Coalitional Agency Comment

https://www.mindthefuture.info/p/towards-a-scale-free-theory-of-intelligent/comment/121341909

But if I want a complex plan to happen, I need to successfully coordinate every aspect of it. So, unlike predictions of observations, predictions of actions need to have some mechanism for giving a single plan control over many different actuators.

You might be interested in the “wide market” framework in our recent paper: https://arxiv.org/pdf/2503.05828 where we point out that a key feature of real-world markets is that full control isn’t auctioned off at each step, but instead intelligently partitioned into different components (which economists call goods) and bids are placed over portions of control.

Re: Alice-Bob cake-cutting

Unfortunately this criticism is not convincing to me, both in this context and in various “social choice” settings where it is described as a problem. Our intuition about fairness comes from diminishing marginal utility (and risk-aversion) – if the problem instead assumes linear utilities, then it is totally right for this intuition to be violated.

But in general I do agree with your intuition that “aggregating agents corresponds to incentive-compatible decision procedures”. I had expressed a similar thought recently in terms of markets in particular:

Collectives of agents can be modeled as agents when they trade Take two agents A and B which action sets \(X_A\) and \(X_B\) and utility functions \(U_A(x_A, x_B)\), \(U_B(x_A, x_B)\). In general if they are individually maximizing their utility functions, then maybe their chosen actions \((x_A^*,x_B^*)\) will be some Nash-equilibrium of the game — but it may not be possible to interpret this as the action of a “super-agent”.

There are two ways to interpret the words “the action of a super-agent”:

• as the action that maximizes some “total utility function”, where this total utility function has some sensible properties (like being increasing in each agent’s utility)
• if the two agents could co-ordinate and choose their action, there is no other action that would be better for both of them — i.e. is Pareto-optimal. In fact it is a basic result in welfare economics that these two definitions are (under some assumptions) equivalent. And furthermore by the fundamental theorems trade achieves Pareto-optimality — i.e. trade allows the collective to be taken as a super-agent.

More precisely by “trade” we mean: perfect information, zero transaction costs, and (I guess the last one is only relevant in economics) competitive market structure. I guess it also depends on perfect property rights/perfect assurance, which is implicitly assumed under zero transaction costs.