Social Networks and Action Space in Cities

Abstract

This chapter builds on Jacobs’s insights into social networks as a cohesive force in cities. It introduces social-network concepts into market-process economics, links it to Jacobsian economics, and grounds them both on a common social theory. In doing so, it further develops the concepts of Jacobs Density and action space.

This chapter draws in part from Ikeda (2012).

We now know that social networks help bring coherence to the amazing diversity cities generate. In her biography of Jacobs’s early life in Scranton, Pennsylvania, Glenna Lang quotes Jacobs on the importance of inclusivity and informality in these networks:

The most important thing is that there are networks of people who know each other and the more inclusive they are the better…. [I]n order to have an efficient and inclusive network of people who know each other, the very basic thing about it is people knowing each other in a public and often in a very casual way.” (Lang, 2021: Loc. 2469, 2471)

Jacobs in Death and Life is the first to use the term “social capital” in essentially the sense it is used by scholars today,¹ that is, as stable social networks that increase the value of its member’s human capital (Coleman, 1990: 300). Sociologists and mathematicians have further refined the concept in ways that are congenial to both Jacobsian analysis and market-process economics, as we will see.

Now, social capital can be either inclusive or exclusive in nature. Both forms are important in a living city—inclusive networks contribute dynamism, exclusive networks stability—but Jacobs is not always clear which meaning she has in mind. The quotation above, for example, is characteristically ambiguous in this respect. She says social networks need to be “inclusive” but also that their members should “know each other.” So, are strangers welcome to these networks or not? This is something I will try to sort out in this chapter.

I have said that Jacobs in her early work relies less explicitly on the market process per se and more on these social networks to explain how cohesion and complementarity take place among a great city’s heterogeneous elements. In this chapter, I explain in some detail how entrepreneurial competition operates in both markets and social networks. This also develops the theme of Chap. 4 of how markets and cities take differences that have historically driven people apart and turn them into value-producing complementarities.

I have also noted that Jacobs seems to take for granted individual freedom of choice, mobility, and association in her analysis, and that these are implicit in her discussion of urban diversity and cohesion. How otherwise would the transformation of diversity into complementarity take place so robustly in a great city if social institutions and pressures (private or governmental) hampered the process? Without freedom of this kind we would be less able to act on gainful opportunities we discover among heterogeneous urban elements. As we have seen, we are more apt to discover these valuable connections when we can freely and safely make contact in public spaces. Jacobs makes this point using the example of city sidewalks.

Lowly, unpurposeful and random as they may appear, sidewalk contacts are the small change from which a city’s wealth of public life may grow. (Jacobs, 1961: 72)

Such informal contact might last only for a moment, as when strangers navigate around each other on a busy sidewalk. Or it may linger, as when we fawn over a stranger’s pet on the street, strike up a conversation with someone in a bar, or when we nod at a “familiar stranger” in an apartment lobby (Milgram, 1972). These contacts may lead to nothing substantial, but sometimes they do. This is especially the case at gatherings, such as a party or even a formal meeting, where we get to know new people in a context in which we may be familiar. Contacts like these might involve riskier, longer-term commitments, such as starting a friendship or getting a job offer. To engage in mobility of that kind requires the freedom to make and break social connections. It also requires trust of some kind. In this chapter, then, the roles of freedom, social and economic, and trust are made explicit.

I begin by further explicating market-process economics with particular emphasis on the nature and significance of entrepreneurship. This allows me to show how adopting certain concepts from social-network theory, some of them pioneered by Jacobs herself, increases the explanatory power of market-process economics. Next, I interpret Jacobs’s insights on the importance of face-to-face contact in the light of social-network theory, and link this to the concept of Jacobs Density. (This gets just a bit technical, but I trust the patient reader will see its value.) I am then better able explain how social-network theory can be easily and usefully integrated into market-process economics, providing another common bond with Jacobsian economics. The penultimate section delves further into the meaning and significance of trust, which is so central to Jacobs’s analysis of urban safety and to the dynamics of social networks. The final substantive section draws some very general policy conclusions.

1 Cities and the Market Process

As I mentioned before, long before cities became a popular subject among scholars, economists had addressed the question of how cohesion in the sense of systemic order tends to emerge out of independent, individual actions. They asked, for example, how do countless buyers and sellers competing for scarce resources manage to coordinate their personal buying and selling plans without a central authority telling them what to do?

For instance, the Scottish moral philosopher and reputed father of economics Adam Smith explained in 1776 how self-interest constrained by peaceful competition drives the successful operation of markets via an “invisible hand,” which his famous book The Wealth of Nations (Smith, 1976[1776]) helped to make more visible. As this line of thought progressed over the next 100 years, a core problem for economic science became to develop the link between individual actions and orderly social outcomes through the medium of markets. In the late nineteenth century, the French economist Léon Walras pioneered a mathematical method to specify the conditions under which individual decisions in many separate markets throughout an economy simultaneously dovetail in an economy-wide “general equilibrium” (Walras, 1977[1874]). As economics developed through the twentieth century, two fundamentally different approaches emerged: (1) the microeconomic analysis of equilibrium outcomes in which individual decisionmakers have perfect knowledge and don’t make systematic mistakes and (2) the analysis of economic outcomes as primarily determined by the interaction of macroeconomic aggregates—such as aggregate demand and supply and national output—where errors in the private sector recur regularly and lead to systemic crises that require effective government interventions to correct.

The story is of course much more involved and far more interesting than I have described here. The point, though, is that, with some noteworthy exceptions, mainstream economic theory has strayed from studying the connection between individual actions and systemic outcomes, such as how markets enable individual plans to dovetail over time, even when our knowledge is imperfect. Instead, under the powerful influence of mathematical equilibrium theory and macroeconomic aggregation, the competitive process of discovery—an entrepreneurial process—all but disappeared from the literature (Kirzner, 1997). At the same time and largely under the same influences, the kind of social institutions we examine in this book—for example, public space, social networks, norms of trust and reciprocity—have also faded from economics. Unfortunately, as a result, little in mainstream economics today is particularly relevant for investigating experiment and creativity and the social setting in which they take place.

1.1 Entrepreneurship

One of the exceptions to this historical trend traces its heritage to a founder of modern economics, the Viennese economist Carl Menger, a pioneer of what is known as marginal analysis. Nearly 100 years after Adam Smith, Menger helped to reorient the economic theory of value from backward-looking labor costs, which sees the value of a good as deriving from the historical cost of producing it, toward the forward-looking, subjective perceptions of individual actors, in which a good’s value depends on what we expect its usefulness to us to be in the future. Menger utilizes a “genetic-causal method” by which social order and institutions emerge unplanned from our actions based on our perceptions. That method explains the unintended emergence of a complex social institution, such as money, by tracing its logical evolution through the self-interested actions of individuals over time. Bartering a sack of grain for a goat leads to the use of goats as a medium of exchange, to the use of more-portable and divisible media, and eventually to precious metals and later to coinage, banking, and paper currency (Menger, 1981).²

In the same vein, a student of Menger’s, Eugen von Böhm-Bawerk, developed a time-based theory of capital, that is, produced means of production, one of the central problems of which is how heterogeneous capital goods, spread over an entire economy, can without central direction form complex structures of diverse complementary inputs that over time eventually become goods that we directly consume (Böhm-Bawerk, 1959: 23). Or, as author Leonard Read expresses it, “How do you make a pencil?” How do you combine bits of knowhow, skill, wood, rapeseed oil, and myriad heterogeneous elements scattered around the world to create something as seemingly simple as a pencil, such that it has greater value than all of its components taken separately (Read, 1958)?

In turn, one of Böhm-Bawerk’s students was Ludwig von Mises, whose contributions to economic theory, especially to the problem of economic calculation under socialism, set the stage for some of the most important debates in twentieth century economics. Mises was in his day the clearest exponent of how money prices enable entrepreneurs to coordinate their plans via profit and loss signals, across industries and across time, without the need for deliberate, central planning. Mises’s protégé Friedrich A. Hayek, winner of the Nobel Prize in Economics in 1974, develops this theme in one of the most cited articles in economics, “The use of knowledge in society” (Hayek, 1945). There, Hayek explains how market prices themselves can serve as knowledge surrogates that, when individuals are free to adjust their plans without excessive external constraint, tend to accurately reflect the relative scarcities of the underlying resources (Thomsen, 1992). When market prices do this accurately, they perform the feedback Jacobs describes in her book The Nature of Economies (written in the style of a dialog):

“Price feedback is inherently well integrated,” said Hiram. “It’s not sloppy, not ambiguous. As [Adam] Smith perceived, the data carry meaningful information on imbalances of supply and demand and they do automatically trigger corrective responses. So data and its purport and responses are all of a piece.” (Jacobs, 2000: 110)

The price system according to Hayek enables us to harness knowledge that we are completely unaware of because it is embedded contextually in the “knowledge of the particular circumstances of time and place” of individuals dispersed across an entire economy (Hayek, 1945: 80). Leonard Read’s pencil is a simple but effective example of both this knowledge problem and its solution via the price system. (Recall that I have noted the similarity of Hayek’s “local knowledge” to Jacobs’s “locality knowledge.”)

Israel M. Kirzner, a prominent American student of Mises and someone we also encountered in the last chapter, has gone on to develop an entrepreneurial theory of the competitive market process, which views entrepreneurship as alertness to profit opportunities that arise when people make mistakes owing to their radical ignorance (Kirzner, 1973). Adding another dimension to Mises’s explanation of the role of money prices in economic calculation and to Hayek’s explanation of the signaling role of market prices, Kirzner argues that entrepreneurial discovery relies on market prices for arbitrage opportunities (buying low, selling high) created by the misjudgments of buyers and sellers, who may be overly optimistic or pessimistic about the future. Without entrepreneurial discovery, we wouldn’t be able to correct our mistakes by removing “radical ignorance,” that is, relevant knowledge we don’t know we don’t know.

While these ideas are consistent with Jacobs’s economics, much of it, including competition and entrepreneurship and what I said earlier about the underlying assumption of economic freedom, is mostly implicit in her writings. By the same token, economic theorists, perhaps under the influence of equilibrium analysis and macroeconomic aggregation, have mostly failed to appreciate the importance of social institutions and fluid social networks that are important elements in Jacobs’s theory of city-centered, economic development.

1.2 Extending the Boundaries of Market-Process Economics

Thus, economists in the “mainline” Mengerian tradition³ of economics have understood the market process as an evolutionary and dynamic phenomenon, and the causes and consequences of purposeful human action (Mises, 1963). They have, however, placed less emphasis (though more than most) on the “thick” social context in which we discover opportunities at a particular time and place. We might ask, for example, through what medium do we become aware of relevant knowledge? Action never takes place outside a particular spatial context, but is instead always undertaken by someone for something at a certain time and at a certain place.⁴ And how do we become aware of the very “knowledge of the particular circumstances of time and place,” the local, contextual knowledge, that helps us to interpret and evaluate those price signals and social institutions?

Others have addressed the importance of the temporal dimension of action; that action necessarily takes place through time, adding an underappreciated element of complexity into economic analysis (O’Driscoll & Rizzo, 1985). But it is at least as important to recognize that action is never placeless; that where people can and do choose to act can be equally important.

2 Action Space and Social Networks

We have noted that Kirzner (1973) characterizes entrepreneurship as alertness to pure profit opportunities and as essentially an act of arbitrage, of buying low and selling high. But his analysis takes place at a high level of abstraction and doesn’t tell us how we are first exposed to the information that leads to the discovery of those opportunities. Where does that information come from and how reliable is it?

Suppose someone tells me that I can buy apples around the corner for one dollar apiece and then sell them across the street for two dollars. Does this information represent an opportunity to earn a pure arbitrage profit? I contend that it does not until we can satisfactorily answer two questions: (1) What is our relationship to the sources of the information and (2) how reliable are they? The first question is about the nature of interpersonal contacts; the second is about trust. The answer to both questions lies in social networks—the entrepreneurial-competitive process is embedded in social networks. Social networks provide the channels through which information flows to and from the entrepreneur. One never buys and sells in the abstract, whether in the market for plumbers or in the market for corporations. It is always necessary to some extent to ask, “Buy low from whom, sell high to whom?” The issues of trust, reciprocity, and trustworthiness immediately enter each side of the exchange. These issues in turn are tied to place.

Within a network or set of networks, finding a reliable source of information (which might also carry information to others) and making a discovery from information gained from that source are both creative acts. In the first case, entrepreneurs make a valuable personal connection in a way that others have not; in the second, they recognize and profitably interpret information passing through that connection in a way that others have not. An online platform or video may broadcast a vast amount of information indiscriminately across a vast number of people, but the most critical information for entrepreneurship tends to come to us through personal contacts, often from people we may not know very well.

These creative acts—of forming and dissolving social ties and of discovering profit opportunities—take place in action space.

2.1 The Nature of Action Space

What exactly is “action space”? Simply put, an action space is where we do things; it is the physio-social environment in which we can act. And by “act” I mean making a conscious decision to do something or not, to execute a plan however big or small.

Now, to put more content into the concept, I need to talk about what is required for us to act, to “do” something. The first three prerequisites for human action are (Mises, 1963: 13):

• 1. A felt uneasiness

• 2. A vision of a state of affairs in which our uneasiness is reduced

• 3. Means available to realize that vision

Adding a final condition makes these four conditions sufficient for taking an action:

• 4. Awareness of the means to realize that vision

If we feel perfectly at ease, we would have no reason to act. But suppose we feel uncomfortably thirsty; we feel ill at ease. So, do we now act? No, because we don’t yet know if there is a better alternative to being thirsty. For instance, we could imagine the possibility of not feeling thirsty or of feeling less so. However, it is still not possible to act because the means to remove our thirst, perhaps a button to request a glass of water, may not be available to us. If we had access to such a button, it would satisfy the third condition. But we would not yet act if we were unaware that pressing the button (or some other action) would remove our thirst. Thus, the first three conditions are necessary to make a choice or to execute a plan, but they are not sufficient. To act requires the fourth condition: that we are aware of the button and its significance.

Imagine waking up fully conscious, but not knowing where we are. We notice we are lying down, covered in something white, surrounded by pale walls and some objects. We feel painfully thirsty (condition 1) and we can imagine not being so thirsty (condition 2). But how can we choose to act without knowing more about the space we are in? Suppose we see that next to us is a call button (condition 3). We still don’t do anything unless we know the meaning and significance of that object. If suddenly we realize that we are lying in a hospital room, the thing next our bed is a call button, and pressing it connects with someone who can relieve our thirst (condition 4), we can now act. We can choose to press the button—or not. That is, under these circumstances, choosing not to press it would also be an action.

And if, say, the button doesn’t work or no one responds, now that we know (or believe we know) where we are, other possible actions may present themselves. We could call out or walk (if able) to the nurses’ station for help—once we understand the rules of behavior and the possible connections we might have with others in that space.

In our initial conscious but unwitting state, the space we occupy is not yet an action space for us (although it may be for the hospital staff). We don’t know what to do or indeed if anything at all can be done to improve our situation. Once the first three conditions are fulfilled, however, it then becomes an action space, a hospital room, where the possibility of taking an action exists. As long as we are unaware of the means that are available to remove our uneasiness, we would not act, even though in some objective sense everything is in place for us to do so. The fourth element is missing.

What does this have to do with cities?

Remember my discussion of Kevin Lynch’s “city image” back in Chap. 3? We each have a mental image or mental map that serves as shorthand for understanding the place we wish to enter and navigate. That image changes over time as our experience grows. The image of a local is different from that of a tourist. We can thus add a social dimension to Lynch’s more physically based concept. Not only does our image contain physical structures and land-uses—Lynch mentions paths, edges, nodes, districts, and landmarks—it also holds social elements that we expect to find there. Who will we see and how will they (and we) behave? The social dimension makes a place more navigable.

Suppose we are considering taking a six-kilometer walk for exercise. What might our image consist of if the walk takes place in the countryside? There are certain aspects we first must consider. There is the physical aspect: weather, trees, trails, terrain, pleasing wildlife, shelter; the aspect of security: lighting, angry bears, muggers, other eyes on the “street”; and the social: who we might encounter along the way (welcome or unwelcome). Expectations such as these will determine where we choose to walk or whether to go out at all.

And, of course, this also applies to walking in urban locations. There is the physical aspect, which includes the land-uses or granularity of the city blocks we pass along; security, in terms of which streets are safe and which to avoid; and the social dimension of how crowded with strangers the public spaces will be and where we might likely meet people we know. Whether we plan to walk in a particular location depends on these kinds of expectations.

I have lived in New York City for decades. Nevertheless, there are entire districts I have never been to, some of which I do plan to explore someday, while others I do not. My city image consists not of the entire city, but of a patchwork of streets, blocks, and neighborhoods. A subset of those are my action spaces—places I am able and willing to do something in—while the rest of that city image are not my action spaces, at least for now. My action spaces need not be places I have actually been to, but where I think I know what to expect to some degree.

In short, action spaces are where we believe we may encounter certain people, places, and things. They contain our expectations about how people will behave and the kinds of contacts we might have with them. Not all action spaces are created equal, nor is a given action space potentially fruitful at all times. It depends on who and what is in that space, our expectations, and our alertness. Entrepreneurship happens in action space.

Being creative, making connections, and making discoveries are necessarily unpredictable. We cannot say with certainty where valuable ties will be made or unmade, or which action spaces will bear fruit, otherwise someone would probably have already made or unmade them. And even if we are exposed to information that contains a profit opportunity, there is no guarantee we will in fact recognize it (Ikeda, 2007). The “who, what, and how” of a discovery depends on the spatiotemporal context, that is, the “where and when.”

We also cannot predict how a social tie, having been established between person A and person B for one purpose, might later serve other purposes that neither A nor B could have foreseen (i.e., multiplexity). For example, a regular customer might tell you about a new competitor who has moved into your neighborhood, a teacher might introduce you to a future business partner, your sister-in-law turns out to be an excellent tax attorney, or a colleague might offer a tip about someone working on a project related to your own (Desrochers, 2001).

Again, some sources of information, a broadcast about stock prices for example, may be impersonal, but still have a high degree of reliability. Even in that case, however, the broadcast will depend on someone making critical decisions along the way, the owner or managers of the platform, for example. Usually, the most important entrepreneurial information, information that tips the decision-making balance one way or the other, comes through personal channels, often informally. Important decisions big and small rely on information conveyed by flesh and blood people who are connected to us in ways that are not arbitrary. From choosing a stock to choosing a mechanic to choosing the site of a new business, making a decision in the “impersonal market” depends a great deal on how much we know about the people with whom we plan to work or from whom we plan to buy or sell. And we may never know those countless others who are also involved, but are far upstream or downstream from us in a production network. Trust—reliance on another when we may be taken advantage of—is an essential element in that process.⁵

We know Hayek (1945) argued long ago that the price system is a marvel at coordinating the decisions of myriad anonymous decisionmakers, while at the same time economizing on the amount of information anyone needs to know to perform successfully up and down the supply chain. What he didn’t emphasize is that, nevertheless, each decisionmaker has to possess an enormous amount of contextual knowledge about the local situation, much of it gained from face-to-face contact (Ikeda, 2002). This contextual knowledge includes knowledge about personal connections and their reliability or relevance. Who we would ask for advice about potential investors for a project need not be the same person who we would ask about projects to invest in. And what we can safely say to different people is an important skill in all aspects of life. This ability to tell who we can trust and for what purpose and to what extent is vital, even though we may not be able to explain how we do it, even to ourselves. So Hayek is right about the price system economizing considerably on the technical knowledge we need to, say, build a house (“knowing that“), but we should not underestimate the amount of contextual knowledge required to decide who to ask about where to find the best house for the lowest price (“knowing how“).

Now, if our information were perfect, there would be no need either to make or to break social connections, at least for the purpose of coordinating our plans, because the problem of having to acquire relevant information from others would not exist. Like price signals, social networks are a way of coping with less-than-perfect information. Like price signals, social networks enable us to utilize the tastes and human capital of others who would otherwise be inaccessible. As sociologist Ronald Burt observes: “Through relations with colleagues, friends, and clients come the opportunities to transform financial and human capital into profit” (Burt, 1995: Loc. 155). And economist Paul Seabright adds: “Just as nobody can plan an artistic revolution, nobody quite plans the networks that make them possible” (Seabright, 2004: 111).

This raises important questions about the relation between entrepreneurship and action space, which is where making and breaking connections with social networks happens. How do entrepreneurs alter social networks and why do they do it? What does it mean to trust? What is the nature of that trust? What are the unintended consequences of entrepreneurship in action space?

I believe introducing some technical concepts from social-network theory will help answer these questions and extend the Jacobsian-cum-market-process framework of analysis.

2.2 Density, Distance, and Structure

What is a social network in this context? A social network is a set of people (or nodes) who are connected to one another through personal ties (Degenne & Forsé, 1999: 28).

In a very basic sense, then, a social network is an organized set of people that consists of two kinds of elements: human beings and the connections between them. (Christakis & Fowler, 2009, p. 13)

The origins of a network may be planned or unplanned, although once established, they will change in unforeseeable ways. Social networks are thus spontaneous orders. As this suggests, social networks may have vague boundaries. However, despite the claim of Degenne and Forsé that “no network has ‘natural’ frontiers; researchers impose them” (1999: 22), I believe it is possible in practice to identify nonarbitrary social networks—such as our immediate family, close friends, or colleagues—even though their frontiers may be fuzzy and changeable.

The ties between any two people may be relatively weak or strong. The sociologist Mark Granovetter (1973) defines the strength of a tie between persons as an increasing function of the following elements:

• 1. Its duration

• 2. Its emotional intensity

• 3. The level of intimacy

• 4. Frequency of exchange of services

To this list, Degenne and Forsé (1999: 109) add a fifth criterion, multiplexity (m), which is the ability to transact several kinds of exchange, for different purposes, concurrently within the same tie; or for the algebraically inclined,

$$ m=n/p $$

where n is the total number of different kinds of exchanges and p is the number of agent-pairs effecting at least one kind of exchange (ibid: 46), so that there may be more kinds of exchanges (n) than personal connections we have with others (p). Recall the example of your sister-in-law as your tax attorney.

It is sometimes useful to talk about an ego network, which is simply a social network considered from the viewpoint of a particular person (ego) in that network. If z_jq is a variable that indicates a relationship between agent j to agent q, and if N_i is the size or the number of agents in ego’s (i’s) network, then we can derive a simple measure of the density of ego’s network by dividing the sum of all actual relationships between all of the agents in that network (z_jq = 0 if there is no relationship between j and q, z_jq = 1 if there is) by the maximum possible number of relations among all of the agents in the network, or N_i(N_i –1)/2.⁶ In algebraic terms it looks like this.

$$ Network\ Density=\left({\sum}_j{\sum}_q\kern0.28em {\mathrm{z}}_{jq}\right)/\left[{N}_i\left({N}_i-1\right)/2\right],j\ne q $$

Network Density is then the ratio of actual connections to all possible connections in a given network and is a percentage that varies between zero and one.⁷ For example,⁸ the network in Fig. 5.1 has 9 connections out of a possible maximum of 28 (e.g., agent 1 is directly connected to agents 2 and 3, but only indirectly connected, through agents 2 and 3, to agents 4 through 8).

Fig. 5.1

Network A

Its density is therefore

$$ \mathrm{D}=9/28=0.32, $$

or is 32%.

Next, the distance between any two agents, i and j, is the shortest path (minimum number of ties or “degrees”) between them. You can calculate the average distance that a person would expect to travel to reach any other person in a network, as follows: For a given person, find the total distance she would have to travel to reach each and every other person in the network on separate journeys, then sum these distances over all N persons and divide that result by N_i(N_i –1)/2. For Network A the average distance is (64/28 =) 2.29 degrees. In other words, agent 1 (or any other agent in the network) would have to travel over an average of 2.29 ties to reach anyone else in the network. (I have shown one way to calculate the average distances for Networks A and B in the Appendix to Chap. 5.)

Now, the structure of a network refers to the way in which the nodes are connected (or not) to one another. Network B in Fig. 5.2 has the same number of nodes and ties as Network A, but because they are connected differently we say the structure is different.

Fig. 5.2

Network B

Next, an agent i is said to be structurally equivalent to agent j to the extent i and j have the same contacts in the network (Burt, 1995: 276). In Network C in Fig. 5.3, for example, agents 1 and 2 are structurally equivalent.

Fig. 5.3

Network C

Because agents 1 and 2 are structurally equivalent, the tie connecting them does not help either one to reach any other agent in the network (other than each other); that is, it does not reduce the average distance for agent 1 or 2. From that strategic point of view, such a tie is said to be redundant.

Burt (1995: 270) discusses another form of redundancy that is not based on structural equivalence but on cohesion. Cohesion here⁹ means having a strong tie with another agent who has access to and possesses the same information as you do, so that knowing her gives you no strategic advantage. “Cohesion concerns direct connection; structural equivalence concerns indirect connection by mutual contact” (Ibid: 277). So, redundancy is an increasing function of both structural equivalence and cohesion.

2.3 Population Density Versus Network Density

I have noted that in the real world, we don’t randomly distribute ourselves across space. Most of the time we choose to occupy locations for specific reasons because some places are more conducive than others for certain kinds of action. Sociologist William H. Whyte (1980), for instance, explains why we may choose to sit or stand in certain spots in a public plaza according to how comfortable, convenient, safe, and interesting it is. Larger agglomerations, such as cities, attract people for similar reasons with the added draw of economic opportunity, cultural diversity, and privacy (Jacobs, 1961: 56, 143). Of course, terrain and natural resources strongly influence the site and situation of settlements. But hills, rivers, and harbors are valuable only because we find them useful for particular purposes—trade, defense, or beauty, for example. Whether something constitutes a resource is entirely a matter of our perception of its usefulness.

In the late nineteenth century, public authorities and the modern urban-planning profession began to regard the congestion and squalor that accompanied the rapid development of cities as a major public-policy problem. Their solution, broadly speaking, was to bring open space to urban residents (e.g., Le Corbusier) or to move urbanites out to the countryside (e.g., Ebenezer Howard). They regarded population density as a source of social ills if not a vice in itself, a view which I will critique in Chap. 7. The tide began to turn in favor of density in the latter third of the twentieth century, in part because of Jane Jacobs,¹⁰ and for better or worse, planners began to see density as a virtue.¹¹

As we have seen, other things equal, in a population rich in diversity of human capital and tastes, the closer we live to one another (without overcrowding) and the greater our freedom of movement, the greater is the likelihood that formal and especially informal contacts will occur. These contacts in turn form the basis for mutually beneficial trades and other forms of voluntary contact and association that result when urbanites discover valuable complementarities.

Skeptics will point to continuing advances in communication and transport technology, which seemingly annihilate physical distances among people, as serious challenges to the raison d’être of the traditional city. Each wave of technical change—telephony, radio, television, the Internet; the railroad, car, airplane—has indeed increased the possibility and perhaps the appeal of living in greater physical isolation while remaining socially connected. Ebenezer Howard’s “Garden City“or Frank Lloyd Wright’s “Broadacre,” each predicated on low-density and relatively autonomous residential development (the former transit based, the latter automobile based), have never been within closer reach. While in the last decades, the relative density of the traditional city center has generally been falling throughout the developed world, urbanized areas anchored to one or more central cities have at the same time grown apace and is estimated to account for 75% of the global population by the mid-twenty-first century (Burdett & Sudjic, 2008). Population gradients, the change in population density as we move away from the center, have also shifted upward (i.e., higher density for any given radius) even as they have flattened out (Bruegmann, 2006). And technical advances in communication and transport have certainly perturbed the evolution of the city, but not stopped it.

There is no denying, however, that technical change, especially the rise of cyberspace and mobile communication, has had an enormous impact on the way we interact. For instance, apps like Tinder can make first contact with strangers easier and greatly extend the range of connections beyond what is possible from face-to-face contact or word of mouth, alone. However, while advances of this kind might for some represent a partial substitute for bar hopping, etc., for most of us, it would be challenging to carry on a romance exclusively over social media or from distant locations.¹² They complement social interaction, not substitute for it. Typically, we really don’t get to know another person very well until we physically meet someplace. And an FTF date arranged through an app will mean encountering people we didn’t expect, which again creates unknown networking possibilities.

Nevertheless, despite the persistent human propensity to agglomerate, it may be helpful to retool the standard concept of population density in the face of these changes with the aid of social-network theory. Therefore, in Section 3, I offer the concept of “Jacobs Density,” which may be better suited to this novel environment.

2.4 The Importance of Network Structure

Economic development, by which I mean (with Jacobs) economic growth that consists of innovation and the increasing division of labor and knowledge, is driven by entrepreneurship. To address the two questions posed at the beginning of this chapter—how agents acquire and then diffuse entrepreneurially relevant information—it is important to appreciate how even small differences in network structure can dramatically influence social distance. One way to clarify this point is to compare the two networks in Figs. 5.1 and 5.2.

We already know that Network A has a density of 0.32. Network B, using the same algorithm, has the same density. However, while the average distance in Network A is 2.29, the average distance in Network B is lower at 1.93. To reach anyone else in the network, the distance any given agent has to travel would be about 15% shorter in Network B than in Network A. The networks have the same number of connections but they have different structures. If the goal is to facilitate the movement of entrepreneurially relevant knowledge, other things equal, Network B has a structural advantage over Network A, the shorter average distance among the agents within the network.

This simple example suggests that a change in network structure that reduces the average distance between agents can shorten the “social distance” between them. And by closing this distance, structural changes—by which I mean here adding or subtracting ties to different agents—can increase the flow of entrepreneurially relevant knowledge and thereby increase the likelihood of profitable discoveries and development. It also suggests that we can do this without a net increase in the number of ties (i.e., people we know), or by adding ties indiscriminately, which is costly.

2.5 Social Distance, Strength of a Tie, and Diversity

What exactly is social distance? I have been treating social distance as the minimum number of ties or “degrees of separation” between two agents. In Fig. 5.2, for example, agent 7 is the most socially distant from agent 1 (at three degrees of separation) compared with anyone else. The maximum social distance between any two agents in Network B is three degrees and the minimum is one degree. Earlier I calculated “average distance” by taking the weighted average of those distances.

But social distance seems to have at least two other meanings in the literature. The first has to do with the level and kind of interaction between two agents. This is essentially Granovetter’s concept of a weak versus a strong tie. The weaker the tie between two agents—that is, the shorter the duration and the less intimate, emotionally intense, frequently used, and multiplex the contact—the more socially distant they are said to be. Therefore, I will subsume this aspect of social distance into the concept of “strength of the tie.”

The second meaning of social distance relates to what are called “affective” and “normative” social distances. Affective social distance varies inversely with the level of sympathy one feels for another (Bogardus, 1947). While important, this concept of social distance is for the moment not relevant. More relevant is normative social distance, which pertains to whether an agent is regarded as an insider or outsider to the group or social network (Karakayali, 2009).¹³ This includes cultural differences—for example, Christian versus Muslim, urbanite versus ruralite, American versus Japanese. Related to the concept of normative social distance are differences in an agent’s knowledge and skills (which together constitute her human capital) and differences in tastes, since we can infer from Granovetter that someone very different from us in respect of these factors are more likely to be outside than inside our social networks. While differences in knowledge, skills, and tastes may not always be normative differences, it will be convenient to treat them as if they were. I will therefore fold “normative social distance” into the concept of “human diversity.”

In sum, I treat the level and kind of personal interaction between agents as factors in the strength of a tie, and normative social distance as factors in their diversity. Doing so will help me to distinguish social distance, qua “degrees of separation,” from both the “strength” of a particular tie and how “diverse” two agents are from each other.

While conceptually separate, these factors do interact. Most importantly, closing social distance can (though it need not) result over time in the strengthening of ties which can, because of more frequent and intimate contact, reduce the diversity among more strongly tied agents. This is a matter of the dynamics of action space, to which I will return later. For now, let us return to the concept of density and how we might most usefully interpret it, especially in the context of modern technology.

3 “Jacobs Density”

Recall that the simple definitions of population density and network density are, respectively, the number of individuals per unit area and the ratio of actual to potential ties within a given network. In some respects, in terms of promoting entrepreneurial discoveries, network density is less important than the diversity of the agents in a network, similar to the way population density is secondary to the diversity of land-use. That is, population density alone fails to do the heavy lifting some urbanists expect it to do. Following Jacobs, population density interacts reciprocally with mixed primary uses, street intricacy, and “old buildings” to generate valuable land-use diversity. For example, Smart Growth policies impose “green belts” and other interventions to increase population density hoping it will produce a host of benefits, from community building to environmental sustainability to reducing income inequality and suburban sprawl (Leccese & McCormick, 2000: v–vi). And in the case of social networks, I have shown that sometimes network density has little to do with closing social distance because, there, “average distance” may be the more relevant concept. Moreover, the correlation between measured population density and economic vitality is tenuous at best (Gordon & Ikeda, 2011). Instead, diversity—in land-use and human capital—rather than density per se is a principal condition for economic development.

For Jacobs “high concentrations of people at different times during the day” are mostly needed to supply a steady stream of eyes on the street in public space around the clock (Jacobs, 1961: 37) and to feel safe and comfortable using public space (as a result of the interaction of all four generators of diversity). Personal proximity is also valuable when it increases the likelihood that we will have informal contact with others who are socially distant but complementary to us.¹⁴

So, I think the intuition that density is in some way an important factor in fostering greater contact is a strong one. After all, other things equal, it makes sense that the more people in an area, the more contacts there will be. The following is my attempt to align that intuition with a view of economic development, as an entrepreneurial competitive process, by means of a concept of density that is applicable to both abstract social networks and to actual urban environments.

I mentioned in Chapter 4 an alternative to conventional density called “Jacobs Density,” defined as “the level of potential informal contacts of the average person in a given public space at any given time” (Gordon & Ikeda, 2011: 448). It is possible to conceptualize Jacobs Density in terms of action space and social network theory.

The Jacobs Density of an action space is the total number of potential contacts Ego can access through direct contacts divided by the actual number of direct contacts Ego has. Jacobs Density differs then from the measure of network density, which is the ratio of actual to all possible connections in a given network. Jacobs Density is related to network density, but places greater emphasis on potential rather than actual network contacts. Here is a simple illustration of increasing Jacobs Density.

In Fig. 5.4, Ego in the first case forms a triad with John and Mary in one of her action spaces, which indirectly connects her to Juan, Jamal, Marcie, and Mariko, who may be outside that particular action space.

Fig. 5.4

Example of Jacobs Density (JD)

If Marcie later creates a new link with Morticia, with whom Ego had previously no or only very distant social contact, Ego’s Jacobs Density increases by 0.5, as is shown in Fig. 5.5.

Fig. 5.5

Example of increasing Jacobs Density

Morticia was previously entirely outside Ego’s network and socially distant from Ego, but Marcie now constitutes a “bridge” that shortens the distance between them, but at the same time increases the degree of human (normative) diversity in the network by including Morticia.

Ego can also herself strategically choose to break an old tie and form a new one if she discovers the opportunity to do so and the expected net benefit is positive. In the third case, Ego believes that although cutting ties with John would lose her three connections, she can by so doing expect to increase her Jacobs Density by forming a new tie directly with Frank in her action space and indirectly link with Fergie, Fernando, Alice, Alina, and Kalim (Fig. 5.6). Perhaps Ego believes her connections with John, Juan, and Jamal are unlikely to serve as a conduit to diverse and socially distant people.

Fig. 5.6

Example of strategic ties to increase Jacobs Density

Once again, it is possible to make changes in the structure of a social network that leave standard network density unchanged (in this case, by keeping the number of Ego’s direct connections constant at two), but reduce average social distance, and thereby create new sources of potentially novel information for entrepreneurial discovery.

Note that in each of these three cases, I have limited the distance between Ego and the farthest contact to three degrees, following the finding of Christakis and Fowler (2009: 485) that influence and information typically degrade significantly beyond three degrees of separation. If influence and information did not degrade in this way, and if it is true that any two people on earth are separated by around six degrees, as mathematician Albert-László Barabasi (2003: 25–40) reports, then everyone’s Jacobs Density would be nearly the same extremely large number, or approximately JD = 53,000,000: that is, the current population of the world of just under 8,000,000,000 divided by the maximum number of contacts a person can have at any time, which according to experimental psychologist Robin Dunbar (1992) is around 150 persons. Since each of us is a member of several, perhaps partially overlapping, social networks—family, friends, school, work, club, and so on—our potential contacts might indeed comprise a significant percentage of the world population. But in this case, if Christakis and Fowler’s 3-degrees rule holds, our Jacobs Density in any given action space would be a great deal lower.

We have thus far discussed two independent factors that can promote entrepreneurial discovery. The first is an increase in Jacobs Density, which potentially expands the amount and diversity of information that we can access through our contacts. The second is a reduction in average social distance, which because of the 3-degrees rule means less information would be lost among people in a particular network. If Ego were to link directly to Marcie, or indeed anyone in the network beyond John and Mary, the average distance in the network would fall.

What is the relation between action space and Jacobs Density? Action space consists of a physical and social dimension, and Jacobs Density relates to the social. Action space, then, is more than mere physical extension. Within a given area, there may be at any time higher or lower Jacobs Density. For instance, we can expect, other things equal, that potential Jacobs Density increases as the concentration of people and the granularity of land-uses in that area increases, because the possibility of connecting with more diverse and socially distant persons increases. In a small town of, say, 10,000 residents the low concentration of people and courser granularity of land-uses will result in fewer encounters with strangers (as friendly as locals may be to those they meet). Whereas, in a great city, within that same space, higher concentration and finer granularity increases Jacobs Density. (This is also true when comparing two cities with equal populations, with one livelier than the other.) It is quite possible for the same Jacobs Density to occur in a great city in a fraction of the action space of a town. The more “things to do” in an action space, the greater the Jacobs Density will tend to be.

In its present, purely conceptual form, Jacobs Density, like the more conventional average social distance, is not easily operationalizable.¹⁵ Nevertheless, I believe the concepts of Jacobs Density and of average social distance help us to see behind the intuition that density is somehow related to entrepreneurship and economic development. Density in this sense still depends partially on physical proximity, but Jacobs Density goes beyond that to consider the diversity and social distance among the people to whom we are indirectly linked via mutual connections.¹⁶ And it is now possible to say more.

4 Connected or Trapped?

At a given time, action space both constrains what we can know and liberates our creative powers. The number and strength of ties that at any moment connect us also limit what we might become aware of. For example, doctors who spend most of their time among patients and professional colleagues are unlikely to discover a profit opportunity in, say, the construction business. But those very limits may prevent the information generated in a dynamic economy from overwhelming them, allowing them to focus on recognizing meaningful patterns that may lead to valuable discoveries in their specialties. As Ronald Burt observes, “Given a limit to the volume of information that anyone can process, the network becomes an important screening device” (Burt, 1995: Loc. 212). Indeed, in a dynamic economy, the areas on which we focus may be changing all the time, and cognitive limits keep the number we can be aware of at a fairly manageable level. At the same time, however, making direct and indirect connections with socially distant networks increases the Jacobs Density of our action spaces and shortens average distances in our networks, effectively increasing within those limits the number of areas from which we might draw new and useful information, enabling us in a sense to be smarter and more creative. A doctor might notice that a technique used to brace delicate walls in a building renovation could be applied to the setting of bones in the human body.¹⁷

Besides Jacobs Density and shorter average social distances, there are two other factors to consider in evaluating the entrepreneurial effectiveness of an action space: prevailing norms and levels of trust.

4.1 Norms

Beyond those in our networks and our relationships to them (i.e., Jacobs Density and social distance), which we have just covered, there are also the norms and conventions prevailing in them and our action spaces. In some cultures, for example, a restaurant on a weekday is a more socially acceptable time and place to conduct business than, say, a funeral; elsewhere it may be the opposite. More importantly, the greater the freedom with which we can observe or mingle with others, the better the chances that we will encounter diverse and perhaps novel information that we might then interpret in profitable ways. As Burt observes:

Everything else constant, a large, diverse network is the best guarantee of having a contact present where useful information is aired. This is not only to say that benefits must increase linearly with size and diversity…but only that, other things held constant, the information benefits of a large, diverse network are more than the information benefits of a small, homogenous network. (Burt, 1995: Loc. 247)

Here norms of inclusion are crucial. What makes a social network inclusive or exclusive? What is it that enables us to form a new tie with someone we don’t already know or break a tie with an old acquaintance? The answer depends on trust.

But I contend that we attach two fundamentally different meanings to the word “trust” and that by differentiating between them, we can learn something essential and interesting about the dynamics of social networks in living cities.

4.2 Trust

If we understand trust as purely a function of how well we already know someone, how well person A knows person B, then we might say the stronger the tie,¹⁸ the more likely A will trust B, if B is trustworthy. Political scientist Russell Hardin (2002: 58) refers to this kind of trust as cognitive trust, or trust based on how much we know about someone. Again, in the context of a static network structure, in which ties are neither forming nor dissolving, stronger ties correlate with greater cognitive trust. The downside of this is that over time, strong ties are likely to grow redundant—everyone in the network knows all the same people. In a completely static world, novelty and diversity would eventually disappear owing to what we earlier called “redundancy by cohesion” (Burt, 1995: Loc. 18).

There is, however, another phenomenon that also goes by the name of “trust” that, while relevant for static social networks, is even more important for dynamic social networks.

4.3 The Dynamics of Action Space

As we saw earlier, simply multiplying weak ties willy-nilly may raise simple network density and shorten average distance, but it is costly and does not necessarily increase Jacobs Density. A person would do better to focus on nonredundant ties. Burt, again:

But increasing network size without considering diversity can cripple a network in significant ways. What matters is the number of nonredundant contacts. (Burt, 1995: Loc 255)

Back in Fig. 5.1, for example, the tie between agents 4 and 5 is nonredundant. It is also a bridge, which Degenne & Forsé define as follows:

An edge is a bridge between two parts in a graph when it is the only link that spans the two parts, that is, every node in one part can only reach a node in another part via that link…. An edge can be considered a local bridge if it is the shortest path between two parts of a graph, that is, where all other chain lengths are 2”. (Degenne & Forsé, 1999: 110)

The entrepreneurial discovery of a new nonredundant tie will be profitable if it yields greater benefits than the cost of establishing the new tie. (Which also includes the expected costs of breaking an old tie, because Dunbar’s Number places a limit on the number of ties we can have at any one time.) According to Burt (1995), ties with lower redundancy, perhaps even bridges, can be found in what he calls “structural holes,” which are the social network analog to Kirzner’s entrepreneurial arbitrage opportunities.

Structural holes “are disconnections or nonequivalencies between players in the arena” (Burt, 1995: Loc. 47), but as such they are also unexploited “entrepreneurial opportunities for information access, timing, referrals, and control” (Ibid). In the context of social networks, therefore, entrepreneurship manifests itself in the discovery of strategically valuable ties that span structural holes. Structural holes shorten average distances but, crucially, there is no certain indicator that a structural hole is present. The hole itself is an “invisible scam of nonredundancy waiting to be discovered by the able entrepreneur” (Ibid: Loc. 648). In other words, a structural hole is veiled in radical ignorance.

Note the close similarity to market-process theory and specifically to Kirzner (1973). As it is for Kirzner and market-process economics, for Burt, “competition is a process, not just a result,” whereas “most theories of competition concern what is left when competition is over” (Burt, 1995: Loc. 102). Moreover, Burt states “the structural hole argument is a theory of competition made imperfect by the freedom of individuals to be entrepreneurs” (Ibid: Loc. 111). These imperfections represent profit opportunities to alert entrepreneurs, who can establish the weak ties that span structural holes, shorten social distances, and increase Jacobs Density.¹⁹ Entrepreneurship is thus critical in forming these weak ties. Over time, competitive rivalry helps entrepreneurs to identify structural holes qua profit opportunities, just as in market-process theory.

Where social-network analysis goes beyond the Kirznerian analysis is the recognition that when an entrepreneur E buys from A and sells to B, this is not only an act of arbitrage, it also establishes a triangular relationship among E, A, and B. That relationship may not last beyond the single exchange, but it represents a weak tie if the agents have had little or no contact before. All three agents form a transitive relation (Christakis & Fowler, 2009: 339). If the relation persists, it can later transmit novel information from more distant networks, with A or B or E acting entrepreneurially with another agent D. Or in time, it can serve multiplex uses beyond the original trade function (e.g., A and B might become friends as well as business partners).

Although structural holes may exist in one’s existing networks, they are, as we have seen, most likely to be found between people in different networks or cliques. That is because, owing to homophily, that is, the tendency to form stronger ties with those with whom you share more characteristics (Christakis & Fowler, 2009: Loc. 308), strong ties tend to bind people into a network that is relatively homogenous with low average distances from other network members, so that any new ties will tend to be with persons from other, likely more diverse, social networks.

In terms of the complementarities and cohesiveness discussed in the previous chapter, weak ties are crucial: “weak ties are essential to the flow of information that integrates otherwise disconnected social clusters into a broader society” (Burt, 1995: Loc. 364). And the new nonredundant tie or bridge must initially be a weak tie because “no strong tie is a bridge” (Granovetter, 1973: 1364).²⁰

Now, Christakis and Fowler argue that

[p]eople with high transitivity live in densely clustered cliques where everyone knows everyone else. People with low transitivity, in contrast, tend to have friends in several different groups. Such people often act as bridges between completely different groups of people (Christakis & Fowler, 2009: Loc. 3694).

In a social network that has been around for a very long time, it may be extraordinarily difficult to discover structural holes because so many ties would already have been formed among its members (Granovetter, 1973), approaching maximal (non-Jacobs) network density. Because of structural equivalence or cohesion, over time, ties will become more and more redundant. So, in long-established and static networks, we should expect transitivity to be very high, but there will also be few opportunities for the entrepreneurial discovery of either new bridges or new complementarities within existing pools of economic use. Strong ties would dominate. We are more likely to find low transitivity and structural holes among socially distant and more diverse networks. As Burt observes,

As you expand your inventory from your closest, most frequent contacts to your more distant, contacts tend to be people like yourself before you reach a sufficiently low level of relationship to include people from completely separate social worlds. (Burt, 1995: Loc. 387)

This was illustrated earlier in Figs. 5.5 and 5.6. But this raises a paradox.

If by “trust” we mean “cognitive trust”—agent A’s propensity to rely on another agent because she knows him well via a strong tie (Hardin, 2002; Ikeda, 2007)—and if agents in diverse and socially distant networks are most likely to be strangers, how can weak ties form in the first place? From whence comes the trust that would enable her to connect to another agent, about whom she knows little or nothing? Cognitive trust is the basis of the strong ties with agents in networks closer to A’s own. Now, it is true that an agent C, who may be acquainted with both A and B, can serve as a bridge between them. This, however, simply pushes the question one step back: If only cognitive trust exists, how did the tie between C and A and B first form? (This is the ambiguity I pointed to in the Jacobs quote at the beginning of this chapter.) Indeed, it stands to reason that at some time in the past, C was not strongly tied to both—perhaps to neither.

I believe the paradox can be resolved by identifying a fundamentally different phenomenon which we also call “trust.”

4.4 Behavioral Trust

That concept is behavioral trust, which I have defined elsewhere as “an act of choice that overcomes uncertainty or a lack of knowledge” (Ikeda, 2007: 219). Let me try to be more precise.

In a probabilistic sense, we can define “complete knowledge” of another agent’s trustworthiness as 100% certainty, and “complete ignorance” as 0% certainty. Suppose then that A thinks she needs to feel more than 75% certainty before cognitively trusting B enough to trade with him. Following the sociologist James Coleman (1990: 99), in simple algebraic terms we can describe this as the point at which

$$ Gain\kern0.28em x\kern0.28em (0.76)> Loss\kern0.28em x\kern0.28em \left(1-0.76\right), $$

That is, where the expected gain is greater than the expected loss. At a level higher than 75%, A will then cognitively trust B. For example, if Gain = $100 and Loss = $300, and her certainty level is 75%, A would be exactly indifferent between trusting or not trusting B if her level of certainty were exactly 75% and definitely trust B even if it were higher.

Suppose, however, that A can only trust B up to 60%, but that to engage in trade with B she still needs to feel at least 76% certain. Here we can say that A does not cognitively trust B and will not trade because the expected value of the Gain, E(G), would be less than the expected value of a Loss, E(L). Now, A would trust B if, say, Gain > $200 and Loss < $100 because then E(G) > E(L). Indeed, with the cognitive-trust approach, A would have no choice but to trust B, that is, not to do so would be “irrational” according to standard economic theory. But if neither A nor B can alter the gains and losses then, given the initial gain, loss, and certainty level, behavioral trust is what could enable A to trade with B and overcome the 16 percentage point gap if that is what A chooses to do. Behavioral trust, then, gives A the possibility of taking a kind of “leap of faith.”

In other words, while cognitive trust is a psychological propensity (Hardin, 2002: 58)—that is, you either have it or you don’t—behavioral trust is teleogical, an act of choice taken in the presence of “radical uncertainty” or uncertainty not subject to an ordinary probability calculus, in contrast to Coleman’s notion of trust based on what economists call “calculable risk” (Coleman, 1990: 97–108).²¹

An agent who cognitively trusts says: “I can trust you because I know you very well.” An agent who behaviorally trusts says: “I don’t know you very well, so I’m going to have to trust you.”

Cognitive trust, based on our familiarity with another person, is thus the strong fiber that binds a network together.

Behavioral trust, on the other hand, is what enables the formation of a new tie. Because, by definition, we form a weak tie with someone we don’t know very well or at all, especially a socially distant person with a very different background from ourselves, the level of cognitive trust will be close to zero. To form a tie, to have contact, and establish a relation with a stranger requires a degree of faith.²²

Breaking a tie may involve both kinds of trust.²³ Should we leave our hometown, family, and childhood friends for the strange, big city, or not? Letting go of a relationship or a familiar clique or network may be based purely on calculation of given estimated benefits and costs, and when the former exceeds the latter, a rational agent automatically severs the tie. Typically, however, we lack the information to make such a fully informed decision and we then have to choose based at least in part on behavioral trust. The choice to seek some unspecified opportunity, perhaps in a different country, can again involve a lot of faith. Which way we choose is indeterminate, making such decisions sometimes very hard.

A few caveats here. Strengthening a tie doesn’t necessarily mean that A will automatically place greater reliance on B. After all, A’s repeated contact with B may simply confirm her opinion that he is a scoundrel. There may be members of our family with whom we have very strong ties that we have learned are untrustworthy, and so forth. In fact, under these circumstances, relying on someone we are strongly tied to would require behavioral trust! Nevertheless, with more knowledge, we, like A, can place greater reliance on our evaluations of another’s trustworthiness or lack thereof. Nor is it the case that a social network consisting of relatively strong ties need be ipso facto an exclusive one since familiarity is one thing and norms of exclusivity are another. In practice, however, we can infer from Granovetter that members of a strongly tied group will tend to be quite similar, especially over time, with respect to the things that draw them together—for example, kinship, status, ideology, race, religion, age, language, musical interests—which can act as a thick filter for membership. Finally, even a relatively inclusive social network will have some members who are tied strongly to one another through cognitive trust, otherwise the network would not last, and weak ties do strengthen over time. What makes a social network relatively inclusive are the norms within the group governing its decision to admit members via weak ties and the rate at which those ties are allowed to strengthen.

4.5 Freedom and Competition

As mentioned, the ability to form weak ties and to dissolve strong ties also depends on the norms held by people across society that influence the level of individual freedom to move among the various networks. Again, Jacobs seems to take this for granted. I am speaking here specifically of the freedom to enter or exit any social network we choose to, assuming that network is willing and able to allow us to do so, and our tolerance to let others do the same. “Freedom” in this sense includes the legal-rights triumvirate of private property, freedom of contract, and the rule of law that we typically associate with economic freedom.²⁴ Of course, “social pressure” might issue from traditional norms and conventions that, despite the presence of formal grants of freedom, stifle the movement of persons across either geographic or social distance. The law may give same-sex couples the right to marry, for example, but strong disapprobation from family and community members may discourage those who might wish to.

When either social pressure or legal coercion prevents contact with outsiders, at least some will feel trapped as the thickness of ties encroaches ever further into their personal autonomy. You could say that in the extreme case, all private space becomes public space. But from the point of view of entrepreneurial competition and economic development, it may be closer to the truth to say that in these stifling circumstances, all public space becomes private space in which no strangers are permitted. Ties would be interchangeable and redundant through both cohesion and structural equivalence—that is, everybody knows everybody else really, really well²⁵—and structural holes disappear.

Improving our situation as we see it, entails not only forming new ties (that may turn out to be no better than the old ones) but also, crucially, letting go of old ones; adding new friends, colleagues, suppliers, customers, and competitors and leaving familiar ones behind. Adding new ties may indeed necessitate cutting or loosening old ones, when we take into account Dunbar’s Number, especially when the ties are strong, because of the limited number of personal relations we are able to maintain (Christakis & Fowler, 2009: Loc. 3914). Norms of tolerance are obviously key to free entry and exit. But equally important is the freedom to criticize and to do so passionately, short of violence. Radical tolerance and radical criticism are complements. To paraphrase something from the previous chapter, tolerance without criticism is insipid; criticism without tolerance is intolerable.

Freedom of that kind, which we might call “social freedom,” creates both the opportunity and the necessity to enter and exit. That it creates the opportunity is clear enough. It is competition, however, that makes it necessary. The fact that entry and exit into social networks is free (although actually forming or dissolving ties may involve costs) makes the process of discovering structural holes in action space a competitive one. The agent who fails to effectively and profitably make and break ties is at a competitive disadvantage.

Recall that competition takes place along two different dimensions. Entrepreneurial agents compete over already-established networks, and they also compete to form and dissolve connections. Competition thus refers not only to the activities of rivals who are using already-established networks through which they acquire information about, say, prices and quantities, but it also refers to their attempts to profitably change the very structure of their networks, by filling structural holes or increasing Jacobs Density.

To summarize: Social networks are a way of coping with imperfect knowledge. Free entry and exit into and out of the networks that occupy our action spaces enable us to discover opportunities and to gainfully alter the structure of our networks. Behavioral trust is essential in that dynamic, and without it we would be unwilling to either form new weak ties or cut old strong ones. Trade is typically the catalyst here, with personal contacts as the main source of the information about trades—for example, price signals, tips, assurances, and so on. Once aware of this information, we evaluate it and its sources and may then choose to form a relationship with a new contact. We can, of course, make valuable connections by means other than trade. Nevertheless, a casual or informal non-market contact often opens the door for important, multiplex trading opportunities in the future, even if that is not why we make the contact in the first place.

(The next chapter applies these concepts to the process of economic development, and in so doing may help the reader to get a firmer grasp of them.)

But because of our cognitive limits, changing the structure of our networks will have some unpredictable consequences. These are some of them.

4.6 Unintended Consequences

As we have seen, a new tie may become multiplex, or others may later use a tie in ways we may or may not like.

Also, the same connections that bring information to us often help to diffuse the knowledge we generate back out to our networks and beyond. Sometimes we don’t mind this happening (even if we don’t intend it), as when we earn a reputation for trustworthiness. Other times we may, as when we get a reputation for untrustworthiness, or when we wish to keep rivals in the dark about a discovery we have made.

Another important unintended consequence arising from competitively restructuring a social network occurs when ties grow stronger over time.²⁶ As trade increases, the frequency and intimacy of contact increases between A, who reflects the values and norms of her network, and B, who reflects the values and norms of his. Then, following Granovetter (1973), over time differences between their respective networks may lessen as they learn more about one another. So, while a higher degree of homogeneity and homophily may reduce some kinds of conflict, the downside is that overall diversity—which can inspire novelty and innovation in commerce and culture—will also tend to decline over time. Relations become more redundant and therefore less complementary. Sufficiently high social freedom may counteract this homogenizing tendency to some extent, by spurring mobility and experimentation, both within an existing network community and across the greater global network. In this way, it may be possible to maintain high levels of cultural and economic development while maintaining a relatively stable system of social networks. Freedom to experiment and innovate means diversities will likely re-emerge so that the development can continue.

Also, making and breaking ties have third-party or “external” effects. As Paul Seabright notes:

They [social networks] are the outcome of the various affinities that move ordinary people in their choices of where to live and work. Every time someone moves, she changes the environment she leaves and gives a new character to the environment she joins, without intending or necessarily even being aware of it. And the most innovative people have always been footloose, restlessly seeking out opportunities over time and space. (Seabright, 2004: 111)

Moreover, if someone severs an old tie by leaving a network, it may thereby create a kind of external benefit for those “left behind,” as they become marginally less redundant than they were before the old network structure changed. If A severs ties with B, and the shortest way for C to reach B had been through A, it opens a structural hole between C and B that someone—B, C, or some other agent D—might profitably fill. At the same time, if A connects to a new network by bridging a structural hole, this raises to some degree the level of redundancy in the new network and lowers the value of making a new connection to it, which is a kind of external cost.

Finally, when A connects with a nonredundant agent N, she increases both the Jacobs Density for her own network and the Jacobs Density of anyone connected to her. If N then forms a connection with a diverse, socially distant agent with a different set of connections, that would further increase A’s Jacobs Density. This corresponds to Fig. 5.5. Of course, N could also sever a tie that would reduce A’s Jacobs Density. Other things equal, however, A would find it in her interest to support freedom of mobility in general to maximize her own average Jacobs Density, which down the road could unintentionally promote economic development.

How does this relate to urban design?

5 Implications for Urban Design: Fostering Social Capital in Action Space

We noted in Chap. 4 that the specific form of social network called social capital is one of the key factors in Jacobs’s analysis of how the design of public space can profoundly influence economic development. According to Burt (1992: Loc. 194): “Social capital is at once the resources contacts hold and the structure of contacts in a network.” Recall for Jacobs “social capital” contributes to a city’s cohesion in the face of an inflow of outsiders (Jacobs, 1961: 138), which is particularly relevant to economic development and the market process.²⁷ Granovetter (1973) elaborates on the concept in his work on social networks, and mathematicians such as Barabasi (2003) then formalize aspects of Granovetter’s work. Finally, as we have seen, Burt (1995) applies social-network theory to the study of entrepreneurship in the context of imperfect competition. Here we may bring the circle back to Jacobs.

The difference between weak and strong ties is the basis for the difference between what political scientist Robert Putnam (2000) calls “bridging social capital” that is inclusive toward outsiders, and “bonding social capital” that is exclusive. The terminological parallel between bridging social capital and a network “bridge” seems more than coincidental. The same norms of tolerance and criticism that foster free entry and exit across social networks also underlie bridging social capital. Bridging social capital, as the name suggests, promotes weak ties between socially distant and diverse agents. It rests on norms and beliefs that value inclusivity as well as change. On the contrary, bonding social capital and the norms that sustain it serve to increase homogeneity, homophily, and strong ties among agents in a network. It promotes exclusivity, stability, and stasis. As a result, bonding social capital, while a stabilizing element in social orders, tends to dominate in less dynamic and less socially free orders. In creative market processes, then, bridging social capital is at least as important as bonding social capital (Ikeda, 2007, 2008).

5.1 The Design of Public Spaces and Social Capital

Jacobs describes some of the mechanisms by which social capital is either nurtured or undermined by the physical environment. As we know, Jacobs, influenced by William H. Whyte (Flint, 2009: 26), pioneered the analysis of the way the design of public spaces affects economic development. Whyte (1980) offers specific recommendations at the micro level based on his classic time-lapse studies of public spaces, after recording the effects of location, seating, light, accessibility, and other factors on how people use public plazas in New York City. His research emphasizes the importance of safety, location, comfort, and seating in the design of those spaces, and it has been applied by city planners—perhaps nowhere more successfully than in Bryant Park in Midtown Manhattan (Gratz, 2010: 123).

In addition, we know from the previous chapter that Jacobs’s analytical framework explains how, given the proper conditions, safety, trust, and land-use diversity emerge spontaneously in successful urban environments. These are the fruits of strong social capital. Recall that she recommends minimizing visual dullness (short blocks), buildings of different ages (old buildings) that lower the cost of experimentation, multiple attractors to bring people into public areas (mixed primary uses), and a local population high enough to supply a flow of people throughout the day and year (population density). These measures help to make public space relatively safe and secure, a prerequisite for the formation of social capital (Jacobs, 1961: 30, 143–221).

5.2 Border Vacuums, Cataclysmic Money, and Visual Homogeneity Again

Although mindful that those conditions would manifest themselves differently depending on time and place, Jacobs argues that they would encourage the prime ingredient for economic development: informal contact in public space, the “small change from which city’s wealth of public life may grow” (Jacobs, 1961: 72). On the other hand, for Jacobs border vacuums, cataclysmic money, and visual homogeneity undermine social capital in the same way that the erosion of social freedom would do so. These run counter to spontaneous economic development because they undermine granular land-use diversity and produce what Jacobs aptly calls a “great blight of dullness” (Ibid: 41). People generally avoid dullness, unless they wish to be unseen, and fewer people means fewer “eyes on the street” and higher levels of perceived, and eventually actual, danger (Ibid: 257–317). Jacobs Densities fall and action spaces shrink or disappear altogether.

Norms that discourage informal contact with strangers, and thus the formation of bridging social capital would, like a border vacuum, block free interactions that promote the discovery of serendipitous complementarities among socially distant persons. Indeed, cataclysmic money, border vacuums, and visual homogeneity—by discouraging the kind of informal contact that breeds social capital—might themselves over time engender norms and beliefs that are more exclusive than inclusive, more intolerant than tolerant of strangers. Again, the result is a downward spiral that Jacobs calls a “dynamic of decline,” in which the lack of interest in a public space results in fewer eyes on the street, which reduces the perception of safety, which discourages people from sharing the public space, which in turn means fewer eyes on the street, and so on.²⁸

In general policy terms, the design of public spaces should advance the diversity of people, places, and things—ideally creating the sort of safe, trust-promoting environments in which network-rich action spaces can emerge. This is obviously a challenge, given the typical mindset of divisive urban politics. Left to its own resources, however, local politics may be more responsive to genuine local needs or at least do less harm than policies financed, initiated, and directed from higher levels of governmental administration, where the knowledge problem is even more intractable. This is an issue that we will explore in some depth in Chaps. 8 and 9.

6 Concluding Thoughts

Social networks furnish conduits through which we send and receive information. By discovering structural holes, we alter our networks, unaware of all the consequences, in a way that can increase Jacobs Density, shorten average social distance, and facilitate the flow of information. So while market prices serve as guides to entrepreneurial discovery and social cooperation, they are not the only guides. When knowledge is imperfect, social networks also convey relevant information to decisionmakers. In that sense, social networks, and changes in their structure enabled, by freedom of mobility and norms of tolerance and trust, are as important to the market process as prices.

Our action spaces enable us to plug into those networks. What is their conceptual status?

The concepts of purposeful action and entrepreneurship may be more fundamental to market-process economics than action space. But while we can grasp the nature of entrepreneurship without invoking action space, I believe the concept of action space is essential for understanding how entrepreneurship operates in real markets. Trying to understand what promotes or suppresses entrepreneurship without considering action space is like trying to understand how well a car performs without considering roads. Thinking seriously about how we actually acquire and convey information in the market process reveals the importance of the spatial environment, in particular the spatial environment in a city.

In this chapter, I have presented a way of employing social networks to integrate Jacobs’s analysis of urban processes with market-process economics. In this way, social-network theory may also serve as a useful link between Jacobsian-cum-market-process economics and their common social theory. In the next chapter, I will use this integrated socioeconomic framework to present and interpret the mechanics of Jacobs’s theory of economic development.