Self-recommending decision theories for imprecise probabilities

A PDF version of this post is available here.

The question of this blogpost is this: Take the various decision theories that have been proposed for individuals with imprecise probabilities---do they recommend themselves? It is the final post in a trilogy on the topic of self-recommending decision theories (the others are here and here).

One precise kitten and one imprecise kitten

More on self-recommending decision theories

A PDF of this blogpost can be found here.

Last week, I wrote about how we might judge a decision theory by its own lights. I suggested that we might ask the decision theory whether it would choose to adopt itself as a decision procedure if it were uncertain about which decisions it would face. And I noted that many instances of Lara Buchak's risk-weighted expected utility theory (REU) do not recommend themselves when asked this question. In this post, I want to give a little more detail about that case, and also note a second decision theory that doesn't recommend itself, namely, $\Gamma$-Maximin (MM), a decision theory designed to be used when uncertainty is modeled by imprecise probabilities.

A cat judging you...harshly

 

Self-recommending decision theories

A PDF of this blogpost is available here.

Once again, I find myself stumbling upon a philosophical thought that seems so natural that I feel reasonably confident it must have been explored before, but I can't find where. So, in this blogpost, I'll set it out in the hope that a kind reader will know where to find a proper version already written up fully.*

I'd like to develop a type of objection that might be raised against a theory of rational decision-making. Here, I'll raise it against Lara Buchak's risk-weighted expected utility theory, in particular, but there will be many other theories to which it applies.

In brief, the objection applies to decision theories that are not self-recommending. That is, it applies to a decision theory if there is a particular instance of that theory that recommends that you use some alternative decision theory to make your decision; if you were to use this decision theory to choose which decision theory to use to make your choices, it would tell you to choose a different one, and not itself. We might naturally say that a decision theory that is not self-recommending in this sense is not a coherent means by which to make decisions, and that seems to be a strong strike against it.

A self-recommending Timothy Dalton