Recently we held a workshop in Edinburgh titled Mathematics for Governance Design, consisting of a roughly 50/50 split between social scientists and category theorists.

The workshop was organised by Philipp and myself from the CyberCat Institute together with Seth Frey, Saba Siddiki and Josh Tan from (in an overlapping way) Metagov, the Institutional Grammar Research Initiative and the Computational Institutional Science lab. It was funded and hosted by the International Centre for Mathematical Sciences as part of their Mathematics for Humanity programme of events.

We designed the workshop to have as little scheduled time as possible and as much unstructured working group time as possible - inspired by our past experience running a workshop at Wytham Abbey and originally inspired by Dagstuhl. And it was a resounding success: it felt like the theme of the week was seeing famous people who we would never expect to interact with each other interacting. The danger of running a workshop like this is that the two different groups would form cliques and only interact with each other under duress, but the exact opposite happened.

Probably my personal highlight was being able to meet Matilde Marcolli and talk about our shared interest in the very hard question of how to surpass the well-known scalability barrier for human self-organisation (for example written about extensively by Elinor Ostrom). We agreed that compositional game theory and related categorical cybernetics methods could plausibly have a role to play for building models of social situations consisting for example of groups of groups arranged in an approximate hierarchy. (When taken as revolutionary this is an aspect of anarcho-communism, although my personal interest is a bit too theoretical to call it that.) In fact I should write a blog post on the general topic of hierarchies of lenses, which is something I’ve talked extensively about with several people, most notably Toby Smithe in the context of modelling the human cortex. I talked quite a bit it in high level terms in this blog post, but a more technical post might be in order.

Another highlight was being able to finally engage with institutional grammar and think seriously about how it could relate to open games. There is some past work (this and this, plus a paper I wrote earlier this year with Vincent Wang-Maścianica that isn’t released yet) on connections between open games and natural language, but to me the limiting factor has always been that the open game semantics of individual words must be hand-crafted, which will not scale beyond the tiniest of toy examples, and there has never been a plan for it besides “maybe hand-craft enough examples to fine-tune an LLM and hope for the best”. My immediate thought now is that the type of natural language texts we would like to apply this to will often factor through an institutional grammar representation, in a way that is likely to be extremely useful for game-theoretic analysis. I learned last week that institutional grammar has already been connected to agent-based models, and if it is possible to go to an agent-based model then it should be not significantly harder to go to a game-theoretic model. The benefit, of course, is that Nash equilibrium is a very standard perspective for thinking about the theoretical nature of institutions.

Of course we understand as well as anybody that interdisplinary research is extremely hard and we should not expect immediate technical results after bringing together two such different groups. But we felt real excitement in the room, and we have every reason to expect multiple new collaborations to be formed, and we are already planning a successor workshop next year.