Equality and Freedom as Uncertainty in Groups.

In this paper, I investigate a connection between a common characterisation of freedom and how uncertainty is managed in a Bayesian hierarchical model. To do this, I consider a distributed factorization of a group's optimization of free energy, in which each agent is attempting to align with the group and with its own model. I show how this can lead to equilibria for groups, defined by the capacity of the model being used, essentially how many different datasets it can handle. In particular, I show that there is a "sweet spot" in the capacity of a normal model in each agent's decentralized optimization, and that this "sweet spot" corresponds to minimal free energy for the group. At the sweet spot, an agent can predict what the group will do and the group is not surprised by the agent. However, there is an asymmetry. A higher capacity model for an agent makes it harder for the individual to learn, as there are more parameters. Simultaneously, a higher capacity model for the group, implemented as a higher capacity model for each member agent, makes it easier for a group to integrate a new member. To optimize for a group of agents then requires one to make a trade-off in capacity, as each individual agent seeks to decrease capacity, but there is pressure from the group to increase capacity of all members. This pressure exists because as individual agent's capacities are reduced, so too are their abilities to model other agents, and thereby to establish pro-social behavioural patterns. I then consider a basic two-level (dual process) Bayesian model of social reasoning and a set of three parameters of capacity that are required to implement such a model. Considering these three capacities as dependent elements in a free energy minimization for a group leads to a "sweet surface" in a three-dimensional space defining the triplet of parameters that each agent must use should they hope to minimize free energy as a group. Finally, I relate these three parameters to three notions of freedom and equality in human social organization, and postulate a correspondence between freedom and model capacity. That is, models with higher capacity, have more freedom as they can interact with more datasets.