ultimatum Game (Henrich et al. 2005), numerical calculations (Hyde & Linn 2009; Tsetsos et al. 2012), and ratings of attractiveness by body-mass index (George et al. 2008). If these constraints change over time, the mean of the normal distribution shifts accordingly.

2.2. Northeast: Socially based decision making with transparent payoffs

As opposed to the northwest, where individuals recognize new beneficial behaviors and make decisions on their own, behaviors spread socially in the northeast quadrant. Once they learn about a new behavior, through any number of social processes (Laland 2004; Mesoudi 2011), agents along the northern edge clearly understand the rationale for adopting it in terms of payoff. As the transparency of payoffs begins to blur, however, there is less and less conscious weighing of options and more use of heuristics – efficient cognitive processes, whether conscious or unconscious, that focus only on a portion of the available information. One heuristic is to simply copy what others are doing, whether it is copying the majority (Laland 2004) or copying the behaviors of individuals with the most skill or prestige (Atkisson et al. 2012; Henrich & Gil-White 2001).

When decisions are based on either success or perceived fitness, eventual outcomes will parallel those of the northwest; human behavioral ecologists call this the “phenotypic gambit” (e.g., Low 2001; Nettle 2010). The northeast quadrant can therefore apply on a longer time scale, in which an adaptive equilibrium is reached by social-learning processes. Different culture-specific mean offers in the Ultimatum Game, for example, reflect the costs and benefits of group adaptation in a wide range of different environments (Henrich et al. 2006). As long as there is some individual learning and decision making going on within a population – that is, anywhere but along the extreme eastern edge of the map – the eventual outcome can be the same as if all learning and decision making were independent. Along the extreme eastern edge, where there is no independent learning at all to inform the socially learned (imitated) practices in circulation, adaptive potential to an exterior environment is lost. For example, fishermen who always copy other, perhaps more successful fishermen can get stuck in a poorer part of a fishery and fail to locate better areas (Allen & McGlade 1986). Efficient communal fishing requires some individual boats to randomly probe other areas of a fishery than the ones that look apparently the best based on past catch experience (see Mesoudi 2008).

2.2.1. Patterns in the northeast

Along the northern edge of the northeast quadrant, population size affects the efficiency with which agents learn and retain new and better behavioral strategies (Henrich 2010; Shennan 2000). This northeast pattern results from plotting the sizes of sample populations, N pop,I, on the x-axis and the number of tools or inventions in those populations on the y-axis. A linear correlation between these variables is predicted for small-scale, adaptive societies (Henrich 2010), which was demonstrated empirically by the number of tools recorded on different Oceanic islands at early European contact (Kline & Boyd 2010). This pattern distinguishes the northeast, as in the other three quadrants population size should not affect the likelihood of adaptive innovations (e.g., Bentley & O'Brien 2011; Bentley et al. 2007; Henrich 2010).

One pattern that is consistent with behavior along the far eastern edge of the map is the breakdown of the Law of Large Numbers and the Central Limit Theorem. The idea is this: As the product of the intensity of choice and the strength of social interactions, b t J t , grows larger than some threshold, one can show (Amaro de Matos & Perez 1991; Brock & Durlauf 2001b; Repetto 2006) that the Central Limit Theorem underlying the Gaussian distribution breaks down, and more-complicated distributions – mixtures of Gaussian distributions – appear. This behavior is consistent with the east side of the map because it can't happen unless there is positive social influence. However, it can happen when social influence is weakly positive but intensity of choice is high enough so that the product of social influence and intensity of choice exceeds the critical threshold that causes the breakdown of the Central Limit Theorem. Intuitively, what is happening here is a pile-up of correlated behaviors caused by the interaction of social influences coupled with strong enough intensity of choice, which can become large enough to prevent the familiar “washing out” of weakly correlated or zero-correlated effects.

A simple model for this resembles the Gaussian model except that agents do not judge directly which behavior is best but rather which behavior is most popular. If agents copy with a probability proportional to the existing popularity, but with some error, the result should be a log-normal distribution of popularity levels (Fig. 2a, northeast). This is a common pattern, and established models4 of proportionate advantage (or “preferential attachment” for networks) assume that the popularity of a choice in the current time slice is proportional to its popularity at the previous time slice multiplied by some growth rate normally distributed over time (e.g., Adamic & Huberman 2000; Huberman & Adamic 1999; Stringer et al. 2010; Wu & Huberman 2007). The result is a log-normal distribution of the accumulated popularity that spreads outward through time on a logarithmic scale, such that turnover is fairly minimal – the most popular choices tend to remain popular (Fig. 2, northeast).

2.3. Southeast: Social decision making without transparent payoffs

The southeast quadrant combines the lack of transparency of payoffs found in the south with the social learning of the east. This is the part of the map where, for the discrete-choice area, J t is large and b t is small. It stimulates the researcher to try to uncover and measure processes that cause the choice system to be located in this quadrant, that is, where social forces are strong and the intensity of choice across available options is small. The low intensity of choice may be the result of a large standard deviation of the random elements in the choice process, and that, in turn, may be a result of a lack of information about the choices relative to the differences in underlying values of the choices. The farther south we go, the less transparent payoffs become. Just to the south of the “equator,” agents might lack knowledge of the benefits of the behavior itself, or even of the qualifications of the people they might learn from, so they imitate based solely on popularity (frequency-dependent decisions) (Eriksson et al. 2007). In the extreme southeast, not only are the options themselves equivalent (as in the southwest), but so too are the people who potentially serve as models. It is as if each person points to someone else and says, “I'll have what she's having” (Bentley et al. 2011).

The null model for the southeast is imitating others as if it were done randomly, which is also known as the neutral model because there is an ignorance – a neutrality – in saying, “I'll have what she's having.” As we discuss below, the neutral model usually requires some minority of independent learning to fit the data, so rarely do real-world situations plot along the extreme eastern edge of this quadrant, which is reserved for complete herding, where everyone imitates someone else (e.g., Helbing et al. 2000).

Another type of behavior that one might argue belongs in the southeast is confirmation bias plus weak feedback loops (Strauss 2012). Strong feedback loops induce rapid learning toward the best choice, but weak feedback loops do the opposite. Confirmation bias is a form of mistaken choice and/or mistaken belief that requires repeated challenge and strong immediate feedbacks to change, even though it may be wrong, and perhaps very wrong. Although it is true that confirmation bias and weak feedback loops have nothing to do with social pressures per se, Strauss's (2012) “filter bubble” – one of six reasons he sees for increasing polarization among U.S. voters – is a channel through which the Internet can reinforce one's own confirmation bias from “linking” that individual to other Internet users with similar preferences. This force could act “as if” it were an increase in peer-group social-influence strength, J t .

2.3.1. Patterns in the southeast

In the extreme southeast, socially based decisions are made, but payoffs among different options completely lack transparency. In this extreme, a simple null model is one in which agents copy each other in an unbiased manner – not intentionally copying skill or even popularity. For maximum parsimony, this can be modeled as a process of random copying. This is not to say that agents behave randomly; rather, it says that in the pattern at the population scale, their biases and individual rationales balance out, just as the errors balance out in the other quadrants. It is “as if” agents are ignorant of the popularity of a behavior.

One version of the unbiased-copying model (e.g., Mesoudi & Lycett 2009; Simon 1955; Yule 1924) assumes that N pop agents make decisions in each time step, most of whom do so by copying another agent at random – not another option at random, a behavior that belongs in the southwest, but copying another agent's decision. This model also uses the individual learning variable, μ. Varying this parameter shifts the longitude on the map (μ can be seen as a distance from the eastern edge at μ = 0, with μ = 100% at the extreme western edge). In the core of the southeast, μ is usually rather small, say, 5% of agents choosing a unique, new variant through individual learning. This model can be translated, in a mathematically equivalent way, from populations to individuals by effectively allowing previous social-learning encounters to populate the mind, so to speak. In this Bayesian learning model, social-learning experiences are referenced in proportion to their past frequency (such as number of times a word has been heard), with occasional unique invention (Reali & Griffiths 2010).

Unbiased-copying models predict that if we track individual variants through time, their frequencies will change in a manner that is stochastic rather than smooth and continual (northwest and northeast) or completely random (southwest). The variance in relative popularity of choices over time should depend only on their prior popularity and on the population size, N pop. If we use evolutionary drift as a guide, the only source of change in variant frequencies, ν, over time is random sampling, such that the variance in frequencies over time is proportional to ν(1−ν)/N pop (Gillespie 2004). The popularity is thus stochastic, with the only factors affecting popularity in the next time step being the current popularity and population size. Unbiased-copying models yield highly right-skewed, or long-tailed, distributions of popularity, as shown in Figure 2a (southeast).

This means that turnover (Fig. 2b, southeast) is a diagnostic difference from the northeast quadrant, in that in the southeast the accumulation of innovations – the cultural “ratchet” (Tomasello et al. 1993) – should not correlate strongly with population size in the southeast (Bentley et al. 2007; Evans & Giometto 2011). As Bettinger et al. (1996) point out, although there are μ N pop inventions per generation in large populations, “the rate at which they will become fixed is an inverse function of N pop. [T]he two exactly cancel, so that . . . the turnover rate is just the reciprocal of the innovation rate” (p. 147). Although the problem becomes more complicated if the variants are ranked by frequency, such as a “top 10 most-popular list,” the result is essentially the same. As long as a list is small compared with the total number of options (top 10 out of thousands, for example), the list's turnover is continual and roughly proportional to the square root of μ, that is, it is not strongly affected by population size (Eriksson et al. 2010; Evans & Giometto 2011).

2.4. Southwest: Individual decision making without transparent payoffs

The southwest quadrant, where agents interact minimally and choose from among many similar options, is characterized by situations confronted individually but without transparent payoffs. In other words, it is as if agents were guessing on their own. Although this may be a rare situation for individuals in subsistence societies, it may well apply pervasively to modern Western society, where people are faced with literally thousands of extremely similar consumer products and information sources (Baumeister & Tierney 2011; Bentley et al. 2011; Evans & Foster 2011; Sela & Berger 2012). One candidate phenomenon, however, is entertainment, as preferences can vary such that choices at the population level appear to be random (we present an example in the next section). If hurried decisions are biased toward the most recent information (Tsetsos et al. 2012), for example, the outcome may appear “as if random” with respect to payoffs. In consumer economics, an effective, practical assumption can be that “purchase incidence tends to be effectively independent of the incidence of previous purchases . . . and so irregular that it can be regarded as if random” (Goodhardt et al. 1984, p. 626, emphasis in original).

2.4.1. Patterns in the southwest

Whereas the null model for the southeast is imitating others as if it were done randomly, the null model for the southwest is choosing options. In the southwest quadrant, we expect popularity to be governed by pure chance (Ehrenberg 1959; Farmer et al. 2005; Goodhardt et al. 1984; Newman 2005). In short, the probability of any particular choice becoming popular is essentially a lottery, and as this lottery is continually repeated, the turnover in popularity can be considerable (Fig. 2b, southwest). Ehrenberg (1959) provided an idealized model for the guesswork of the southwest quadrant, where the distribution of popularity follows the negative binomial function,5 in which the probability falls off exponentially (Fig. 2a, southwest). Choices made by guesswork are uncorrelated, yielding a diagnostic pattern, as the exponential tail of the distribution is a sign that events are independent of one another (e.g., Frank 2009).

3. Is human decision making drifting to the southeast?

We expect that, in the big-data era, certain aspects of decision making have moved to the southeast, especially given the exponential increase in information and interconnected population sizes (Beinhocker 2006; Bettencourt et al. 2007; Hausmann et al. 2011). In the subsections below, we consider three examples: language and ideas, relationships, and wealth and prestige.

3.1. Language and ideas

Considering the deep evolutionary roots of human sociality, it is not surprising that social learning (northeast) is how small-scale societies have adapted and accumulated technical knowledge for most of human existence (Apicella et al. 2012; Henrich et al. 2001; 2005; Hill et al. 2011). Clearly, the ratchet of cumulative cultural evolution (Tomasello et al. 1993) requires a balance of individual and social learners and decision makers (Mesoudi 2008; Rendell et al. 2011). Often, a small amount of informed individual learning goes a long way, amplified by a majority context of social learning, even among animals (e.g., Couzin et al. 2005). This mix is essentially a description of the northeast quadrant, with b t set to high transparency and J t set at a level of mainly social learning.

As technology has evolved and become something that is cumulative, it has become a phenomenon of the northeast quadrant. In the northeast, if social learners copy the best strategies and thereby make the best decisions (Bentley & O'Brien 2011; Henrich 2004; Mesoudi 2008), larger populations will find better technologies faster because there are more individual learners producing information, assuming that individual learners are a fixed proportion of the population.

As another practical measure, increased population size, N, should correlate positively with the rate of new innovations, which has been shown to be linear in small-scale societies (Kline & Boyd 2010). In modern cities, however, the correlation has become superlinear, where the number of inventions grows proportional to N 1.24 (Bettencourt et al. 2007b). Bettencourt et al. suggest two alternative explanations for this superlinearity: either inventors are individually more productive in a larger city or there are a disproportionate number of inventors in larger metropolitan areas. Both explanations seem consistent with location in the northeast. If it is the former, then most likely inventors are able to take advantage of more information and not be overwhelmed by it. If it is the latter, then it is still a northeastern pattern, only with a higher proportion of individual learners in the population.

Changing patterns may signal a shift toward the southeast with increased population densities and urbanism. In 1900, approximately 13% of the world's population lived in urban areas. That figure reached 29% in 1950 and 49% in 2005, and it is expected to rise to 60% by 2030 (United Nations 2006). This increase in density could lead human populations away from optimality, in contrast to naturally selected relationships, such as the way the heart rate of organisms shows an optimized, inverse-scaling relationship with body size. As Bettencourt et al. (2007a) observed, there is no such optimization for a modern city, where walking speed scales with population size: The pace of urban life increases with city size in contrast to the pace of biological life, which decreases with organism size.

Of course, as stressed by Romer (2012) and many others, institutions must support innovation, otherwise a large population density does not matter. In other words, when population size is large, individuals on their own cannot search the full space of ideas and must rely on institutions (or, more recently, on search engines) to ensure transparency. As transparency decreases and social influence increases through a combination of inexpensive social-learning opportunities and multiple similar options, there are now ubiquitous highly right-skewed popularity distributions with continual turnover of contemporary commercial markets (Beinhocker 2006).

Now, in the big-data era, the process of science and invention – the creation of ideas – has become well-documented. If science proceeds ideally (Kitcher 1993), it ought to plot in the northeast, where social learning is well-informed and seminal works by academic leaders are selectively adopted and developed by followers (Rogers 1962). Indeed, bibliometric studies show the most successful (highly cited) scientific mentors are those who train fewer protégés (Malmgren et al. 2010), which confirms high J t (more social interaction) together with high b t (more transparency). Also consistent with characteristics of the northeast, citations to scientific articles, and also patents, exhibit a highly right-skewed distribution with only slow turnover in the ranked popularity of citation rates (Bentley & Maschner 2000; de Sola Price 1965; Stringer et al. 2010). This regularity also applies to the keywords used, as Figure 3 shows for a tradition of academic papers. Note that the distribution of word frequencies is log-normal but the turnover within the most popular keywords has been minimal.

Figure 3.

Figure 3.

Distribution and turnover of keywords among all the articles citing a certain seminal article (Barabási & Albert 1999): (a) Timelines of relative frequencies (number of keyword appearances divided by total number of words for the year), using the top five keywords of 2005 (logarithmic y-axes); (b) cumulative frequency distributions of all keywords. Open circles show distribution for 2001 and filled circles for 2005.

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Further support of scientific publishing's being a phenomenon of the northeast comes from Brock and Durlauf's (1999) use of the binary discrete-choice framework to examine potential social effects on the dynamics of “Kuhnian paradigm shifts” when evidence is accumulating against a current paradigm. Instead of the rapid acceptance of the new paradigm depicted in the northwest time-series plot of Figure 2b, Brock and Durlauf show that social pressures can easily lead to “sticky” dynamics of popularity around the old paradigm but then to a burst of speed toward the new paradigm once a threshold is passed. Consider a population, N pop,t , of scientists, each of whom takes a position on an academic debate. We can represent this by a continuum that is divided into equal-sized “bins.” If J t  = 0, meaning that there are no social influences and each academician makes up his or her own mind independently, we might expect a normal distribution centered on the median (mean) academician. As transparency, b t , increases (moves northward), the spread of the distribution narrows. As social influence, J t , increases (moves eastward), the distribution can become bimodal or even multimodal – a mix of normal distributions centered at different means. The map, therefore, leads us to investigate the strength of social influences whenever we see evidence of polarization, that is, evidence of multimodal distributions.

Not surprisingly, compared to more-transparent scientific usage of words necessary to communicate new ideas, the public usage of language is more prone to boom-and-bust patterns of undirected copying in the southeast quadrant. Using raw data in Google's freely available files, we obtained the yearly popularity data for a set of climate-science keywords such as biodiversity, global, Holocene, and paleoclimate (established against a baseline of exponential growth in the number of words published over the last 300 years, a rate of about 3% per year). As we show (Bentley et al. 2012), most of the keywords fit the social-diffusion model almost perfectly. Indeed, almost all of them are becoming passé in public usage, with turnover suggestive of the southeast. Conversely, when we examined the narrow realm of climate-science literature, we found it plots farther north, as its keywords are not nearly subject to the same degree of boom and bust as in the popular media, with a consistency similar to that shown in Figure 3.

With the exceptional changes of online communication and texting, could language itself be drifting into the southeast? Perhaps it has been there for a long time; Reali and Griffiths (2010) suggest that the best null hypothesis for language change is a process analogous to genetic drift – “a consequence of being passed from one learner to another in the absence of selection or directed mutation” (p. 429). We see at least some southeast patterning in published language. By at least 1700, the frequency of words published in English had come to follow a power law, now famously known as Zipf's Law (Clauset et al. 2009; Zipf 1949). There is regular turnover among common English words (Lieberman et al. 2007), but turnover among the top 1,000 most-published words seems to have leveled off or even slowed between the years 1700 and 2000, despite the exponential rise in the number of published books (Bentley et al. 2012). This deceleration of turnover with growing effective population is intriguing, as it is not expected for the northeast. A southeast trend is also indicated as online language is copied with much less transparency regarding the quality of the source (Bates et al. 2006; Biermann et al. 1999). This would, then, be a long way from the origins of language, which presumably began in the northwest, as straightforward functions such as primate alarm calls have low J t (individual observation of threat), high b t (obvious threat such as a predator), and exhibit Gaussian frequency distributions (Burling 1993; Ouattara et al. 2009).

3.2. Relationships

A specific category of language, names within traditional kin systems, acts as a proxy for relationships by informing people of how to behave toward one another. For traditional naming systems, the distribution of name popularity is constrained by the number of kin in different categories, but, of course, first names are socially learned from other kin. Good examples that use big data are the naming networks of Auckland, New Zealand, which Mateos et al. (2011) have visualized online (http://www.onomap.org/naming-networks/fig2.aspx). Mateos et al. also looked at 17 countries, finding that first-name popularity distributions retain distinct geographic, social, and ethnocultural patterning within clustered naming networks. Many traditional naming systems, therefore, belong in the northeast quadrant, after evolving over generations of cultural transmission into adaptive means of organizing social relations (Jones 2010).

If traditional naming tends to map in the northeast quadrant, then the exceptional freedom of naming in modern “WEIRD” (Western, Educated, Industrialized, Rich, and Democratic) nations (Henrich et al. 2010) fits the fashionable nature of the southeast model (Berger & Le Mens 2009). Studying recent trends in Norwegian naming practices, Kessler et al. (2012, p. 1) suggest that “the rise and fall of a name reflect an ‘infection’ process with delay and memory.” Figure 4 shows how the popularity of baby names yields a strikingly consistent, nearly power-law distribution over several orders of magnitude. Also expected for the southeast, the twentieth-century turnover in the top 100 U.S. names was consistent, with about four new boys' names and six new girls' names entering the respective top-100 charts per year (Bentley et al. 2007).

Figure 4.

Figure 4.

Distribution of the popularity of boys' names in the United States: left, for the year 2009; right, top 1,000 boys' names through the twentieth century, as visualized by babynamewizard.com.

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Although it should not be surprising if names traditionally map in the northeast, and have shifted southeast in Western popular culture, what about relationships themselves? For prehistoric hominins, one of the most basic resource-allocation decisions concerned the number of relationships an individual maintained, which was constrained by cognitive capacity and time allocation (Dunbar 1993). We would expect such crucial resource-allocation decisions to plot in the northwest, with low J t and high b t . We therefore expect a Gaussian distribution of number of relationships, although the mean will vary depending on how costly the relationships are. Indeed, the “Dunbar number” (Dunbar 1992) limit of approximately 100–230 stable social relationships per person6 refers to a mean of this normal distribution, which varies according to relationship type (e.g., friendships, gift partners, acquaintances).

Figure 5 shows that the mean number of gift partners among hunter-gatherers is Gaussian, with a mean of a few or several individuals (Apicella et al. 2012). The data are from surveys (subjects were asked to whom they would give a gift of honey) of more than 200 Hadza (Tanzania) women and men from 17 distinct camps that have fluid membership (Apicella et al. 2012). The Gaussian distribution in Hadza “gift network” size surely reflects the constraint of living in camps of only about 30 individuals. In the post-industrial West, with the differences of time expenditure, we might expect a larger mean number of relationships, but still with the same evidence for low J t and high b t of the northwest. Figure 5 shows how the distribution is similar to that of close friends among students at a U.S. junior high school (Amaral et al. 2000). We expect the distribution mean to increase even further as relationships go online. The mean number of Facebook friends per user (Lewis et al. 2008, 2011) is indeed larger, and yet still the distribution follows almost the same Gaussian form when scaled down for comparison (Fig. 5). This Gaussian distribution of friends per Facebook users is consistent, with their interaction network being bounded at around 100 (Viswanath et al. 2009). Given that the friendship distributions are consistent for the different categories of relationships, we assume their Gaussian distributional form has been consistent through time, as expected for the northwest (Fig. 2b).

Figure 5.

Figure 5.

Gaussian distributions of social ties per person as examples of behavior in the northwest. Open circles show hunter–gatherer gift-exchange partners, gray circles show school friends, and black circles show Facebook friends. The main figure shows cumulative distributions of social ties per person; the unboxed inset shows the same distribution on double logarithmic axes (compare to Figure 2, northwest inset); and the boxed inset shows the probability distribution. Data for the hunter–gatherer gift-exchange partners are from Apicella et al. (2012); for school friends from Amaral et al. (2000); and for Facebook friends from Lewis et al. (2008; see also Lewis et al. 2011).

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Unlike Facebook, other online social networks (e.g., Skitter, Flickr) show more fat-tailed distributions in numbers of relationships; these right-skewed distributions resemble information-sharing sites such as Digg, Slashdot, and Epinions (konect.uni-koblenz.de/plots/degree_distribution). Krugman (2012) points out how the number of followers among the top-100 Twitter personalities is long-tailed, and indeed the continually updated top 1,000 (on twitaholic.com) is log-normally distributed, as confirmed by a massive study of over 54 million Twitter users (Cha et al. 2012). Checking in June 2012 and then again in the following November, we found that the log-normal distribution of followers remained nearly identical (in normalized form), despite Twitter growing by roughly 150,000 followers a day.

These heavily right-skewed distributions place Twitter in the east, with high J t , but is it northeast or southeast? Overall, the turnover and right-skewed popularity distributions of Twitter would appear to map it in the southeast. By tracking the most influential Twitter users for several months, Cha and colleagues (2010) found that the mean influence (measured through re-tweets) among the top 10 exhibited much larger variability in popularity than the top 200. This can be roughly confirmed on twitaholic.com, where the mean time on the top-1,000 Twitter list on June 10, 2012, was 42 weeks, with no significant correlation between weeks on the chart and number of followers. Twenty-four weeks later, the mean time on the top-1,000 list had increased by six weeks. At both times, the lifespan in the top 10 was only several weeks longer than that in the top 1,000, suggesting surprisingly little celebrity (prestige) bias as opposed to just unbiased copying that occurs in rough proportion to current popularity.

These changes appear to reflect the media more than the individuals within them. Twitter, for example, is more a broadcasting medium than a friendship network (Cha et al. 2012). Unlike with traditional prestige, popularity alone on Twitter reveals little about the influence of a user. Cha and colleagues found that Twitter allows information to flow in any direction (southeast) rather than the majority learning from a selected group of well-connected “influentials” (northeast). Because information flows in all directions, we place Twitter in the southeast, as it “does not follow the traditional top-to-bottom broadcast pattern where news content usually spreads from mass media down to grassroots users” (Cha et al. 2012, p. 996). This suggests information sharing may be shifting southeast even if actual relationships are not. Indeed, there is evidence for a critical level of popularity, where the downloading of “apps” from Facebook pages shifts eastward on our map, that is, from individual decision making to socially based decision making (Onnela & Reed-Tsochas 2010).

3.3. Wealth and prestige

Although Twitter exhibits a new, grassroots role in terms of influencing and spreading information, there is no doubt that just about all the members of the top-1,000 on Twitter are prestigious, at least by the definition of Henrich and Gil-White (2001), in that millions of people have freely chosen to “follow” them. If prestige and popularity are to become synonymous on Twitter, then prestige on this medium will plot in the southeast, as people naturally copy those whom others find prestigious rather than make that determination individually (Henrich & Gil-White 2001). To an unprecedented level, Twitter clearly exploits our preference for “popular” people, which “evolved to improve the quality of information acquired via cultural transmission” (Henrich & Gil-White 2001, p. 165). Twitter celebrities are thus more able to act as “evangelists” who can “spread news in terms of . . . bridging grassroots who otherwise are not connected” (Cha et al. 2012, p. 997).

Most of the top-1,000 Twitter personalities are also wealthy, of course, and prestige, wealth, and popularity are well entwined in this medium. Could this signal a future shift toward the southeast? We would normally map gift-giving in the northeast, as a transparent means of maintaining relationships and reducing risk through social capital (Aldrich 2012). Even in the West, patterns of charity still exhibit northeast patterns. Charitable giving in the United States from 1967 to the present, for example, has exhibited a log-normal distribution per category (religion, education, health, arts/culture, and so on) that did not change appreciably in form over a 40-year period (Fig. 6). Nor did the rank order of charitable giving by category change. It is immediately striking what a long-term, sustained tradition charitable giving is among generations of Americans.

Figure 6.

Figure 6.

Charitable giving in the United States: left, past 30 years, at the national level; right, relative growth of several categories of charitable giving in the United States, over a 40-year period (popularity is expressed as the fraction of the total giving for that year, on a logarithmic scale). Data from Giving USA Foundation (2007).

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As charitable-giving habits are inherited through the generations, the wealth of the recipients, such as universities and churches, depends on this northeast pattern. It should not be surprising, then, if wealth itself shows a northeast phenomenon, even in small-scale societies. Pareto distributions of wealth typify modern market economies, but even in traditional pastoralist communities, for example, wealth may follow the highly right-skewed form of the northeast. Figure 7 shows how distributions can vary. We would map Karomojong pastoralists (Dyson-Hudson 1966), whose cattle-ownership distribution is the most Gaussian (Fig. 7), farther west than the Ariaal of northern Kenya (Fratkin 1989) and the Somali (Lewis 1961), whose wealth is highly right-skewed (Fig. 7). This fits with ethnographic information, as Karomojong pastoralists culturally impose an equality among members of each age set (Dyson-Hudson 1966), whereas Ariaal herd owners “increase their labor through polygyny, increased household size, and the hiring of poor relatives” (Fratkin 1989, p. 46). Transparency of wealth increases with the rising cost of competition and the agglomeration of power, as powerful tribes expand at the expense of smaller groups (Salzman 1999).

Figure 7.

Figure 7.

Wealth among pastorialists, with a cumulative probability distribution plot comparing published ethnographic data from the Somali (Lewis 1961) with gray circles, the Ariaal (Fratkin 1989) with white circles, and Karomojong (Dyson-Hudson 1966) with filled black circles.

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Given these northeast patterns for the fairly static distributions of wealth and prestige in traditional societies, what could we expect from emerging southeast patterns in an online society? On the one hand, we have a pull toward the southeast in highly social realms of information overload such as Twitter. On the other hand, powerful search engines that help people find the most relevant information from others, the ubiquity of social rating, and the increased relevance of “grassroots” influences (Cha et al. 2012) may keep things in the northeast, as social learning is better informed. If intelligent search technology gains the upper hand on information overload, then b t increases and the crucial variable is J t . If J t is low, then prestige or exclusive access to resources is less transferrable from one person to another, and inequality is lessened.

4. Discussion and conclusions

To address collective behavior in the big-data era, the map we present here, with its dimensions of social influence and transparency of payoff, has allowed us to situate big data in a much broader perspective, alongside data from past and present societies. Although some of the conclusions we make from these data are clear from qualitative observation, the new world of big-data research makes it impossible to personally witness all of the decisions being made. We therefore have sought a set of empirical signatures that can be detected in massive sets by simple statistical means, which we might someday even see automated. The mapping then helps identify the more granular tools of various social-science research traditions that will be most useful for a particular case study: the northwest (economic), the southeast (cultural-historical), the northeast (both), and the southwest (neither).

The map quadrants can be characterized by different patterns – change through time and distributions of popularity – that can be gleaned from the kinds of data that the behavioral sciences hope to understand. The map is more than an academic exercise. It becomes highly practical with respect to public policy, for example, by providing direction over whether it is more effective to disseminate information in the northwest, engage targeted “word of mouth” campaigns in the northeast, or place many bets more randomly in the southeast (Bentley et al. 2011; Sela & Berger 2012; Watts & Hasker 2006). The map provides a means for evaluating population-level trends in the kinds of decision-making categories noted earlier – voting, opinions on climate change, mating, health care, consumer trends – which we see beginning to move to the southeast.

This can be important in a world where policy may not match the way human decisions are made. Much of traditional social science and policy has used the northwest as its base assumption that public behavior is dictated by cost/benefit ratios and incentives, even if slightly flawed or biased in perception (e.g., Kahneman 2003). This comprehensive practicality is why the map is not just another theoretical classification scheme. It allows a data-driven study question, reframed as a hypothesis, to be tested with appropriate datasets by examining whether b t , the degree of transparency of payoffs, decreases through time and whether J t , the intensity of social influence, increases through time for contexts in which the (b t , J t ) discrete-choice framework is appropriate. Because these dimensions are general, realms of behavior can potentially be linked through this approach. For example, the discrete-choice framework has been used to document the rise of polarized political behavior in the United States: Li and Lee (2009) found J t  > 0 for the Clinton–Dole presidential election, and McCarty et al. (2006) linked this polarization to the dramatic rise in income inequality.

Of course, b t and J t are not everything. One interesting future project would be to explore the effects of other dimensions (parameters) that we have deliberately avoided with our simplified map. Where social learning is well informed, personal biases such as trust, prestige, and status will obviously matter (e.g., Eriksson et al. 2007; 2010; Henrich & Gil-White 2001). Perhaps the most important phenomenon we might next consider is how the structure of social networks affects the dynamics of social learning (e.g., Borgatti et al. 2009; Dodds & Watts 2005). The map quadrants relate to contemporary debates such as the “spread” of obesity (Christakis & Fowler 2007) or voting and consumer preferences (Aral & Walker 2012), in which each debate revolves around whether certain behaviors are really spreading along a directed network as opposed to like-minded people simply associating (e.g., Shalizi & Thomas 2010). The map changes the discussion about interaction networks. Rather than a “wiring diagram” between human beings, what matters is understanding how the dynamics of decision making derive from overall network structure (Ormerod 2012). For example, highly clustered social networks appear to favor the spread of norms of cooperation (Ohtsuki et al. 2006) and norms of innovations by introducing them repeatedly to individuals through different neighbors of a cluster (Centola 2010; Helbing & Yu 2009; Lorenz et al. 2011).

More generally, Lieberman et al. (2005) identified those social-network arrangements favorable to selection (northeast) versus random drift, or undirected copying (southeast), in the sorting of variation. These generalized networks fit the map well. In Figure 8, we have placed in the southeast the diffuse networks that Lieberman et al. (2005) identify with drift and in the northeast the hierarchical networks they associate with selection. Figure 8 illustrates how the map organizes the behavior of a binary dynamic-choice system. The northwest quadrant illustrates that when the intensity of choice, b t , is very large, P +,t will be close to one when the net payoff to +1 is positive (the dot is solid black) and will be close to zero when the net payoff to +1 is negative (the dot is solid white). This case corresponds to a very strong force of selection in Krakauer's (2011) evolutionary dynamics, meaning that the replicator equation has a large value of b t . The mix of dots with various shades of gray in the southwest depicts the wide range of values of P +,t when b t is very small, even when the net payoff to +1 is positive. The directed networks (with either black dots or white dots for the choices) depicted in the northeast quadrant are intended to capture the idea that social influence will be very strong (and P +,t will be close to one or zero) when b t is large, even if J t is of moderate size. The various shades of gray in the directed network in the southeast quadrant are intended to capture the idea that many values of P +,t are likely to be observed because b is small.

Figure 8.

Figure 8.

A representation of how social-network structure (or lack thereof) fits onto the map (schema adapted from Lieberman et al. 2005). In each quadrant, circles represent agents, and shades represent their choices. In the east, arrows represent social influences through which agents make most of their choices, whereas in the west, agents make choices independently.

Low resolution version High resolution version

The network rendition of the map helps us match big-data patterns to practical or theoretical challenges. If one aims to shift collective behavior from the herdlike southeast to the more-informed northeast, then learning networks ought to become more directed and hierarchical. In fact, it appears that hierarchical networks are a natural component of group adaptation (Hamilton et al. 2007; Hill et al. 2008; Saavedra et al. 2009) and may provide a crucial element to the debate over the evolution of cooperation, for which punishment of non-cooperators appears to be insufficient (Dreber et al. 2008; Helbing & Yu 2009; Rand et al. 2009).

In this way, the map puts big data into the big picture by providing a means of representing, through case-specific datasets, the essence of change in human decision making through time. In a given context, we may wish to assess, from population-scale data, whether people are still responding to incentives and/or behaving in near-optimal ways with respect to their environment (e.g., Horton et al. 2011; Nettle 2009; Winterhalder & Smith 2000). If so, then cumulative innovations should generally improve technological adaptation over time or even human biological fitness (Laland et al. 2010; Milot et al. 2011; Powell et al. 2009; Tomasello et al. 1993). Conversely, if the vicissitudes of social transmission, fads, and cultural drift are driving innovation, then such improvements are not guaranteed (e.g., Cavalli-Sforza & Feldman 1981; Koerper & Stickel 1980).

A big question is whether change in hominin evolution has been roughly clockwise, from the individual learning of the northwest, to the group traditions of the northeast with the evolution of the social brain, to the south – particularly the southeast – as information and interconnected-population sizes have increased exponentially through time (Beinhocker 2006; Bettencourt, Lobo & Strumsky 2007). If we consider the smaller societies of human prehistory, crucial resource-allocation decisions would plot in the northern half of the map, and the more specific behaviors would range between the northwest and the northeast. Because Homo economicus is located at the extreme northwest, he does not appear to be the primary model for human culture, considering that the deep evolutionary roots of human sociality, social-learning experiments, and ethnographic research all suggest that social learning is how small-scale societies have adapted to environments for most of human existence (e.g., Apicella et al. 2012; Byrne & Russon 1998; Henrich et al. 2001, 2005; Tomasello et al. 2005). The ideal position in the northeast appears to be dictated by the spatial and temporal autocorrelation of the environment and the cost of individual learning (Mesoudi 2008).

The examples we discussed in section 3 place many social-network media on the east side of the map. This does not necessarily mean that people are fundamentally changing, however, although perhaps they are to a small degree (Sparrow et al. 2011). Rather, it means that online environs sort behavior differently. In our Internet world of viral re-tweets and their associated scandals, interest in a “world brain” – a science fiction of H. G. Wells's – has been reborn, as the number of people exchanging ideas in an economy determines the complexity of a nation's science and technology (Hausmann et al. 2011).

When humans are overloaded with choices, they tend to copy others and follow trends, especially apparently successful trends. If too far southeast, this corrodes the distributed mind. One realm where this may clearly be important is academic publishing. Should we worry that academic publishing may drift southeast? A drift in this direction certainly seems possible, especially with quality no longer transparent among an overwhelming number of academic articles (Belefant-Miller & King 2001; Evans & Foster 2011; Simkin & Roychowdhury 2003). To maintain transparency in the northeast, it seems sensible to maintain support for rigorous, specialist-access academic journals, against pressure to blur scientific publications with blogs and social media (Bentley & O'Brien 2012).

Could a drift southward be even a more-general trend? Successful technological innovations generate a multitude of similar options, thereby reducing the transparency of options and payoffs (O'Brien & Bentley 2011). One consequence of this proliferation of similar alternatives is that it becomes more and more difficult for learning processes to discover which options are in fact marginally better than others. This pushes decisions southward and paradoxically may mean that modern diverse consumer economies may be less-efficient crucibles for the winnowing of life-improving technologies and medicines than societies were in the past and some traditional societies are today (Alves & Rosa 2007; Marshall 2000; Voeks 1996). It might be argued that the drift in mass culture toward the southeast is not a particularly fit strategy, as the propensity for adaptation found in the north is lost.

We might assume that because we've spent most of our evolutionary history in the north, the “best” behaviors, in terms of fitness, are the ones that become the most popular. It could be argued that important health decisions ought to lie in the northwest, and in traditional societies it seems that's the case – such decisions are not strongly socially influenced (Alvergne et al. 2011; Mace & Colleran 2009). To the extent that there is social influence, it typically comes from close kin (Borgatti et al. 2009; Kikumbih et al. 2005). As modern mass communication becomes available, however, the cost of gaining health information socially declines – a shift eastward on the map – but it also makes socially transmitted health panics more common (Bentley & Ormerod 2010).

In conclusion, we note that it is easy to be intimidated by big-data studies because the term really means BIG data. In these early days of big data, however, many studies seem to show us the obvious. In the best case, big-data studies will not compete with more traditional behavioral science but instead will allow us to see better how known behavioral patterns apply in novel contexts. In fact, they may even validate the most basic Bayesian analysis of human behavior there is, which is human experience. Humans sample the actions of their peers just by living among them for a lifetime. This takes us back to the northwest: Popularity does not guarantee quality. As long as people trust their own individual experiences, even in observing the behavior of others, a collective wisdom is possible.

ACKNOWLEDGMENTS

We thank Barbara Finlay, Herbert Gintis, David Geary, and our anonymous reviewers for excellent comments and advice on earlier drafts. We also thank Daniel Nettle for his many insights and suggestions for strengthening the argument, and Jonathan Geffner and Sumitra Mukerji for their editorial and production assistance.

References

NOTES

1.We can be more precise in the context of empirical statistical work by specifying (b t , J t ) as functions of covariates and parameters of interest to estimate – for example, b(x t , θ b ), J t  = J(x t , θ J ), where x t is a vector of potentially relevant covariates, which can include past values of the same covariates as well as past average choices over potentially relevant reference groups (for potential “contagion” effects) and average choices over potentially relevant reference groups (for potential “contextual” effects) (Manski 1993). Here, θ b and θ J are vectors of parameters that can be estimated. Once estimation is done, hypotheses can be proposed and tested using statistical methods. The era of “big data” opens up new possibilities for empirical work, formulation of hypotheses, and formal statistical testing of these hypotheses versus plausible alternatives.

2.The intense interest in these distributions, such as power laws, has led to a productive debate such that multiple alternative right-skewed distributions are now critically compared, with recognition that subtle differences in distributions can be informative as to the processes that produce them (Frank 2009; Laherrère & Sornette 1998; Venditti et al. 2010).

3.Care must be taken with the assumption that patterns in the northwest will always be Gaussian. Here is an example to the contrary. Consider the discrete-choice model with two choices {–1,+1} and with b t and J t being anywhere from zero to infinity. Let h t  = u +,t u ,t , which is just the payoff difference of the two options. Then, the probabilities of choice at date t are given by



Suppose that h t exhibits a Gaussian distribution with zero mean and finite variance. As b t approaches infinity, we observe only P +,t  = 0 or 1. Here we see that a Gaussian distribution of h t is turned into a bimodal distribution with all mass at 0 or 1, even though we are in the northwest quadrant of the map. In the southwest, b t is small. At the extreme south it is zero, and P +,t  = 1/2, P ,t  = 1/2, no matter the value of h t . Now, given that h t exhibits a Gaussian distribution with mean zero and finite variance, we can see that a small value of b t will produce a unimodal, hence “Gaussian looking,” distribution of P + when the system is in the southwest quadrant. As we move north by increasing b t , we expect eventual bimodality of the distribution of choice probabilities, {P +,t }, as we sample this choice process over time with increasing b t .

4.One established model assumes the popularity, n t , of a choice at time t as proportional to its popularity at time t – 1:



where g t , normally distributed over time, expresses the fluctuating rate at which agents in the population make new decisions. The result is a log-normal distribution of the accumulated popularity that spreads outward through time on a logarithmic scale. The model holds that the probability of a behavioral option accumulating popularity n at time t is given by



where g 0 is the mean of g over time, with standard deviation σ. The position g 0 t and width σ 2 t of the log-normal peak increases with time t, such that the accumulated popularity distribution for options of the same age (e.g., citations of journal articles published in the same year) spreads outward through time on a logarithmic scale. This model can also be fit dynamically, as described by Wu and Huberman (2007): For each behavioral choice at time t, one calculates the logarithm of its popularity minus the logarithm of its initial popularity when the sampling started. Then to represent time t, the mean versus the variance of these logged values is plotted. Repeating this for all time slices in the sample, the resulting cluster of points will yield a linear correlation between the means and variances of the logged values (i.e., for this area of the northeast quadrant).

5.In the negative-binomial theorem, the probability of k choices of specific option x, given that there have been k+r total choices overall, is as follows:



6.A group size of 150 often is quoted as an average, but Dunbar never used either an average or a range in his original paper (Dunbar 1992), which had to do with neocortex size and group size in nonhuman primates. Group size in humans was addressed in later papers (Dunbar 1993; 1998). Often misunderstood is that Dunbar was referring to “meaningful” relationships, not simply the number of people one remembers: The social brain hypothesis is about the ability to manipulate information, not simply to remember it” (Dunbar 1998, p. 184).