This is a special post for quick takes by Thomas Kwa. Only they can create top-level comments. Comments here also appear on the Quick Takes page and All Posts page.
Coherence implies mutual information between actions. That is, to be coherent, your actions can't be independent. This is true under several different definitions of coherence, and can be seen in the following circumstances:
When trading between resources (uncertainty over utility function). If you trade 3 apples for 2 bananas, this is information that you won't trade 3 bananas for 2 apples, if there's some prior distribution over your utility function.
When taking multiple actions from the same utility function (uncertainty over utility function). Your actions will all have to act like a phased array pushing the variables you care about in some direction.
When taking multiple actions based on the same observation (uncertainty over observation / world-state). Suppose that you're trying to juggle, and your vision is either reversed or not reversed. The actions of your left arm and right arm will have mutual information, because they both depend on whether your vision has been reversed in related ways.
This would be a full post, but I don't think it's important enough to write up.