May be I'm just ignorant, but I tried to skim the beginning of this, and it's honestly just hard to even accept their set-up. Like, the fact that any of the terms[^] (`y`, `H`, `p`, etc) are well defined as functions that can map some range of the reals is hard to accept. Like in reality, what "an elite wants," the "scalar" it can derive from pushing policy 1, even the cost functions they define seem to not even be definable as functions in a formal sense and even the co-domain of said terms cannot map well to a definable set that can be mapped to [0,1].

All the time in actual politics, elites and popular movements alike find their own opinions and desires clash internally (yes, even a single person's desires or actions self-conflict at times). A thing one desires at say time `t` per their definitions doesn't match at other times, or even at the same `t`. This is clearly an opinion of someone who doesn't read these kind of papers, but I don't know how one can even be sure the defined terms are well-defined so I'm not sure how anyone can even proceed with any analysis in this kind of argument. They write it so matter-of-fact-ly that I assume this is normal in economics. Is it?

Certain systems where the rules a bit more clear might benefit from formalism like this but politics? Politics is the quintessential example of conflicting desires, compromise, unintended consequences... I could go on.

[^] calling them terms as they are symbols in their formulae but my entire point is they are not really well defined maps or functions.