Expected value theory recommends sometimes taking bets that we expect to lose.
We should not adopt decision theories that recommend sometimes taking bets that we expect to lose.
You reject 3.
Yitz rejects 1.
This is not a matter of making more or fewer assumptions. Instead, it’s a matter of weighing which of the propositions one finds least plausible. There may be further arguments to be made for or against any of these points, but it will eventually bottom out at intuitions.
Oh wait sorry I got confused with totally different comment that did add an extra assumption. My bad...
As for the actual comment this thread is about, expected value theory can be derived from the axioms of VNM-rationality (which I know nothing about btw), whereas proposition 3 is not really based on anything as far as I’m aware, it’s just a kind of vague axiom of itself. I feel we should restrain from using intuitions as much as possible except when forced to at the most fundamental level of logic — like how we don’t just assume 1+1=2, we reduce it to a more fundamental level of assumptions: the ZFC axioms.
In summary, propositions 1 and 3 are mutually exclusive, and I think 1 should be accepted more readily due to it being founded in a more fundamental level of assumptions.
Then it becomes a choice of accepting the VNM axioms or proposition 3 above.
Like I said, I agree that we should reject 3, but the reason for rejecting 3 is not because it is based on intuition (or based on a non-fundamental intuition). The reason is because it’s a less plausible intuition relative to others. For example, one of the VNM axioms is transitivity: if A is preferable to B, and B is preferable to C, then A is preferable to C.
That’s just much more plausible than the Yitz’s suggestion that we shouldn’t be “vulnerable to adversarial attacks” or whatever.
It’s also worth noting that your justification for accepting expected value theory is not based on the VNM axioms, since you know nothing about them! Your justification is based on a) your own intuition that it seems correct and b) the testimony of the smart people you’ve encountered who say it’s a good decision theory.
Consider three propositions:
Expected value theory is true.
Expected value theory recommends sometimes taking bets that we expect to lose.
We should not adopt decision theories that recommend sometimes taking bets that we expect to lose.
You reject 3.
Yitz rejects 1.
This is not a matter of making more or fewer assumptions. Instead, it’s a matter of weighing which of the propositions one finds least plausible. There may be further arguments to be made for or against any of these points, but it will eventually bottom out at intuitions.
Oh wait sorry I got confused with totally different comment that did add an extra assumption. My bad...
As for the actual comment this thread is about, expected value theory can be derived from the axioms of VNM-rationality (which I know nothing about btw), whereas proposition 3 is not really based on anything as far as I’m aware, it’s just a kind of vague axiom of itself. I feel we should restrain from using intuitions as much as possible except when forced to at the most fundamental level of logic — like how we don’t just assume 1+1=2, we reduce it to a more fundamental level of assumptions: the ZFC axioms.
In summary, propositions 1 and 3 are mutually exclusive, and I think 1 should be accepted more readily due to it being founded in a more fundamental level of assumptions.
Then it becomes a choice of accepting the VNM axioms or proposition 3 above.
Like I said, I agree that we should reject 3, but the reason for rejecting 3 is not because it is based on intuition (or based on a non-fundamental intuition). The reason is because it’s a less plausible intuition relative to others. For example, one of the VNM axioms is transitivity: if A is preferable to B, and B is preferable to C, then A is preferable to C.
That’s just much more plausible than the Yitz’s suggestion that we shouldn’t be “vulnerable to adversarial attacks” or whatever.
It’s also worth noting that your justification for accepting expected value theory is not based on the VNM axioms, since you know nothing about them! Your justification is based on a) your own intuition that it seems correct and b) the testimony of the smart people you’ve encountered who say it’s a good decision theory.
Yes this is exactly what I’m saying