3.1. Structural similarity between map and territory

One way of arguing for the epistemic value of NDG models is to claim that “the aspects of the models here that lead to disadvantage are features of the real world” (O’Connor and Bruner Reference O’Connor and Bruner2017, 115). According to this view, the cultural red king effect offers a “how-potentially” story for the emergence of discrimination in academia, meaning that it is an “effect that has the potential to really occur” (O’Connor and Bruner Reference O’Connor and Bruner2017, 116). Bruner (Reference Bruner2017) advances such a view, albeit in a carefully hedged formulation:

At the heart of this argument is the claim that there exists an important structural similarity between the map and the territory. It is useful to compare this claim to Michael Weisberg’s (Reference Weisberg2012) discussion of similarities between models and their target systems. Weisberg differentiates between attributes and mechanisms of each and argues that “models are similar to their targets when they share many, and do not fail to share too many, features that are thought to be salient” (794). His primary example is Schelling’s (Reference Schelling1978) chessboard model of neighborhood segregation and he argues that “Schelling’s model would be informative if it shared important features with the real population dynamics of Philadelphia” (ibid.). He also links this similarity between model and target system to the difference between a how-possibly explanation and an account that is part of the actual explanation of a target phenomenon (786). In the case of NDG models, an example of an attribute would be the occurrence of discrimination, and examples of mechanisms would be the structure of a bargaining-interaction, the updating of a strategy, or the dissolution of a pairing. There seem to be good reasons to doubt that fundamental mechanisms of the model are shared by the target and, conversely, seemingly essential mechanisms of the target are absent from the model.

The first question is whether the way that workload and authorship are negotiated in academic collaboration is the same mechanism as NDG bargaining. In NDG bargaining, each participant makes a hidden demand, then they are revealed and if the sum of demands is too high, the collaboration fails. There is no chance for reacting to the demands of the other by adjusting one’s own demands, so this form of bargaining arguably does not meet the minimum criteria for how we define a negotiation. Furthermore, the way actual workloads and authorships are decided can take a variety of forms. Sometimes the most powerful collaborator just decides the order of authorship, or it is determined by existing, but potentially implicit, social norms. Sometimes coauthors make a good-faith attempt to determine who needs publication credit the most and who is best suited for each part of the work. It is not a priori obvious that actual academic collaborations are generally organized through utility-maximizing bargaining at all.

Assuming that individual utility-maximization is the driving force behind this interaction, there seem to be strong constraints on real-world academics that render successful strategies in the model completely unviable. If the only risk were the failure of this particular project, as it is in the model, individuals might learn a strategy for optimizing the work/credit ratio. But in reality, the effects of demanding something your coauthors are unwilling to grant you go far beyond the paper in question. The crucial difference is that agents in the model only have two strategies, one for in-group and one for out-group interactions. In stark contrast, human beings remember past interactions with specific individuals and adjust their behavior accordingly. In the model, an agent can just make high demands to see what happens and learn from that, with no consequences beyond this instance of negotiation. In reality, making high demands that end up wrecking a potential collaboration will reduce your chances for future collaborations, thus making a whole category of learning-trajectories that can occur in the model unfeasible. Because the utility of any single collaboration is not just individually relatively unknown to actual academics but also the opportunities for future collaborations and the effects that these future collaborations will have on one’s career both depend in part on the outcome of the present project, it seems unrealistic to assume that academics have accurate knowledge of the utility of successful collaborations before they embark on the next one.

Neither is it obvious without further investigation that the kind of learning that happens in NDG models is at all possible within the structure of professional academia. In his discussion of related game theoretic claims about the evolution of morality, Arnon Levy (Reference Levy2011) distinguishes between two kinds of learning, success learning and source learning. In success learning, “individuals adopt new behaviors in a payoff-driven fashion,” where payoff is understood as “broadly akin to utility” (179). This notion of success learning encompasses not only a cultural interpretation of the replicator dynamic but also the kind of learning used in the agent-based NDG models where agents either adopt the strategy that would have given them the highest payoff last round or adopt the strategy of another more successful agent. This is contrasted with source learning, where “one follows in the footsteps of salient individuals,” for example, “parents, teachers, superiors, celebrities” (180). Levy argues that source learning has been unduly neglected in the modeling of the emergence of morality citing arguments from psychology and anthropology that emphasize the importance of source learning (181–82). Because Levy focuses on the same kinds of models that produce the cultural red king effect—discussed as “divide the cake” games, which is a synonym for NDG—his points may be relevant for our discussion too (172). Perhaps a far stronger claim can even be made in the case of academic collaboration: Source learning sounds plausible, whereas success learning sounds implausible. In Rubin and O’Connor’s (Reference Rubin and O’Connor2018) models, the “[s]imulations were run for 1,000 rounds” (386). In real academia, the opportunities for learning how to navigate collaborations successfully is several orders of magnitude lower. Even if junior academics had complete knowledge of their payoffs in any potential collaboration, the need to get it right very quickly makes it more plausible that learning is largely and especially at first a matter of source learning.

At first glance, Bruner’s (Reference Bruner2017) description seems to apply reasonably well to both map and territory: “[I]ndividuals (i) can condition their behavior on group membership and (ii) learn to act in a way which promotes their self-interest in strategic contexts” (426). However, instead of shared features, a closer look reveals very different mechanics at work in the NDG models and our (pretheoretic) understanding of academic interactions. We trust that the San Francisco Bay Model informs us reliably about the effect of potential infrastructural interventions because the model is “three-dimensional and proportional” and filled with actual water (Potochnik et al. Reference Potochnik, Colombo and Wright2019, 89). Because these two elements and the way in which they are combined all appear very similar to the real San Francisco Bay, we trust that it is a reliable map of the territory. In contrast, none of the fundamental aspects of NDG models discussed previously individually appear to be very similar to their counterparts in the target phenomenon.

3.2. Empirical support

A further strategy for supporting the epistemic value of the cultural red king effect focuses on empirical confirmation. Mohseni, O’Connor, and Rubin (Reference Mohseni, O’Connor and Rubin2019) take this route and motivate their approach like this:

This sounds highly promising, as it seeks to answer the question “can the cultural Red King really occur in human groups” (ibid.)? However, the import of this experiment for our concerns is diminished by the fact that it consisted in human subjects playing the NDG. The “results show that minority groups do end up at payoff-inferior outcomes with significantly greater frequency,” so the cultural red king effect occurs not just in computer simulations of the NDG but also when real humans play the NDG (16). We now know that NDG models can reliably inform us about the dynamics of real-world NDG, but we are not really interested in that. Our main question is still open: Which human practices besides NDGs can be usefully modeled by NDG, and is the process of distributing the workload and authorship of academic collaborations one of them?

Empirical investigation of this main question seems both far more important and far more difficult. Indeed, O’Connor and Bruner (Reference O’Connor and Bruner2017) argue that part of the epistemic role of such models is that they “can direct our attention to an effect that has the potential to really occur, and prompt further investigation, both theoretical and empirical, into this effect” (116). Similarly, Rubin and O’Connor take their results to “generate a theoretically well-grounded hypothesis for why we see such patterns” in epistemic communities (400). Although it is not made explicit in the paper, it seems plausible that the hypothesis they have in mind would go something like “the cultural red king effect causes some of the discrimination we observe in academic collaboration practices.” An important task for cultural red king research would then be to devise ways of rendering this hypothesis empirically testable. Rubin and O’Connor note that “[i]t is notoriously difficult to generate empirical data testing cultural evolutionary pathways,” which is why they “instead employ game theoretic models” (382). While an “empirical turn” in the literature on formal models within philosophy of science—as called for by Edouard Machery (Reference Machery2022)—might improve their epistemic credentials, the amount of additional work this would require seems to negate a large part of what makes these models so attractive in the first place: their extreme simplicity and tractability.

3.3. How-possibly explanations

One common phrasing in the literature on the cultural red king effect casts it as a how-possibly explanation for discrimination occurring in human social interactions. Bruner takes it to “demonstrate how minorities could possibly come to be systematically disadvantaged” (414). O’Connor and Bruner (Reference O’Connor and Bruner2017) describe it as “a version of ‘how-possibly’ modeling—it specifies under what conditions a surprising effect can possibly arise” (116). They also state that they “use evolutionary game theoretic methods to show that minority groups can end up disadvantaged in academic interactions like bargaining and collaboration as a result of this effect” (101). What kind of possibility do these phrases express? And do they all express the same kind?

To clarify this subtle and vexing question, we can import a distinction between causal possibility and factual possibility made by Ylikoski and Aydinonat (Reference Ylikoski and Emrah Aydinonat2014). They are contributing to a long-standing discussion in the philosophy of economic models on “the epistemic import of highly abstract and simplified theoretical models” (19). Their main example is Schelling’s (Reference Schelling1978) chessboard model and many of the moves made in this debate are identical to those in the debates about the cultural red king effect, making their work very useful for our purposes. To distinguish between different kinds of how-possibly explanations, Ylikoski and Aydinonat introduce the notions of causal and factual possibility. “First, there is the question: if the scenario had taken place, would it have produced the effect to be explained? Let us call this causal possibility” (26). Causal possibility is determined based on our “general causal knowledge” (ibid.). In contrast, factual possibility also requires “compatibility with facts known about that particular causal history” (ibid.). A scenario can only be considered factually possibly if it “is consistent with the facts we know concerning the particular explanandum phenomenon at hand” (ibid.). Only if a scenario is both causally and factually possible can it be “considered a possible explanation of the particular fact at hand” (ibid.).

If we interpret part A of Rubin and O’Connor (Reference Rubin and O’Connor2018) as a scenario that offers a how-possibly explanation for a particular occurrence of discrimination in academic collaboration, we could judge that it is causally possibly: If the scenario had taken place, the cultural red king effect would have occurred. However, we could also judge that it is not factually possible: Part A starts with a population of individuals who behave in completely nondiscriminatory ways, and we know with reasonable certainty that no present-day academic collaboration network developed from a past stage in which academia was free from discrimination based on race and gender. Our takeaway from this is that not all how-possible explanations are also factually possible. It is not enough to outline an explanation that is causally possibly for it to be “considered a possible explanation of the particular fact at hand” (Ylikoski and Aydinonat Reference Ylikoski and Emrah Aydinonat2014, 26). It also has to be consistent with the known facts about the particular situation and its causal history.

I have argued that the scenario in part A does not meet Ylikoski and Aydinonat’s criteria for a “possible explanation of the particular fact at hand” (ibid.). But it might be the case that this is a more general limitation, which includes all models in Rubin and O’Connor (Reference Rubin and O’Connor2018) and all game theoretic models of comparable complexity. For example, all interactions between two “agents” in Rubin and O’Connor (Reference Rubin and O’Connor2018) are both fully private and anonymous. Both participants can use the outcome to adjust one of their own two strategies, but neither of them can take in information about the other’s behavior as tied to a specific individual, nor can anyone else in the network. This is fundamentally and importantly never the case in real academic interactions. Of course, much more complex models could be built, but changing them dramatically enough that they meet Ylikoski and Aydinonat’s criterium of “factual possibility” would arguably make them a different kind of model altogether than the NDG.