Nice post!
I want to push on one thing, though. I’m sceptical of the claim that the ergodicity economics agent violates independence.
As I understand it, the EE agent has a fixed objective: maximize the time-average growth rate of wealth, which is equivalent to maximizing expected log terminal wealth. When the stochastic environment changes — say from multiplicative to additive dynamics — the optimal per-bet policy changes. In the multiplicative case, you Kelly-bet (which looks like log utility applied locally). In the additive case with many independent bets, you behave roughly linearly with each bet (because log is approximately linear for small additive increments relative to total wealth).
But is this actually a violation of independence? Independence says: if you prefer lottery A to lottery B, then mixing both with a common lottery C at the same probability shouldn’t reverse that preference. It’s a constraint on your ranking of probability distributions over outcomes.
What the EE agent is doing seems different. They have a fixed preference over (distributions over) outcomes (log terminal wealth, or equivalently, time-average growth rate). When the dynamics change, the mapping from available actions to outcome distributions changes, so the optimal action changes. But the preference ordering over final outcomes hasn’t changed — the agent still prefers higher log wealth to lower log wealth. It’s the decision problem that’s different, not the preferences.
To put it another way: an EU maximizer with log utility would make exactly the same choices as the EE agent in every case you describe. They’d Kelly-bet in multiplicative environments and behave more linearly in additive ones, because that’s what maximizing expected log wealth requires in each setting. But the EU maximizer with log utility satisfies independence by construction. So how can the EE agent be violating independence while making identical choices?
I think the thing that looks like a context-dependent utility function is really a context-dependent policy derived from a fixed utility function under different dynamics. These seem importantly different, and I’m not sure the independence axiom is violated by the latter.
Thanks, that’s helpful.
What seems clear to me is that our world is the result of fairly simple laws of physics, and our creators wanted to know how those simple laws would play out. They’re saying “if there was a universe with these laws, what would happen”. (This is what I’d meant by “simulation”)
I agree it’s less clear that they’re doing this bc they think those laws also describe a real-world process (somewhere in the multiverse) and they want to predict the outcome of that process. (This is what you meant by “simulation” and I think your def is better.)
So I understand where you’re coming from better now. Thanks!
But I still think we’re in a simulation, in your stronger sense of the word! Why? Bc:
other civs will reasonably believe our laws of physics describe part of the multiverse,
this gives them a strong instrumental reason to simulate this,
absent 1 and 2 there aren’t comparably strong reasons to run vivariums like our world.