December 6, 2021

Exploitability and accuracy

Kevin Blackwell, Bristol

Abstract:  I’ll begin with a very basic, very fast summary of the approach for assessing the accuracy of sets of desirable gambles being developed by Jason Konek; the notions of accuracy that I will discuss in this talk are very much in the same vein, although I will flag some important differences.  (This introduction will also include an even briefer introduction to sets of desirable gambles, for anyone who isn’t familiar with them.)

Next, I motivate an interpretation of the “Falsity” score: how exploitable (by better-informed agents) does an agent’s credal state render them?

I will then go through the assumptions and results of an approach to accuracy that I termed “Select-A-Size Accuracy”, which for two-dimensional sets of desirable gambles (gambles on a binary partition), provides exactly what we want: a family of accuracy scores such that (1) according to every member of this family, every incoherent set of desirable gambles is accuracy-dominated; and (2) for every coherent set of desirable gambles, there is some element of this family which renders that set of desirable gambles not merely accuracy-undominated but Imprecisely Immodest.

… But this approach doesn’t generalize to higher dimensions; I briefly discuss why that is.

Finally, I’ll present some early developments of a game-theoretic approach to accuracy which is closely related to the exploitability notion used in constructing Select-A-Size Accuracy. I will also gesture in the direction of, but not really discuss, another development of this same exploitability notion: Arthur Van Camp’s accuracy order.