Pietraszewski advances a compelling computational theory of how the mind represents social groups. Here, we incorporate several key advances in network science and social network analysis – fields built upon a core set of theory and analytical tools for understanding the structure of social systems. In doing this, we propose an extension and reframing of Pietraszewski's computational theory of social groups that provides intuitive building blocks for generative models that (a) translate to observable patterning of social groups in real-world settings, (b) do not rely on conflict dynamics, and (c) easily scale to characterize higher-order group settings.

In line with core theory in sociology (Blau, Reference Blau1964; Homans, Reference Homans1958; Simmel, Reference Simmel1950), within Pietraszewski's framework any social behaviour is considered a transaction or exchange, with individuals acting based on the net rewards of such relations (Caplow, Reference Caplow1956; Emerson, Reference Emerson1976). In particular, these notions reflect key components of network theory, where the cost–benefit calculations of forming a social relationship may be weighted by the structure and dynamics of existing relationships (e.g., reciprocity or triadic configurations; Cropanzano & Mitchell, Reference Cropanzano and Mitchell2005; Doreian & Krackhardt, Reference Doreian and Krackhardt2001). The probability that individuals occupy a given role within the triad – for example, that they engage in conflict against a lone other – is likely determined by observable individual differences, or ancillary attributes. These ancillary attributes may be socially constructed categorical types that delineate group membership (such as race or ethnicity; Pietraszewski, Cosmides, & Tooby, Reference Pietraszewski, Cosmides and Tooby2014). Quantitative individual differences are equally likely to enter into the event calculus, with individuals' power, status, or resource-holding potential feeding into choices about engaging in conflict (or any other social behaviour; Redhead, Dhaliwal, & Cheng, Reference Redhead, Dhaliwal and Cheng2021; von Rueden, Redhead, O'Gorman, Kaplan, & Gurven, Reference von Rueden, Redhead, O'Gorman, Kaplan and Gurven2019).

Incorporating network theory, we reframe Pietraszewski's account as an instance of mixed “triadic closure” in “signed networks” (i.e., social networks that have both positive and negative relationships; Cartwright & Harary, Reference Cartwright and Harary1956; Heider, Reference Heider1958). A third, positive tie must be specified between two individuals to develop realistic generative models that reliably determine individual roles within any triadic configuration. This third tie could represent any number of social relationships or behaviours (such as kinship, friendship, physical proximity, food-sharing, or co-working) that enter the cost–benefit analysis. In the context of conflict, the tie is assumed to be “positive,” producing benefits or rewards within the “event calculus.” Conflicts are then assumed to be “negative” ties (i.e., that confer action costs). Complementary to Pietraszewski's formulation, we can consider a group as being a dyad or larger set of individuals connected by observable benefit-generating relationships.

Social groups may, therefore, be defined and represented in a way that does not rely on conflict dynamics. This logic can be applied to determine acts that generate benefits, with individuals transferring portions of a finite set of resources (e.g., food, labour, or money) based on the different token or event types within a triad. This may produce an extended number of triadic configurations – either open or closed – that could arguably be different summary representations of social groups (Block, Reference Block2015).

Including the content of a third tie provides concrete and flexible representations of social groups. This is because group membership – per Pietraszewski's definition – is fundamentally a property of a dyad. That is, within a given triad, two individuals must share a group membership. Our marking of group membership, therefore, does not solely rely on there being observable individual markers, but also considers the presence of social relationships. This framework can more easily be extended for group membership to be dynamic (i.e., not strictly fixed), and for individuals to operate within multiple group memberships. Adding in this further complexity may be fruitful, as individuals operate in complex, overlapping relationships (i.e., multilayer networks; Kivelä et al., Reference Kivelä, Arenas, Barthelemy, Gleeson, Moreno and Porter2014), and these relationships may also enter any cost–benefit calculations, allowing easy translation to observed empirical patterns. That is, in many real-world settings, individuals may face a decision to engage in a conflict between the members of two different social groups that they are members of. We can then extend the model to incorporate information about these different group memberships into the event calculus that may, for example, establish rules about roles and representations of groups when conflicts arise between kin, friends, or cooperative partners (Redhead & von Rueden, Reference Redhead and von Rueden2021).

Bringing this all together, our reformulation of Pietraszewski's theory provides a more principled approach to group settings that extend beyond the triad and can easily scale to bounded groups (or networks) of any size. If groups are not observed but ties are, we can calculate probabilities of individuals' roles within a triad, and these roles and relationships will aggregate up to modular population-level networks that will comprise two or more “communities” (e.g., social groups) that we can analytically detect (e.g., Amelio & Pizzuti, Reference Amelio and Pizzuti2016). That is, the information presented about ties may be used to determine group structure across any scale, and has been applied to large-scale international military data to determine groups of countries that form alliances and conflicts (Traag & Bruggeman, Reference Traag and Bruggeman2009). If communities are “observed” – as in the example in Figure 3 given by Pietraszewski – this process becomes somewhat analogous to a class of generative network models (stochastic block models for signed networks) that use observed group structure to determine and/or predict tie formation within and between groups (e.g., Doreian & Mrvar, Reference Doreian and Mrvar2009). In sum, by reframing and extending Pietraszewski's account to incorporate network theory, we are able to establish summary representations of social groups that do not rely on conflict, easily scale to group settings that go beyond the triad, and provide an architecture for generative models of social groups. Through this, a network approach provides a framework for linking abstract cognitive concepts to empirically observed patterns in real-world settings.