Conflict is a matter of perception as well as action. Whether I attack, defend, or wait my turn, I must infer the new state of play in order to decide what to do next. If we want to understand this social feedback loop (Hobson, Mønster, & DeDeo, Reference Hobson, Mønster and DeDeo2021), we have to get clear on what mental representations those inferences are actually about (DeDeo, Reference DeDeo, Walker, Davies and Ellis2017; Hobson & DeDeo, Reference Hobson and DeDeo2015). The limits and powers of those representations become guiding factors in how I act.

Pietraszewski's proposal is an atomic-compositional one. A mind represents the conflict in question by composing together units drawn from a small number of basic types. Tokens of these types, in turn, are triplets of “individuals” interacting in one of four patterns.

There is much to like about this idea. Its atoms are reminiscent of empirical results on conflict motifs (Shizuka & McDonald, Reference Shizuka and McDonald2012), for example. Most appealing, to my mind, is the sheer expressiveness of Pietraszewski's scheme. It seems very likely that, with enough time and patience, his proposed representation system can represent arbitrarily sophisticated conflicts.

But is this actually how the mind gets the job of representation done? Representations must answer to the mind's resource constraints – and a key lesson from the last decade is that the particular nature of those constraints can lead to unexpected cognitive effects (Shah & Oppenheimer, Reference Shah and Oppenheimer2008).

In particular, constraints may well favor more profligate systems with a much larger set of basic symbols. Atomic-compositional systems are efficient in the number of basic types (the “dictionary”), but the size of that dictionary is not always the constraint that matters.

What may, in fact, matter more is not the number of types, but the number of tokens that any particular representation requires, a phenomenon known as sparse coding. The importance of sparse coding was first discovered in studies of the visual system, when Olshausen and Field (Reference Olshausen and Field1997) showed that low-level visual representations could be reconstructed under the assumption that the relevant constraint was not the number of neurons, but the energy required to fire them.

Sparse-coding dictionaries look very different from atomic-compositional ones. Among other things, they mix different levels: Basic units are neither individuals, nor coarse-grained entities, but combinations of both. If our internal representations make use of these sparse codes, then they would be expected to cut diagonally across Pietraszewski's taxonomy, potentially in complicated and hard-to-articulate ways.

Daniels, Krakauer, and Flack (Reference Daniels, Krakauer and Flack2012) conducted the first empirical study of conflict to use sparse coding. The representations they extracted enabled high-fidelity reconstruction of real-world events, a basic adaptive goal for any representation system. As expected, the dictionary mixed levels, so that genetically related groups and unrelated individuals were simultaneously implicated in a single “symbol.”

Such codes provide a counter-hypothesis to a priori atomic-compositional systems. They may also explain how participants can reason effectively across multiple scales; in our study on conflict in Wikipedia, for example, DeDeo (Reference DeDeo2016) found that antagonists compete against a background of hidden variables that characterize group-level activity. Turnover in these conflicts online may approach 70% per day (DeDeo, Reference DeDeo2014) – meaning that after a few days the “same” conflict will have an entirely new collection of participants while maintaining recognizable patterns of strategic interaction.

Although sparse coding is a response to constraints on information processing, a related phenomenon, compressed sensing, is a potential response to constraints on information acquisition (Donoho, Reference Donoho2006). Compressed sensing schemes allow complex environments to be known “at a glance.” When the representations being inferred have the correct properties, the number of observations required can be far fewer than the potential number of configurations. Compressed sensing may provide a (algorithmic) mechanism for the sensing of gestalt, and a second alternative to the atomic-compositional hypothesis

In either case, what makes the codes more efficient also makes them more difficult to communicate. A Wikipedia editor may make effective decisions by manipulating a sparse-coded representation, but the complexity and unusual nature of those codes may mean they are unable to express the basis of that decision to someone else.

This leads to a critical gap – and one that Pietraszewski's account may be able to fill. Conflict is, as the game theorists teach us, a fundamentally social matter. We don't simply fight with each other: we fight alongside each other. That places a premium on the ability to communicate and establish common knowledge about our beliefs.

The distinction between private and public representations is crucial. Mercier and Sperber's (Reference Mercier and Sperber2011) argumentative account, for example, distinguishes the basis on which we come to believe things, and the basis on which we argue for those beliefs to others. Because conflict requires communication among allies, it may be a terrific test case for the interaction of these two systems.

On the one hand, resource constraints lead to hard-to-articulate, but efficient, representations at the private, internal level. On the other hand, the need to communicate to others leads to a separate set of more easily grasped atomic-compositional representations such as Pietraszewski's. If I wish to draw someone into an alliance with me, I may well use language that maps quite closely onto Pietraszewski's four-term taxonomy.

Consider, for example, Machiavelli's analysis of conflict in The Prince. The general on horseback may have a head full of sparse codes, but Machiavelli's text is one Pietraszewskian story after another, a constellation of motifs of alliance, displacement, and betrayal. Indeed, Machiavelli's text often struggles to explain why sophisticated military strategists fail to make what are (to him) the most obvious moves – perhaps because those moves are obvious only when framed in an atomic-compositional framework, rather than in the internal representations that might be used by the participants themselves.

Whether or not Pietraszewski's framework matches the internal representations, a dual model leads us to ask what happens when allies and antagonists take the public representations seriously as a basis of action. The most interesting and adaptive features of conflict may arise precisely here, in the competition between the public and private, the parsimonious and efficient.