From the transformation problem to ABMs

11Within the history of MI, Coleman is usually associated with the so-called Coleman’s boat (see, in particular, Coleman [1987]). In Udehn’s terminology, the diagram visually illustrates a “weak” form of MI where macroscopic outcomes are seen as the result of concatenations of dynamic loops between structures and actions—as opposed to “strong” forms of MI where structural conditions, possibly pre-existing and out of the control of actors, are excluded from the focus of the analysis (Udehn, 2001: 292-306). Whilst, as clearly suggested by Raub and Voss (2017), Coleman should be credited with popularizing this non-reductionist form of MI more than for having invented it—strictly equivalent formulations can be found in Boudon (1986: 30), for instance, or, even earlier, among Dutch sociologists who in fact coined the term “structural individualism” (see, for instance, Wippler [1978: 143])—, it seems fair to say that Coleman discussed the main problem posed by the rigorous implementation of this form of MI more explicitly than others.

12Since his highly quoted article on the theory of action, Coleman (1986: 1320-1321) indeed emphasized that the most difficult theoretical problem for action-oriented sociologists is “[…] the means by which purposive actions of individuals combine to produce a social outcome […].” Coleman called this problem the “micro-to-macro problem” but he acknowledged that, in Europe, the expression of “problem of transformation” was often in use (see Wippler & Lindenberg [1987]). When discussing his diagram, Coleman then translated this general statement into a claim about which step of the explanation should require the highest attention (Coleman, 1987: 155). For him, this is the third one, “[…] for it is the third which moves back up from the individual level to the societal level.” Coleman’s chapter in fact is entirely devoted to showing how many strands of the sociological literature have developed explanations that fail fully to elaborate on the specific ways individual actions combine to produce a given social outcome. The failure, Coleman notes, consists in assuming that “simple aggregation” is enough to account for the micro-to-macro transition (Coleman, 1987: 157). The interdependence between actions is the missing element. Some years later, in the Foundations of Social Theory, he re-iterated the point and noted that most of economic theory, too, eludes the micro-to-macro transition by relying on the metaphor of the “representative agent” (Coleman, 1990: 10).

13Interestingly, the same critique simultaneously appeared in economics where Kirman forcefully argued that this metaphor “is not simply an analytical convenience […] but is both unjustified and leads to conclusions which are usually misleading and often wrong” (Kirman, 1992: 117). The reason is that the “representative agent” is a “fiction” (ibid., p. 125) that gives economists the impression of having solid micro-foundations while in fact the specific ways actors’ heterogeneity is transformed into complex macro-outcomes —like economic cycles or price dynamics—, through interdependent behaviors, is simply ignored (ibid., p. 132, 134). [2] It should be noted that, although without using the name, methodological individualism in sociology, too, can adopt this simplification. Boudon, for instance, defines “individualistic” statements as “[…] statements explaining why the ideal-typical individuals to relevant categories behave the way they did” (Boudon, 1998: 176). Only to consider “typical” individuals of a given category amounts to accepting that heterogeneity between individuals within the category can be ignored without consequences: the behavior of one actor is assumed to be sufficient to deduce the aggregate behavior of the whole. In contemporary advanced game theory, the construction of (a limited number of) “types” of players is indeed the standard way to account for actors’ potential heterogeneity in strategic behavior (see, for instance, Fehr & Gintis [2007]).

14To go back to Coleman, the interesting point of his analysis is that he formulated a precise hypothesis to explain why sociologists and economists have been obliged for so long to adopt such simplifying assumptions to handle interdependence and heterogeneity. According to him, the responsible is the “[…] little development of methods for characterizing systemic action resulting from the interdependent actions of members of the system” (Coleman, 1986: 1316). The absence of appropriate quantitative tools would have impeded formal analysis of theoretical models that include action interdependence (and heterogeneity), thus allowing sociologists to do only half of the job (Coleman, 1987: 157), and, on the other hand, as technique tends to feedback into ways of thinking (on this general mechanism, see Abbott, 1988; Abbott, 1990), not having a method suited for interdependence and heterogeneity, may have slowed down advanced theoretical elaboration along these lines.

15To my argument, what now matters is that, around 2000, ABMs entered the social sciences precisely as the methodological solution to study macroscopic patterns and trends from the bottom-up through the algorithmical implementation of hypotheses on the heterogeneous behaviors of heterogeneous interdependent actors.

16In one of the founding manifestos of the field, Joshua Epstein claimed: “Artificial society modeling allows us to ‘grow’ social structures in silico demonstrating that certain sets of microspecifications are sufficient to generate the macrophenomena of interest” (Epstein, 2007: 8). In a call for a stronger link between economics and ABMs, Farmer and Foley, after re-iterating the critique of the “representative agent” and the mathematical toolkit requiring such a simplification, stated: “[…] There is a better way: agent-based models. […] Done right, the agent-based method can provide an unprecedented understanding of the emergent properties of interacting parts in complex circumstances where intuition fails” (Farmer & Foley, 2009: 685, 686). In sociology, Macy and others explicitly recognize that one of the virtues of ABMs is that they “[…] have repeatedly demonstrated how the emergence of macro-social patterns out of micro-social interactions is not always a matter of simple aggregation” (Macy et al., 2011: 252).

17The connection between ABMs and MI was established through this path. MI fundamentally requires explaining macroscopic patterns as resulting from the combination of individual actions. The various ways in which individuals’ actions may be interdependent, and how this interferes with various forms of actors’ heterogeneity, however, make it difficult to study theoretical models in the absence of methods being able to treat both elements formally. ABMs were seen as the technique that could be used to face this challenge.

18Thus, almost naturally, a long list of statements explicitly conceiving ABMs as a “formal implementation of methodological individualism” (ibid.) has appeared over the last few decades (see, in chronological order, O’Sullivan & Haklay [2000: 1413-1414]; Sawyer [2004: 263]; Manzo [2007: 5]; Neuman [2008]; Macy & Flache [2009: 246]; Wan [2011: 188]). These statements are not all based on exactly the same understanding of MI; nor do all authors see the link between ABMs and MI in a positive way. But even those—like O’Sullivan and Haklay (2000: 1413-1414), and Sawyer (2004: 263)—who consider that framing ABMs as a tool for MI may restrict ABMs potentialities do not contest that ABM has a privileged connection with MI in that it allows this perspective to implement its quest for the micro-foundations of social regularities.

The “definition battle”

26The four articles that I have analyzed share a first general, but fundamental, point: they all premise their analysis of the link between ABMs and MI on a specific understanding of MI. The authors have opposite orientations on the status of the selected definition, however.

27The contrast is well illustrated by Marchionni and Ylikoski (2013: 331)—who state that “[…] the debate over the proper definition of methodological individualism is a distraction from the real methodological issues”—and, on the other hand, Di Iorio and Chen (2019: 4)—who claim that “[…] within the frame of philosophical analysis, the problem of the compatibility between MI and ABS cannot be satisfactorily analyzed without considering the debates on the proper definition of MI, i.e. without assuming that the substantial aspects of this problem are relevant.” Both perspectives—which I suggest to call respectively “stipulationist” and “realist”—seem problematic.

28Marchionni and Ylikoski implicitly ask the reader to accept their starting definition of MI as a convention that one must stipulate for the sake of the argument and/or in order to be understood within a certain academic circle. This “stipulationist” stance is problematic because the answer to the question of whether or not ABMs and MI are intrinsically connected in fact crucially depends on the starting definition of MI. Thus, why should one regard as convincing the conclusion of an argument that is premised on a definition of MI that sounds acceptable only for a specific audience? Marchionni and Ylikoski’s claim could also be read as meaning that any starting definition of MI should only grasp the essential features of this doctrine. This view would be in line with Zahle and Kincaid’s starting point according to which “the key MI claim” is that “explanations should be in terms of individuals” (Zahle & Kincaid, 2020: 2).

29However, Zahle and Kincaid’s paper itself shows that several interpretations exist of what an individualistic definition is so that the proposed definitional strategy raises the problems of knowing if one has considered all the possible interpretations and of establishing which one better corresponds to “the key MI claim.” For all these reasons, Di Iorio and Chen’s view seems more transparent in that it overtly raises the issue of the definition of MI rather than trying to bypass it. The shortcoming of their approach, however, is the implicit conviction that some interpretations of MI are more correct than others.

30Ultimately, the stipulationist view—according to which only the essential features of MI (as seen within a certain audience) matter in discussing whether or not ABMs are individualist—like the “realist” one—according to which it is necessary to establish the proper interpretation of MI—underestimate the difficulty of reaching a consensus on how MI should be interpreted. Detailed historical investigations of MI concluded that “methodological individualism exists in a bewildering number of different versions” (Udehn, 2001: 346). Even a single author—like Popper (see Udhen [2001: ch. 7])—or specific variants of MI—like “rational choice individualism” (ibid., ch. 10)—can in fact be received differently. This is not to deny that progresses in understanding what MI is can be made. But this progress may realistically come precisely from accepting the existence of a variety of versions of MI and the absence of a “true version of this doctrine” (Udehn, 2002: 480).

31This lesson is highly consequential for the debate on the connection between ABMs and MI. The existing analyses all premise their assessment of whether or not ABM can be seen as an implementation of MI on a specific understanding of MI without considering the intrinsic difficulty of finding an agreement on how MI should be interpreted. This strategy can only lead to conclusions that are likely to remain controversial: it only suffices to disagree on the chosen definition(s) of MI to be tempted to reject the conclusion on the nature of ABM.

The “ontological battle”

32The difficulty of agreeing on the proper definition of MI is reinforced by a second, and deeper, problem. When arguing in favor of or against a given understanding of MI the authors of the articles under examination are in fact discussing what kind of entities can legitimately be inserted within a given theoretical model. This is the defining feature of what I have termed the “specific” interpretation of MI in the introduction. Now, to defend the legitimacy of this or that entity, the authors inevitably end up with developing, more or less explicitly, an argument on the existence of these entities, and, based on this, on their explanatory primacy. Thus, no matter if this is explicitly endorsed or not, the dispute over the proper content of a MI-inspired model, shifts silently and smoothly into an ontological dispute.

33Similarly to the definition problem, the authors animating the debate on the link between ABMs and MI display opposite views as to the impact that ontology may have on their conclusions. Marchionni and Ylikoski regard MI as “a thesis about explanation, not about ontology,” and claim that ontological arguments are not directly consequential for theses about explanation (Marchionni & Ylikoski, 2013: 332). [8] Di Iorio and Chen challenge this interpretation of MI and claim that the proper understanding of MI—i.e., the non-reductionist variant, in their view—is based on explicit “ontological individualism” (Di Iorio & Chen, 2019: 11). [9]

34Explicitly admitting the potential relevance of the ontological level seems a more defensible perspective. A commitment to the disjunction between the explanatory and ontological levels is indeed likely to be violated in practice as soon as the argument is pushed farther. Zahle and Kincaid well illustrate this potential inconsistency when, after arguing that ABMs are not limited to individualistic explanations, they ask whether ABMs should be still used only to provide individualistic explanations. To challenge one of the possible arguments from the individualist camp in favor of this thesis—namely, that “social phenomena are causally inert”—, they note:

35

[…] as social properties supervene on individualist properties, the latter supervene on biological properties that, in turn, supervene on chemical properties that supervene on physical properties. […] As a result, individualist properties, qua being supervenient, are causally inert too and MIs must admit that it isn’t legitimate to offer individualist (causal) explanations either (Zahle & Kincaid, 2020: 7).

36Although the discussion is framed in explanatory terms, the argument ultimately (but implicitly) is based on the assumption that certain entities of the social and physical realm exist and that these entities are organized in a clearly identifiable hierarchy. This is an ontological debate, not an epistemological one. However, when ontology is explicitly taken into account, as in Di Iorio and Chen’s approach to MI, problems that are likely to trigger further debates that are difficult to settle also arise. Given the focus of my discussion, let me illustrate this point by evoking one of these debates, namely the vexata quaestio of the existence of individuals and of their analytical primacy (for a detailed analysis, see Goldthorpe [2006: ch. 8, 174-183]).

37Within MI, the fact that only individual actors exist is usually regarded as something that goes without saying. To express this point, Hedström proposed the following metaphor: “The causal efficacy of actions would be readily seen if we were able to press a pause button that suddenly froze all individuals and prevented them from performing any further actions. All social processes would then come to an immediate halt” (Hedström, 2005: 28). Similarly, Abell claimed: “The substantive point is that the motor energy of individual actions is necessary for the creation of any pattern of social causality” (Abell, 2003: 259; emphasis in the original). To those authors, it is obviously that the “energy” has its origin in actors’ beliefs and intentions but this does not go at all without saying for scholars of other orientations. Sperber, for instance, formulates this concern as follows: “Individual agency is taken as a primitive in this approach, rather than as a tentative construct that should be unpacked and possibly questioned by psychology and biology” (Sperber, 2011: 64). He remarks that, empirically, “no primary reasons to give pride of place to intentions among the cognitive determinants of behavior;” “attention or memory,” he noted, may equally claim a primary role (ibid., p. 71). From a relational (rather than sub-individual) perspective, Padgett and Powell (2012: 2) formulate a similar objection when they remark that, within MI, actors’ preferences are not further unpacked. [10]

38In sum, as these contrasting statements show, the “definitions” and the “ontological” battles are inevitably related. The defense of interpretations of MI that are specific requires the justification of the legitimacy of the postulated entities, and, to argue in favor of this legitimacy, one is ultimately required to make ontological assumptions explicit, which in turn raises issues that are difficult to ascertain empirically. For these reasons, if the question of the connection between ABMs and MI is addressed by starting with a specific definition of MI, the answer to the question is likely to inherit all the difficulties related to the chosen definition. The assessment of the link between ABM and MI thus remains unstable because it entirely depends on the extent to which an observer agrees on the posited (specific) account of MI.

ABM’s generic properties

42Behind the endlessly diversity of ABMs in terms of macroscopic outcomes, entities, connections, dynamic processes and levels of analysis involved, existing ABMs in fact share fundamental properties that are independent from the specific content of each model. [11] Among these properties, five of them constantly recur across applications. I propose to call them “level-change” propensity, “recursivity,” “fractality,” “generalized interdependence,” and “heterogeneity.” Let me briefly discuss each of them in turn.

43By “level-change” propensity, I refer to ABM’s flexibility in understanding a given pattern in terms of mechanisms that are conceptualized (by the modeler) as located at a different level of analysis. “Level-change” can concern problems where a macro-pattern needs to be understood in terms of micro-patterns (“upward” level-changes) as well as problems where a micro-pattern is conceived of as being impacted by some macro-patterns (“downward” level-changes). For instance, if one wants to understand the specific location of a pedestrian (low-level) within a given physical space (high-level), an ABM can be used to model the way the structure of the environment (macro-patterns) impacts on the likelihood of the pedestrian being in a given point in the space at some point in time (micro-pattern) (Zheng et al., 2009). What matters is that the modeler thinks that moving from one level to another can generate some explanatory gain—whatever the content of these levels and/or the “direction” of the movement are. “Level-change” propensity should be analytically distinguished from the operation of micro-reducing macro-patterns. ABMs are indeed often perceived simply as a tool to demonstrate that macroscopic patterns in fact do not have sui generis properties and that it suffices to understand the behaviour of the parts to explain the properties of the whole (see, for instance, Little’s distinction between “generativity” and complexity [Little, 2016: ch. 5]). Quite the contrary, an ABM is often built to show how moving up and down across levels, i.e. “level-change” propensity, can help to understand the origin of properties that no low-level entity can possess on its own (for an example in the field of social stratification, see Manzo [2013]).

44ABM’s “level-change” propensity is not a static feature. Within an ABM, moving up and down across sets of entities conceived of as located at different levels of analysis is an operation that is repeated iteratively. This is what can be called “recursivity,” which I regard as the second generic feature of an ABM. Recursivity is a direct consequence of the fact that ABM is a simulation-based method. There is no simulation without computational time elapsing. Concretely this means to iterate a set of rules a certain number of times. The intrinsic dynamic nature of an ABM—see, on this point, Miller and Page (2007: 80, 81, 83, 84)—thus implies that the procedures defining the entities’ behaviors trigger a chain of activities, reactions, and updating that constitute the ultimate higher-level outcome of interest through a cascade of loops composed of upward local aggregations and downward effects. As we have seen earlier, the capacity to handle “upward” level-changes was the initial motivation for adopting ABM in sociology, in particular within the MI tradition (see section: The origin of the link between ABM and MI). This should not hide however the fact that, within an ABM, “moving up” is never disconnected from “moving down:” iteratively looping levels over time, i.e. recursivity, is the second deepest generic features of ABM.

45The third one is its fractal nature. By this I refer to ABM’s capacity to realize “level-change” propensity every time one wants to decompose a given level of analysis into more elementary mechanisms. This property is another consequence of the basic unit on which an ABM is based, i.e. computational objects. Within the object-oriented paradigm, everything can be “objectified.” This means that, as soon as a given class of objects is created to represent a given set of entities/properties/activities/connections, another class of objects representing another set of entities/properties/activities/connections that is regarded as internal to the first set can be created to better ground the behavior of the first posited class of objects. For instance, if a given class of objects represents the properties and the activities of a population of actors (still the most frequent use of ABMs in social sciences), the brain functioning of each actor may be modeled by means of another class of objects representing neurons, their properties, activities, and connections; and one can let the two classes of objects depend on, and communicate with, each other. This is done, for instance, when an agent-based model at the actor level is coupled with an agent-based model at the infra-actor level (through the use of artificial neural networks—see, for instance, Hayward [2006]).

46The fourth feature that recurs within ABMs across disciplines is the dependence of one entity’s state(s) and behavior(s) on other entities’ state(s) and behavior(s). This is possible because computational objects can communicate with each other through message passing at the deep level of computer’s memory addresses (Hummon & Fararo, 1995). In fact interdependence comes under three different forms that must be distinguished analytically. First, entity interdependence can be mediated by a global aggregate, namely an outcome derived from the behavior of all entities present in the artificial population that feedbacks into the subsequent behaviors of each entity. Second, entity interdependence can be mediated by a local aggregate, namely an outcome derived from the behavior of all entities to which the focal entity is connected that feedbacks into the subsequent behaviors of the focal entity. Third, when the relevant input for a given entity comes from a single other entity, entity interdependence is purely dyadic. In the latter two cases, the relevant entity’s neighborhood can be defined on a spatial and/or relational basis. In any minimally complex ABM, these forms of interdependence combine in various ways. In this sense, I propose to call “generalized” interdependence the fourth generic feature of ABM.

47Finally, heterogeneity clearly is a fundamental generic property of this method. ABM’s capacity to handle heterogeneous entities again comes from the underlying object-oriented nature of the technique. Objects can be heterogeneous in a variety of ways (Epstein, 2007: ch. xvi, 7). First, objects within the same class, whilst by definition sharing the same properties (and activities), are such that these properties can get different values. Second, objects in different classes by construction possess different types of behavior. Third, by playing with the objects’ scheduling, objects can be represented as being heterogeneous in terms of behavioral sequences (i.e. the time at which a given behavior is realized). Finally, as I remarked at the beginning of this section, objects are conceptually “empty,” meaning that, by playing with variables, vectors or other data structures, the objects’ states can model any attributes of the entities of interest, and, by creating logical and numerical functions over these states, the objects’ “methods” can be used to model every activities of these entities. As a consequence, heterogeneity can also take the form of multiple classes of objects representing different types of entities at different levels of analysis, such as organizations and actors (see Ferber et al. [2005]).

48It should now be clear that “level-change” propensity, “recursivity,” “fractality,” “generalized interdependence,” and “heterogeneity” have a fundamental feature in common: they are not defined with reference to the specific entities, behaviours, connections, and levels of analysis a given model may want to represent. This explains why these properties travel across ABMs in different fields. These properties are “generic” because they are transversal to models representing an infinite variety of specific entities and relationships among them. These five properties can thus be seen as the ingredients that an explanatory problem should have to justify the use of an ABM irrespective of the specific entities involved by the problem at hand. Could one defensibly argue that MI can be interpreted along similar lines?

ABM’s generic properties and MI

49The way James Coleman comments on MI in the Foundations of Social Theory (and related minor writings) constitutes an interesting starting point to assess this hypothesis. Coleman’s understanding of MI has indeed received radically different interpretations, some scholars seeing it as the best example of micro-reductionism (see, in particular, the harsh critique by Jepperson & Meyer [2011]) while others reading it as the most structuralist variant of MI that admits “social wholes, in the form of structures of interrelated positions, which exist independently of the particular individuals who happen to occupy these positions” (Udhen, 2001: 347). In this sense, as Coleman’s MI is seen to span from the “strongest” to the “weakest” forms of MI, it constitutes a useful benchmark to provide a first assessment of the presence of ABM’s generic properties across a variety of possible specific accounts of MI. [12]

50As to “change-level” propensity, which I defined as ABM’s requirement of treating an explanatory problem by moving up and down across levels of analysis, Coleman clearly expresses this idea when he states that his mode of explanation “[…] of the behaviour of social system entails examining processes internal to the system, involving its component parts, or units at a level below that of the system” (Coleman, 1990: 2, 5). Some pages later, he even detaches the principle of not remaining at the same level of analysis from a specific type of entities that one should assign by construction the “lower” level (Coleman, 1990: 5). [13]

51To the objection that Coleman would be in fact emphasizing here only one type of “level-change,” namely “top-down” (whereas, for ABM, I stressed the equal importance of “downward” and “upward” level-changes), a response can be found in another remark where he clearly indicates that system-level regularities should be thought as generated by chains of macro-to-micro constraints and micro-to-macro aggregative events. [14] This principle also clearly implies that Coleman sees moving up and down across set of entities conceived of as located at different levels of analysis as an iterative operation, a feature that I call “recursivity” and I regarded as ABM’s second generic property. [15]

52The third property, i.e. “fractality,” which I defined as the possibility to operate “level-changes” every time a given level of analysis is required to be decomposed into more elementary mechanisms, is also visible in Coleman’s comments on MI when he explicitly acknowledges that the concept of “system behavior” is relative, its content is not defined a priori once and for all, and the principle of looking into the internal component of a given set of entities located at a given level of analysis is independent from the specific types of entities and level at hand. [16]

53“Generalized interdependence,” the fourth generic property that I proposed for ABM, is the easiest feature to find within MI. ABM was imported within MI as the tool that finally enabled social scientists to handle interdependence structures potentially involved in the “transformation” of the “micro” into the “macro” (see section: The origin of the link between ABM and MI). Coleman explicitly stresses the importance of conceptualizing a variety of forms of interdependence that goes far beyond simple dyadic interactions among actors (Coleman, 1990: 20-21). Moreover, he makes the important (but unnoticed) observation that, in some cases, the “macro-to-micro transition” is contained within a given interdependence structure, which is in full agreement with the proposed idea that an ABM is designed to model interdependence both as an aggregation mechanism and a source of constraints.

54The last generic feature that I suggested to be at the heart of ABM is “heterogeneity.” Similarly to interdependence, the quest for a tool able to treat how heterogeneity dynamically travels through interdependent actions, thus affecting macroscopic patterns in not-easy-to-predict ways, was at the origin of the adoption of ABM by MI-oriented economists and sociologists. Despite the absence of an explicit representation of heterogeneity within his acclaimed diagram, Coleman’s overt attack on the metaphor of the “representative agents” (see section: The origin of the link between ABM and MI)—an analytical strategy that ignores actors’ heterogeneity—clearly suggests that he regarded this element as a crucial explanatory ingredient for MI-based theoretical models. [17]

55In sum, Coleman’s meta-reflection on MI is clearly characterized by a number of principles that hold independently of the specific type of entities one assigns a given level of analysis, and even independently from the specific levels of analysis a given explanatory problem may involve. These principles astonishingly resemble the features—namely, “level-change” propensity, “recursivity,” “fractality,” “generalized interdependence,” and “heterogeneity”—that I suggested as the defining generic properties of ABM. As Coleman has been equally well interpreted as the most extreme “micro-chauvinist” (see Jepperson & Meyer [2011: 57]) or the most accomplished “structural individualist” (see Udehn [2001: 292-306]), it seems fair to consider him as speaking for a variety of MI accounts. In this sense, the resemblance that I found between ABM’s and MI’s generic properties within his master work can be regarded as a first test of the working hypothesis that ABM’s generic properties are transversal to “strong” and “weak” forms of MI, and that, consequently, MI can legitimately be conceived in terms of (these) generic properties (i.e. as a generic instrument) rather than in terms of specific entities (and levels of analysis).