You are correct with some of the criticism, but as a side-note, completeness is actually crazy.
All real agents are bounded, and pay non-zero costs for bits, and as a consequence, don’t have complete preferences. Complete agents in real world do not exist. If they existed, correct intuitive model of them wouldn’t be ‘rational players’ but ‘utterly scary god, much bigger than the universe they live in’.
The same is true for the other implicit assumption in VNM, which is doing bayesianism. There exist no bayesian agents. Any non-trivial bayesian agents would be similarly a terrifying alien god, much bigger than the universe they live in.
Each agent has a computable partial preference ordering x≤y that decides if it prefers x to y.
We’d like this partial relation to be complete (i.e., defined for all x,y) and transitive (i.e., x≤y and y≤z implies x≤z).
Now, if the relation is sufficiently non-trivial, it will be expensive to compute for some x,y. So it’s better left undefined...?
If so, I can surely relate to that, as I often struggle computing my preferences. Even if they are theoretically complete. But it seems to me the relationship is still defined, but might not be practical to compute.
It’s also possible to think of it in this way: You start out with partial preference ordering, and need to calculate one of its transitive closures. But that is computationally difficult, and not unique either.
I’m unsure what these observations add to the discussion, though.
You are correct with some of the criticism, but as a side-note, completeness is actually crazy.
All real agents are bounded, and pay non-zero costs for bits, and as a consequence, don’t have complete preferences. Complete agents in real world do not exist. If they existed, correct intuitive model of them wouldn’t be ‘rational players’ but ‘utterly scary god, much bigger than the universe they live in’.
Oh, sorry, totally.
The same is true for the other implicit assumption in VNM, which is doing bayesianism. There exist no bayesian agents. Any non-trivial bayesian agents would be similarly a terrifying alien god, much bigger than the universe they live in.
Do I understand you correctly here?
Each agent has a computable partial preference ordering x≤y that decides if it prefers x to y.
We’d like this partial relation to be complete (i.e., defined for all x,y) and transitive (i.e., x≤y and y≤z implies x≤z).
Now, if the relation is sufficiently non-trivial, it will be expensive to compute for some x,y. So it’s better left undefined...?
If so, I can surely relate to that, as I often struggle computing my preferences. Even if they are theoretically complete. But it seems to me the relationship is still defined, but might not be practical to compute.
It’s also possible to think of it in this way: You start out with partial preference ordering, and need to calculate one of its transitive closures. But that is computationally difficult, and not unique either.
I’m unsure what these observations add to the discussion, though.