In this post, I explore the fundamental conceptual structure of updateless commitments, by constructing a formalism for them.

I say your decision procedure updates on piece of information $p$ if $p$ is logically/computationally upstream of your decisions/actions. Or equivalently, if in a counterfactual where X is different some of your decisions/actions are different.^[1]

An updateless commitment is committing to “not updating on these pieces of information”, for a certain definition of “these pieces of information”.

Say you are deciding which updateless commitment to implement.^[2] Assume $S$ is the set of all pieces of information you could update on in the future.
You could be completely updateless, that is, commit to not updating on any piece of information (or equivalently, commit to not updating on the pieces of information in $S$ ).
You could be completely updateful, that is, not commit at all (or equivalently, commit to not updating on the pieces of information in the empty set).
In fact, your possible updateless commitments correspond exactly to the subsets of $S$ . For example, if $S = {p, q, r}$ , we’ll be able to arrange them in the usual power set lattice:

In the diagram, arrows indicate “is a subset of”. For example, ${p}$ is a subset of ${p, q}$ . And this relation corresponds exactly to “being more updateful than”. For example, “committing not to update on $p$ ” is (strictly) more updateful than “committing not to update on $p$ nor $q$ ”.

But some subsets (and commitments) are incomparable. For example, neither of “committing not to update on $p$ ” and “committing not to update on $q$ ” is more updateful than the other, because each one will know something the other won’t.

More realistically, $S$ will be (countably) infinite, so the lattice will be isomorphic to the following (which is the power set lattice of the natural numbers):

The finite subsets correspond to commitments of the form “I won’t update on [finite set]”.

The cofinite subsets correspond to commitments of the form “I will only update on [finite set]”.

The infinite coinfinite subsets cannot be explicited in this same way (list...

Counterfactuals and Updatelessness

Counterfactuals and Updatelessness