There is no decision theory that isn’t Bayesian... or is there? David Manheim says in a comment under a blog post:

If you’re not making decisions, there’s no need for Bayes. If you are, you’re Bayesian whether you like it or not – there is no decision theory that isn’t Bayesian.

Let us ignore the first couple of statements here; they have been challenged by other commenters, and they are beyond the focus of this post. I am curious about the last statement: there is no decision theory that isn’t Bayesian. I am no expert in decision theory, but this sounds too general to be even approximately true. How crude a generalization is this? Are there no noteworthy decision theories that are nonbayesian?

The An Introduction to Decision Theory book by Martin Peterson (Cambridge, 2009) has chapter 10 titled Bayesian vs Non-Bayesian Decision Theory if this answers your question. Yes, there are non-Bayesian approaches, though I never found them interesting and don't feel competent enough for summarizing them.
