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Experimental design and understanding properties of measures are key elements of statistics.
I would agree, but I hasten to point out that design of experiments is fundamentally an application of the Bayesian decision theoretic machinery (in principle at least). I don’t comprehend this resistance to a broad conception of decision theory. Most objections to it hold up the simplistic Neyman-Pearson behavioristic approach as if that is the only conception around.
In economics, the game theoretic models start from the principle that “rational behavior” maximizes expected utility. Statistical decision theory borrows the formal apparatus of game theory and applies it to the problem Chernoff describes as “estimating the state of nature.” Bayesian Decision Theory also accepts maximization of expected utility as a valid objective. When applied to scientific projects, it amounts to maximizing the information from experiments. The decision theoretic approach is closely related to the information theory one.
Of course “the real world” is more complex, but these theories are a good first order approximation to actions worth considering.