Savage’s Theorem says nothing about dominated strategies or vulnerability to exploitation.
This is conceptually spot on! I want add that, the formal situation for Savage’s Theorem is actually worse than not guaranteeing the dominance requirement. My collegue and I just published a decision theoretic proof that Savage’s axioms forces the agent into strict dominance failures.
Specifically, for every Savage EU satisfying the Savage’s axioms, under the axiom of constructibility, you can construct an act that is strictly dominated by across an entire positive-probability event, yet Savage’s axioms mathematically mandate that . So not only does the desire to avoid dominated strategies fail to entail EU (as you argued), but successfully achieving EU optimization via Savage’s axioms implies that agents are blind to strict dominance.
Moreover, we show that a simple Dutch Book argument is avaible for the Savage’s EU.
This is conceptually spot on! I want add that, the formal situation for Savage’s Theorem is actually worse than not guaranteeing the dominance requirement. My collegue and I just published a decision theoretic proof that Savage’s axioms forces the agent into strict dominance failures.
Specifically, for every Savage EU satisfying the Savage’s axioms, under the axiom of constructibility, you can construct an act
Moreover, we show that a simple Dutch Book argument is avaible for the Savage’s EU.
A detailed discussion is pending LW approval: https://www.lesswrong.com/posts/8ppB4ixfoKdGDqeHf/savage-s-axioms-make-dominated-acts-eu-maxima-9
The full proof can be found here: https://drive.google.com/file/d/15BHxSUR93bN5DQ5spU971gEpGGq6PHRc/view