supplement - question about language in quantiles section

[elray1]

Specifically, this line: https://github.com/aaronger/utility-eval-papers/blob/4e0125a8725aa0c916c723ff7cc2f2ed3873be89/alloscore_manuscript/supplement.rnw#L227-L228

My intuition sits more easily with the idea that the decision maker is going to select a decision $x$ in a way that aligns with the preference that the random future loss $l(x,Y)$ be as low as possible given any realization $Y=y$.

[aaronger]

What does it mean for a random variable to be as low as possible?

[elray1]

I'm not sure.

What does it mean for a decision maker to select a random future loss?

[elray1]

What about "The decision problem is then to select an action $x$ in a way that aligns with the preference that $l(x,y)$ be as low as possible given any realization $Y=y$."?

[aaronger]

That's like buying a stock. It's a random payout. The buying is easy to define... saying why you want to buy it is the hard part.

[aaronger]

Sure. Will replace.

What about "The decision problem is then to select an action x in a way that aligns with the preference that l(x,y) be as low as possible given any realization Y=y."?

[aaronger]

Maybe this:

The decision problem is then to select an action $x$ that aligns with the preference that $l(x,y)$ be as low as possible given any realization $Y=y$. Equivalently, the problem is to choose a random future loss $l(x,Y)$ which is \emph{admissible}, meaning that there is no alternative action $\tilde{x}$ producing a random future loss $l(\tilde{x},Y)$ which is never greater than $l(x,Y)$ and strictly lower for some realization $Y=y_0$.

Admissibility with respect to the loss $l$ is not, however, by itself a very strong decision criterion. To give the decision problem more structure...

[elray1]

It feels like a lot of words that don't clarify the situation to me:

• the phrasing "choose a random future loss" just feels awkward to me
• the phrasing "which is never greater than $l(x,Y)$ and strictly lower for some realization $Y=y_0$" is a lot to process -- and is this actually the criterion that we care about? it feels closer to minimax than Bayes...
• how much of this do we really need to say to advance the reader's understanding of our work?

[aaronger]

I mean, this sentence and the 2 or 3 before and after it could get disappeared if the whole effort seems irreconcilable with immediate goals. That would put us in line with the standard forecast literature treatment.

But for me, a lot is going on in this section conceptually and represents some amount of resolution of several years of confusion with this stuff. I'm pretty sure that admissibility is actually a core component of decision formalization via a loss function and not specific to minimax. And my attachment to the phrase "random future loss" is because the econ-theory and finance alternatives of "prospect" and "contingent claim/payoff" seem much worse, but the concept feels essential to a robust decision theoretic discussion - that is, a random outcome with no a priori distribution. This allows the process of probabilistic opinion formation to be clearly separated from other structural properties of the decision problem, which is something I've found to be missing in so much of the forecasting lit and does feel like a basic agenda item of this whole project.

But again, there is no reason for this stuff to be in this piece of writing if it seems inappropriate. I can cut and paste into something that isn't trying to deal with the decision theory stuff on the fly.

[aaronger]

Meant to add, the driving force in my brain for all of this is the insanely esoteric but (in my opinion) profound page 80 in Dawid. (Love how he calls this a "concrete framework.")