Chapter 6
By Way of Conclusion
We consider the effects of our EDL through the very epistemic prism we have constructed, and we offer an interpretation of the epistemic analysis of networks and interactions as a set of brokering and closure-producing moves, where brokering happens across communities of researchers with different representational and methodological commitments (epistemic game theory, network sociology) and where closure acts at the level of a nascent group that is interested in the epistemic structure and dynamics of interactions and networks. We conclude with thoughts for future directions of research and development.
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The very idea of a language for modeling the epistemic states of individual agents to make forward predictions about the structure and dynamics of social networks and interactions cuts obliquely across models of inquiry in different disciplines.
Game theorists—and epistemic game theorists in particular—consider the data produced by competitive or cooperative interactions as instantiations of equilibria among the actionable strategies of the agents involved. The task of the modeler or the theorist is to reverse-engineer the epistemic conditions that provide sufficient grounds for agents to act rationally and therefore choose strategies that are in equilibrium. Notions of common knowledge, common priors, and the common assumption of rationality emerge as explananda for why agents’ strategies are in equilibrium (which is assumed ex hypothesis).
The fact that equilibrium is assumed—rather than derived or predicted—makes the modeler’s task both easier and more difficult: easier because it fixes a set of propositions about the right representation of a state of affairs (an outcome is the logical and material consequence of strategies that are in equilibrium); more difficult because logical problems with the representation (such as those related to agents’ unawareness or to their logical sloth or lack of logical omniscience) become genuine challenges to the internal validity of the model (either to the assumption of equilibrium or to the epistemic assumptions necessary to ensure it).
Network theorists—who reside at the “empiricist” end of the rationalist-empiricist spectrum—prefer to make “realistic” measurements of variables (e.g., the nature and distribution of ties among agents, flows of information) that may be plausibly (or “realistically”) linked, whether causally or functionally, to some future state of the network or the interaction. The breadth of the variable space considered, and the lack of a formal language for addressing agents’ epistemic states and the impact of these states on information flows, makes propagating the resulting models forward in time a high-variance enterprise: the networker’s modeling tool kit does not have the kind of logical depth that permits game theorists to “look forward” into the future of a set of interactions.
The EDL we have introduced offers an alternative that rectifies the difficulties inherent in both approaches. It uses a set of primitives (agents, propositions, epistemic states) that are intuitive and measurable via instruments such as questionnaires, surveys, or forced choices among gambles, and that jointly allow a sensitive rendition of networked agents’ epistemic states. At the same time, it sets out logical and meta-logical procedures that allow us to perform logically deep forward modeling of the interactions among epistemic states, information flows, and agent-level actions—modeling that is sensitive to distinctions that the analytical apparatus of epistemic game theory does not allow.
Indeed, the “move” that we are advocating can itself be understood through the epistemic prism as an attempt to broker, in the following ways, a closure-inducing “bridge” across disciplinary ways of seeing and doing.
The EDL as an Act of Brokerage
This text is itself an act of brokerage among several disciplines—most markedly between at least two. The first comprises researchers concerned with epistemic game theory, interactive epistemology, and the formal representation of knowledge structures and their dynamics in groups and collections of human agents. This discipline is cohesive in the epistemic sense in that its members share a set of assumptions: (1) assumptions about how knowledge and information are represented: (a) through propositions structured by first-order logic that “refer” to objects and events along with their negations, conjunctions, and disjunctions, and (b) through degrees of belief that obey the axioms of probability theory; (2) assumptions about how knowledge and informational states evolve (e.g., Bayesian kinematics); (3) assumptions about how the beliefs of interacting human agents in turn interact with one another; and (4) assumptions about how agents calculate equilibria in games they may be construed as playing or their interactive equilibration of conjectures regarding other people’s beliefs.
The cohesiveness of this disciplinary group inheres in the distributedness of representations (models) and procedures (rules, algorithms, heuristics) for manipulating them among group members. Equally important, each member knows that every other member is equipped with a common set of representational and procedural bits of knowledge and is prepared to use them in practice, and knows, moreover, that each member knows that every other member knows this. This epistemic structure enables communication among members on the basis of a common “code”: each contributor to the dialogue that constitutes a “research program” uses a code and associated rules for putting words together in such a manner that they will be understood as intended. The use of the code is enabled by norms of communication and justification (provability from parsimonious axioms) that, once again, are distributed and common knowledge among group members and embodied in practicing members who come to recognize each other by “the way they think,” for which the way they speak serves as a proxy.
The disciplinary group on the other side of the brokering bridge we are trying to engineer comprises researchers who study social networks. They commonly represent human groups as networks of agents and their relationships, and they seek to understand the behavior of groups as a function of the structure and dynamics of ties that bind group members through empirical investigations of the structure and dynamics of relational patterns. This disciplinary group is cohesive in that its members share ways of representing human groups.
One way is through network graphs wherein individuals are represented by “nodes” and wherein relations of friendship, collaboration, and interaction (among others) are represented as “edges” connecting these nodes. Another way is through variables of interest in the analysis of the structure and evolution of a network (the strength of the ties that make up the network, the centrality of an individual in her subnetwork, her strategies and tactics regarding tie formation and dissolution, and so on). The modeling tropes shared by this group are clustered around ways and means of describing patterns of relationality among human agents, and they form a distributed representational knowledge base that is more or less common knowledge among social network researchers.
The cohesiveness of this group is predicated not only on the distributedness and commonality of the declarative knowledge that corresponds to the domain of social network analysis but, just as important, on the distributed knowledge of this distributedness—the knowledge that every other member knows that this knowledge is distributed. And, as in the case of epistemic game theory and interactive epistemology, the resulting cohesiveness at the level of representations is only efficacious as a social adhesive if the members of the social network analysis group also share norms of discourse and justification—in this case, phenomenological plausibility, empirical testability and validity—that go hand in hand with the representational basis of the underlying discipline.
Brokers are frequently sources of “good ideas” in their own networks (Burt 2005), but “good ideas” do not just flow across brokering ties that bridge structural holes in any way. Rather, they must bridge structural holes in the in the right way, and the rightness of the right way depends on the epistemic structure of each of the otherwise disconnected subnetworks, comprising both what individual members know—declaratively and procedurally, implicitly and explicitly—and what each member knows that the others know.
The broker treads an epistemic landscape that has considerable interactive depth, and s/he succeeds (or fails) in large part as a function of his/her ability to identify and use the organized, intelligible, common knowledge cores of the interactive epistemic tangle that characterizes the fields s/he is attempting to bridge. This detailed understanding of the common knowledge cores of at least two distinct groups is integral to the broker’s ability to speak the “native language” of each one.
The brokering we are attempting—in real time—relies on our signaling credibly to members of each disciplinary group that we speak their native tongue well enough to be considered worthy interlocutors. This does not merely entail the ability to cite relevant material in the social networks and interactive epistemology literatures and to form correct sentences in the technical syntax of each field. It means being able to employ the specialized codes and knowledge structures that are common or almost-common knowledge within each field in a way that heeds the discursive practices and the justification and validation norms of both.
An epistemic picture of the cohesiveness required for genuine brokerage emerges: it describes the minimal epistemic preconditions for successful coordination and cooperation among individual members of the subnetworks being connected. We are nearly there in terms of describing brokerage as the construction of an epistemic bridge. What is missing is how the broker creates marginal incentives for members of disjoint “communities of practice” to “tune in” to each other’s codes, language systems, paradigmatic problems, and solution procedures. To this end, the broker must understand the canonical problems that in some sense “define the field,” not just the specific language systems for representing phenomena that are indigenous to each subnetwork, and s/he must establish a basis for “gains from epistemic trade” by tailoring the communicative acts that establish a bridge between fields. So, then, what goes into engineering the right epistemic bridge between epistemic game theory and social network analysis?
Interactive epistemology and epistemic game theory, taken together, represent a disciplined attempt to speak precisely and coherently about human beliefs and conjectures in order to explain, predict, criticize, or rationalize human actions and interactions. For epistemic game theorists, formalization is a tool rather than an end in itself. This distinguishes them from logicians, who are more interested in creating a complete and consistent axiomatic system that solves certain technical problems without regard for descriptive accuracy or phenomenological plausibility. Social network theorists are also interested in representations and methods for testing models that use them to explain and predict patterns of human behavior and interaction. The degree of formality and choice of formalisms employed by the two theory groups differ, but they share at least some epistemic objectives relative to which the usefulness of brokerage can be determined.
Key decisions for us as “epistemic bridge builders” in this case are these: what to formalize, how much to formalize, and when not to formalize. Were social network theorists willing (and able) to follow the discussions unfolding in epistemic game theory, they would likely contribute novel problems, dilemmas, paradoxes, and predicaments of direct interest to epistemic game theorists as a result of their direct empirical analysis of real human groups, organizations, and institutions. In turn, they may contribute appropriate ways of representing epistemic states that can be transformed into novel empirical measurement and observation instruments. They could, for instance, use the more elaborate modeling language of epistemic game theory to measure new properties of the structure and dynamics of human networks—such as epinets of various kinds—and examine how epinets influence tie formation and decay, and network dynamics more generally.
Standard semantic models of epistemic rationality and the structure and dynamics of interactive beliefs are based on parsimonious formalizations of human agents’ epistemic states (“states of the world,” “events,” “personal probabilities for events”) that map onto representational tropes (such as the unit interval in real numbers), thus allowing analyses of more logically complex concepts such as exchangeability, conditionality, and equilibrium—often with other substantive assumptions such as independence, common priors, and logical omniscience (Aumann 1976, 1989). The logical depth of such analyses comes at the cost of reduced intelligibility of the formalism by outsiders who may be interested in epistemic phenomena. It also comes at the cost of a loss of representational power that empiricists would rather avoid.
The semantic approach also raises difficulties for the coherent representation of certain epistemic states, such as unawareness (which we termed “oblivion”), that are more or less “self-evidently” relevant to everyday human interaction (Dekel, Lipman, and Rustichini 1998). As we observed in Chapter 1, a syntactic view of epistemic states that focuses on propositions about events, rather than events themselves, as proper arguments of knowledge states can help resolve such difficulties.
Making propositions the “stuff” that epistemic states are made of raises the possibility that traditional game-theoretic concepts (“information partitions,” “states of the world”), which do not translate easily into lay language or an alternative, less formal but still technical language, can be replaced by more intuitive concepts that function as templates for empirical analyses of the contents of networked agents’ minds. A successful epistemic bridge between social network and epistemic game theorists, then, will feature just the right degree of formalization of just the right quantities and their properties to show traditional empiricists the benefit of appropriating the more nuanced distinctions enabled by formal languages; it will also show purveyors of more complex formalisms the benefit of widening their current set of distinctions to include insights from the field.
A second important question to ask as epistemic bridge builders relates to the empiricism of a research practice. Epistemic game theory has evolved as an a priori discipline, spawned by researchers who questioned the logical bases and preconditions for equilibria in games played among ideally rational agents (e.g., Aumann 1976; Brandenburger 1992). Empirical studies of what actual agents actually know about other actual agents with whom they interact—or how different ways of knowing produce different interdependent action regimes—have never been part of the field’s activities or concerns. Social network analysis, in contrast, has never not been about empirical measurement of some property of a pattern of human relations. It may be that logicians are simply uninterested in the empirical analysis of epistemic structures and that empiricists are simply uninterested in logical analyses thereof (in which case, our effort is wasted).
It may also be that the sorts of questions epistemic game theorists want to answer are not addressed by social network theorists because, for example, there are no models that make the right distinctions or perhaps the sorts of novel questions about network epistemics that network theorists want to ask require understanding of a field that takes too much effort for uncertain returns. A successful epistemic bridge, then, will create a language that makes it possible for epistemic game theorists to tune into social network theorists’ empirical analyses and for them to generate insights for social network theorists to conduct novel empirical research.
Seeding Closure. Our work is not only an attempt to build a bridge, however; it is an attempt to seed and catalyze closure. It endeavors to create a common representational basis for crystallizing a network of diverse researchers into a more or less interdisciplinary research group. Research groups are communities of communication and practice. Semiotically speaking, a research community is a set of human agents who write scholarly papers and give talks for and to each other.
A scholarly paper—in an age of technical and linguistic specialization—is a communicative act that uses a code to translate “everyday” or “folk” language into “technical” language. Mastering the dual acts of encoding and decoding is an effortful and “scaffolded” activity (Clark 1988). It corresponds to achieving the standing to speak in the forum of an academic journal or conference by learning the specialized language systems and communication norms that all participants hold in common, and it represents a barrier to entry to the field.
Scaffolding refers to the embedding of technical discourse within a fabric of discourse produced by other members of the same community, such that the “meaning” of various code words can remain implicit. “Beliefs,” for instance, may be represented by probability weights associated with events or propositions about events, and may be governed by a logic of coherence and updating that is taken for granted by members of the research community.
This commonality of the “taken for granted” makes within-group communication both more reliable and more efficient: the meaning of technical jargon need not be communicated when it is transmitted and is also, in some sense, “secure” from eavesdropping by outsiders lacking similar training. This view of a professional or research network gives new meaning to the phrase “closure closes”: it “closes up” the range of possible participants to any dialogue or communication, and it “closes off” participation by outsiders.
Building closure in a new community of communication that spans elements of two distinct disciplinary subnetworks entails creating shared and common knowledge structures that give meaning to network echoes of one’s own written and spoken acts, even when they themselves remain implicit. Networks theorists are interested in making more precise distinctions that guide their understanding of brokerage, closure, trust, and status. Epistemic game theorists are interested in formal representations of interactive knowledge structures in scenarios where the outcomes of an individual’s decisions depend on the decisions of other individuals that accommodate “all of the differences that (could plausibly) make a difference” to the outcome of an interaction.
Achieving closure in a (new) subnetwork that includes members of both of these subnetworks depends on building a language for representing epistemic states—an EDL of the form outlined in Chapter 2 and elaborated in later chapters—that is subtle enough to allow new and useful distinctions yet precise enough to work with more formalistic approaches to prediction and explanation, and that can function as a regulative schema for the interdisciplinary dialogue that makes up the new network.
A regulative schema of this kind must supply the new network with commonly held rules or norms for adjudicating the usefulness of members’ contributions. Closure closes by foreclosing—in the sense of exclusion or disbarment—communicative acts that do not correspond to the set of commonly held communicative norms. It is only relative to such an (often) implicit set of exclusionary rules so that breaches and faux pas can be detected; this detection is essential to the mutual monitoring effect that network closure contributes to social capital.
Because the use of specialized language is almost always a tricky coordination game played among senders and receivers who “try out” and “critique” new ideas, the successful instantiation of this game depends on focal points—rules and norms by which the usefulness of communicative acts is gauged—that are themselves (almost) common knowledge among members of the community that makes up the network. It is for these reasons that we have spoken of and attended to an EDL first and foremost and only derivatively spoken of and attended to models and methods that its adoption enables.
Our Gambit. We have argued for the value of an empirical research program in “network epistemics” that aims to uncover the importance of complex epistemic states to what we mean by social capital and to the ensuing dynamics of networks. Social network theorists have a large accumulated base of empirical know-how surrounding the mapping of patterns of real interacting agents. Epistemic game theorists have a no less impressive set of tools for coherently describing the epistemic states of interacting agents. Bringing the two fields into mutually advantageous contact is nevertheless delicate: empirical correlates—and even interpretation—of the entities that populate formal models are not easily articulated.
Harsanyi’s (1968a, 1968b) well-known “theory of types,” for instance, is notoriously difficult to test empirically by mapping the type of agent onto a set of measurable variables; thus, its use is limited to studying the effects of certain assumptions about the rationality and conjectures of interacting agents rather than the descriptive accuracy of the assumptions themselves. Such limitations may not (always or yet) bother epistemic game theorists, but they bother social network theorists, who tend to be committed to a realist—rather than an instrumental—view of theories and models.
Our communicative bridge thus has to provide novel insight into the patterns of human interaction that are of interest to both network and epistemic game theorists. Having already rehearsed arguments for treating network “cohesion” through an epistemic lens, and shown its importance to the realization of brokerage and closure forms of social capital, we return to cohesion here but turn our attention to its role in the co-mobilization and coordination of networked agents. It is widely accepted among social network theorists that “network embeddedness” enhances the ability of agents to mobilize or coordinate their entire network or subnetworks.
Cooperation and collaboration, in turn, hinge sensitively on solving the sort of co-mobilization and coordination problems of central concern to epistemic game theorists. To the extent that embeddedness enables coordination and co-mobilization, then, the precise ways in which it does so deserve close attention—from both social network and epistemic game theorists.
Way(s) Forward: Why This Is Only a Beginning
We are as much at an end as we are at a beginning. If the foregoing is to serve as an application as well as an exposition of a theory and a set of models, then the EDL will be useful in furnishing a blueprint for inquiry into networks and interactions that generates its own “test cases” and “use cases,” along with its own set of new questions and dilemmas.
There is, nevertheless, a domain of inquiry and analysis that this book—for reasons of compactness—does not touch on, even though the EDL seems tailor-made for it. This is the domain of schemes and procedures that individuals (and “agents”—their formal counterparts) may use to make inferences from what they know or directly believe to what they infer. Moving from state spaces comprising events to state spaces comprising propositions that have truth values and truth conditions makes possible questions such as “What is the calculus of inference—the ‘logic’—that individuals are most likely to employ to synthesize new and valid propositions starting from propositions they believe or know to be true?” This question has several different forms, which take us in different directions.
Logical Form. What is the right logic or the right logics for representing the ways in which individual agents reason using propositions for the purpose of empirically studying behavior? Just as set theory and the probability axioms function as normative and prescriptive schemata for event spaces, so propositional first-order logic may be said to function as a normative schema for the procedures by which agents manipulate sentences. However, it is well known that first-order logic is a poor approximation for the grammatical form of natural language. For example, the axiom of choice states that any proposition is either true or false. But anyone, if asked “Is the king of France bald?” will (correctly) point out that there is no king of France, whereas a language processor constrained by the axiom of choice would be mightily challenged. This does not even take into account the fact that modal, subjunctive, and epistemic logics seem to form an integral part of what humans do when they reason, in propositions, about the world and about the ways other humans reason about the world, as we have seen.
Fruitful inquiry in this domain will be informed by work in the logic design that traditionally has taken place outside of epistemic game theory, network sociology, or microinteractionist sociology—for example, artificial intelligence (Fagin et al. 1995), which tries to determine the “right” logic to ascribe to an individual by direct experimentation (building programs and applications and gauging their usefulness) and by formal work in logic and language design. Syntactic state spaces “let the genie out of the bottle,” as they make possible—indeed, demand—inquiry that transcends the straitjacket of any specific logical form. Deviant logics, fuzzy logics, and many-valued logics may all have a role to play in the ensuing research.
Logical Depth. Quite aside from the most suitable logical form to ascribe to an agent is the logical depth to which that agent is supposed to be able or willing to reason. Recent work in rational choice theory (Lipman 1991) highlighted the problem that “logical omniscience” poses for producing realistic agent models. A logically omniscient agent (assume first-order logic) is supposed to know all of the logical consequences of what s/he knows. Thus, his/her knowledge should be closed under deduction. This is obviously an unrealistic requirement: an agent’s knowing the basic algorithm by which subsequent digits in the decimal expansion of e are produced does not entail that she knows all of the digits of e or that she is (rationally) required to know them or come to know them.
At the other end of the spectrum is the equally unpalatable alternative of imbecility, wherein an agent does not know any of the consequences of what she knows (Moldoveanu 2011). Alice may know that A entails B is true and may know that A is true, but she is not presumed to know that B is true or to be somehow held accountable for knowing, by inference, that it is. So she should not be presumed to know that her dentist is expecting to see her today at 5:00 P.M. from the fact that she knows that today is Tuesday and the fact that she knows that her appointment with her dentist is on (this) Tuesday at 5:00 P.M.
There is, then, an opportunity—or perhaps a requirement—to take the matter of logical depth seriously when we build epistemic models of networked agents meant to represent humans, in a way that heeds the constraints of “no imbecility” and “no logical omniscience.” And, since we are dealing with agents who may choose to reason to greater or lesser logical depths depending on the expected payoff(s) of doing so, we are well advised to make any model of inferential depth and reasoning we end up with responsive to micro-local incentives and constraints, in the same way that other models of choice are.
Informational Breadth: Awareness. In Chapter 2, we made a number of modeling choices regarding the representation of what agents know, how they know, what they know they know (or not), and what they do not know they do not know. We erred in favor of epistemic states at the individual level that are intuitive and easily interpretable in terms of measurement instruments. The representations we advanced were, however, not informed by a systematic account of the informational breadth of an agent’s knowledge base. The problem of finding “the right” informational breadth of an agent’s propositional state space has both theoretical and empirical ramifications.
On the theoretical side, the size of the propositional state space we deploy varies sensitively with the number of propositions we deem to be known, relevant, and so forth. That is because each proposition “about the world” generates a potentially very large number of propositions about what others know about the world (including what they know the agent knows and so forth). For this reason, “dimensioning” an epinet depends most sensitively on the number of propositions we allow into our state space.
On the empirical level, ascribing beliefs and knowledge to an agent is sensitively linked to the design of the instruments with which we measure epinets—surveys, questionnaires, direct observation of behavior, forced-choice experiments. Any empirical model of interacting and relating therefore depends sensitively on what we presume the individuals we model as agents know.
We have raised, potentially, at least as many questions in the last two pages as we answered in all those preceding them, which may befit both our aspiration to provide an “app” and our assurance that, in the epistemic realm, interesting questions are at least as important as the answers we find.