Wouldn’t the Hahn embedding theorem result in a ranking of the subagents themselves, rather than requiring unanimous agreement? Whichever subagent corresponds to the “largest infinities” (in the sense of ordinals) makes its choice, the choice of the next agent only matters if that first subagent is indifferent, and so on down the line.
Anyway, I find the general idea here interesting. Assuming a group structure seems unrealistic as a starting point, but there’s a bunch of theorems of the form “any abelian operation with properties X, Y, Z is equivalent to real/vector addition”, so it might not be an issue.
Wouldn’t the Hahn embedding theorem result in a ranking of the subagents themselves, rather than requiring unanimous agreement? Whichever subagent corresponds to the “largest infinities” (in the sense of ordinals) makes its choice, the choice of the next agent only matters if that first subagent is indifferent, and so on down the line.
Anyway, I find the general idea here interesting. Assuming a group structure seems unrealistic as a starting point, but there’s a bunch of theorems of the form “any abelian operation with properties X, Y, Z is equivalent to real/vector addition”, so it might not be an issue.
Good point, yeah – it’s a lexical ordering, not a unanimous agreement.