Like, I feel like with the same type of argument that is made in the post I could write a post saying “there are no voting impossibility theorems” and then go ahead and argue that the Arrow’s Impossibility Theorem assumptions are not universally proven, and then accuse everyone who ever talked about voting impossibility theorems that they are making “an error” since “those things are not real theorems”. And I think everyone working on voting-adjacent impossibility theorems would be pretty justifiedly annoyed by this.
I think that there is some sense in which the character in your example would be right, since:
Arrow’s theorem doesn’t bind approval voting.
Generalizations of Arrow’s theorem don’t bind probabilistic results, e.g., each candidate is chosen with some probability corresponding to the amount of votes he gets.
Like, if you had someone saying there was “a deep core of electoral process” which means that as they scale to important decisions means that you will necessarily get “highly defective electoral processes”, as illustrated in the classic example of the “dangers of the first pass the post system”. Well in that case it would be reasonable to wonder whether the assumptions of the theorem bind, or whether there is some system like approval voting which is much less shitty than the theorem provers were expecting, because the assumptions don’t hold.
The analogy is imperfect, though, since approval voting is a known decent system, whereas for AI systems we don’t have an example friendly AI.
I think that there is some sense in which the character in your example would be right, since:
Arrow’s theorem doesn’t bind approval voting.
Generalizations of Arrow’s theorem don’t bind probabilistic results, e.g., each candidate is chosen with some probability corresponding to the amount of votes he gets.
Like, if you had someone saying there was “a deep core of electoral process” which means that as they scale to important decisions means that you will necessarily get “highly defective electoral processes”, as illustrated in the classic example of the “dangers of the first pass the post system”. Well in that case it would be reasonable to wonder whether the assumptions of the theorem bind, or whether there is some system like approval voting which is much less shitty than the theorem provers were expecting, because the assumptions don’t hold.
The analogy is imperfect, though, since approval voting is a known decent system, whereas for AI systems we don’t have an example friendly AI.