In the target article, Pietraszewski proposes a computational theory of social groups that is at its core subjective, defining a group in terms of a single individual's representation of it. However, social groups are not subjective: Consider that a person cannot through their own beliefs unilaterally create or destroy a group, or change an established group's membership. Rather, group membership is intersubjective, dependent on representations that are (at least in part) shared among members of the ingroup or outgroup (Dennen & Wieland, Reference Dennen and Wieland2007; Eden, Jones, Sims, & Smithin, Reference Eden, Jones, Sims and Smithin1981; Matusov, Reference Matusov1996; Stahl, Reference Stahl2016; Zlatev, Reference Zlatev2014). The intersubjective nature of groups gives rise to important phenomena in the context of conflict that cannot be explained by Pietraszewski's computational theory because they arise only when people's representations of group membership diverge or are believed to have diverged.

Consider the following examples often observed in conflicts within online communities:

1. (1) A person wrongly believes they are part of a group, whose members keep up the charade until an ultimate act of (apparent) betrayal that reveals the false belief (e.g., cyberbullying).

2. (2) A person becomes romantically involved with a defrauder, scammer, troll, or person with some other ulterior motive (e.g., online dating romance scams; catfishing).

3. (3) A person undermines a group by pretending to be a member of it while covertly acting against its interests (e.g., online sock puppetry and astroturfing; cyber espionage).

4. (4) Two factions of a group each reject the others’ sincerely held beliefs regarding membership in that group, cleaving it in two (e.g., schisms).

5. (5) An aggressor creates a self-fulfilling prophecy when, failing to distinguish between groups, aggresses against them jointly, causing the groups to merge (e.g., in the emergence of some unity movements).

6. (6) One person does not believe a particular group exists, whereas another person cherishes their membership in that group (e.g., identity pride and erasure).

7. (7) A person is unaware of having been banished from a group or silenced within it (e.g., hell banning and shadow banning).

Analyzing any of these phenomena by considering only one individual's representations of group membership would fail to capture their essence. For example, in the case of astroturfing (Leiser, Reference Leiser2016; Sisson, Reference Sisson2017; Zhang, Carpenter, & Ko, Reference Zhang, Carpenter and Ko2013), where a purported grass-roots organizer is, in fact, the agent of a sponsor working against the cause, it is not enough for the group or the public to believe the agent is a member of the group. Nor is it enough for the sponsor or its agent to believe they are not a member. Rather, it is the divergence in understanding about the agent across the sponsor, the agent, the public, and other interested parties, which gives rise to the phenomenon and the harmful consequences to the cause that are associated with it.

Here, I put forward a computational approach that extends Pietraszewski's theory to accommodate phenomena dependent on the intersubjectivity of groups.

The extension begins by zooming out from the focal individual studied by Pietraszewski to consider the representations of all three individuals in the triad (or more generally, any interested parties). Minimally, this is accomplished by endowing each individual with their own representation of the kind put forward by Pietraszewski in terms of which agents will tend to fill the group-constitutive roles. Doing so requires no new computational machinery and permits analysis of diverse phenomena where these representations diverge. For example, in the case of shadow banning, a person is exiled from an online community without their knowledge by a moderator who causes the exiled person's communication to be invisible to other community members (Cole, Reference Cole2018; waxpancake, 2009). It is common for the shadow-banned individual, the moderator, and other community members to each have their own understanding: The shadow-banned individual believes they are part of the group, the moderator believes they are not, and other members of the group may variously believe the individual is a member, a non-member, or does not even exist. A meaningful description of a group must, therefore, allow expression of divergent representations of group membership.

The extension proceeds by enriching the content of each individual's representation to include the representations of other individuals via a process of recursive mentalizing. Although in the previous step, we endowed each agent with a representation that included other agents filling (or not) group-constitutive roles, but not those other agents’ beliefs, in the current step we recurse, enabling each agent to represent other agents’ beliefs (Frith & Frith, Reference Frith and Frith2005). At infinite recursion depth, this produces effects of common knowledge (de Freitas, Thomas, DeScioli, & Pinker, Reference de Freitas, Thomas, DeScioli and Pinker2019; Platow, Foddy, Yamagishi, Lim, & Chow, Reference Platow, Foddy, Yamagishi, Lim and Chow2012; Thomas et al., Reference Thomas, De Freitas, DeScioli and Pinker2016). New computational machinery in the form of recursive mentalizing must be brought to the table, bringing with it the power to model complex social phenomena that depend on misrepresentation and deception, where actions are taken because they are expected to validate another person's wrongly held beliefs or cause them to misinterpret which agents fill group-constitutive roles. Returning to the example of astroturfing, consider that divergence in representations alone is not enough to fully capture its essence – being mistaken as a member of a group is not astroturfing. Rather, the agent must also take an action because they believe it will cause a certain impression in the minds of the public with respect to group membership. A representation of a group in the context of conflict must, therefore, enable individuals to represent the beliefs of others.

Enriching the representation put forward by Pietraszewski to include other agents and their beliefs in a process of recursive mentalizing permits analysis of complex social phenomena that arise from the intersubjectivity of groups.