refuse to formalize

What about what I wrote?

These considerations lead to the following design for the decision algorithm S. S is coded with a vector <P1, P2, P3, ...> of programs that it cares about, and a utility function on vectors of the form <E1, E2, E3, …> that defines its preferences on how those programs should run. When it receives an input X, it looks inside the programs P1, P2, P3, ..., and uses its "mathematical intuition" to form a probability distribution P_Y over the set of vectors <E1, E2, E3, …> for each choice of output string Y. Finally, it outputs a string Y* that maximizes the expected utility Sum P_Y(<E1, E2, E3, …>) U(<E1, E2, E3, …>).

Which part do you find insufficiently formal? Of course I use "mathematical intuition" as a black box without explaining how it works, but that's just like EDT using "prior" without explaining where it comes from, or CDT using "causal probability" as a black box. It's an unsolved problem, not refusal to formalize.