When you were young and innocent, you thought logical positivism and utilitarianism answered all the questions of philosophy. Then you realized that it did not account for uncertainty in inferring things you didn’t directly observe. Then you thought that Bayes’s theorem and Expected Utility theory answered all the questions of philosophy. Then you realized it did not account for logical (or more generally algorithmic) uncertainty.

A better understanding of bounded rationality — i.e. updating on algorithmic information — is the final problem of philosophy. It is interesting to consider some analogous questions, regarding the Efficient Market Hypothesis.

Broke: The market efficiently aggregates all information and conditions on it. (But computing what’s efficient — or even computing arbitrage, like comparing products, picking up pennies from the street, or finding the shortest queue at the mall — is itself a form of labour, and has a cost! If finding the optimal allocation of resources is too expensive, then the market won’t (and shouldn’t) compute it — and in general, the market takes time to compute this equilibrium, i.e. it has its own dynamics.)

Woke: The market is efficient if you account for information/computational power as a resource. (But if compute is itself a resource, then figuring out the optimal allocation of compute is itself an economic problem! — and therefore itself has a market, subject to computational costs, ad infinitum.)

Bespoke: You all have it backwards: the EMH is a definition, defining the “rational way to aggregate information” as the market mechanism. It is an epistemological statement, giving markets their place at the foundations of computational philosophy, analogous to the place enjoyed by Bayes at the foundations of classical philosophy.

To understand what this means in practice: for example, even when the market is exhibiting “out-of-equilibrium behaviour” (e.g. in the process of responding to a supply shock), it is doing the “right” thing, conditional on informational and computational constraints. The specific dynamics exhibited by the market, or the heuristics it employs, are learned behaviours on what to do in such a situation. Well, it may also just not have learned anything for said situation so far and acting on some “prior”, or learned that it’s not worth learning any heuristic in such a situation, etc.

Bounded rationality is “rule utilitarianism” while perfect rationality is “act utilitarianism”.

You know what else is about algorithmic information?

What the Efficient Market Hypothesis tells us is that markets are an example of a boundedly rational mechanism. Moreover, once you look at markets, it is hard to imagine any other example of bounded rationality in the wild. It almost seems as if markets should be the definition of bounded rationality. This would make our whole enterprise vacuous so we shouldn’t do that — but look!

• Markets do the same “kinds of things” as intelligent agents — they form beliefs (prices) and take decisions (allocate goods) from them.
• Beliefs may be incomplete (there’s not an asset for every state of the world) or inconsistent (unexploited arbitrage).
• These beliefs and decisions relate to each other in various ways; propagate.
• Markets have self-awareness: they can reason about themselves (assets representing the market’s own properties) and self-improve.
• Markets “learn” via a mechanism known as capitalism: traders and pathways in a market, when they do good things, gain wealth and therefore influence on the market’s future behaviour. These individual firms etc. are our learned “heuristics” (see [BR1]).
• Markets generalize Bayesian reasoning. See [MI1], and the fact that market-makers in prediction markets generalize the concept of a Bayesian prior. But this needs further elaboration for propagation/BayesNets etc.

One way to salvage the precision of the Efficient Market Hypothesis is as follows: the market “dominates” each of its individual traders, in that it will eventually do at least as well as its best trader.