It's truly remarkable that a question which is of no philosophical significance or interest could generate so many responses on a philosophy forum! — Janus
Yours isn't really a decision tree that the player must make use of since there is no decision for the player to make at the first node. — Pierre-Normand
This is in fact only a "tree" in a charitable sense. — Srap Tasmaner
I'll admit I probably would not understand the philosophical significance of probability distributions even if I had read the relevant posts. — Janus
Sorry, I'm not following this. This sounds like you think I said your expected gain when you have the smaller envelope is zero, which is insane. — Srap Tasmaner
It's truly remarkable that a question which is of no philosophical significance or interest could generate so many responses on a philosophy forum! — Janus
What area of philosophy do you think the significance would obtain? — Janus
It's truly remarkable that a question which is of no philosophical significance or interest could generate so many responses on a philosophy forum! — Janus
The OP asks, "What should you do?"
Think of the problem as being in the same family as Pascal's Wager, involving decision theory and epistemology. — Andrew M
Newcomb's problem is more controversial, even, than the two-envelope paradox. It is also quite rich in philosophical implications. — Pierre-Normand
I'm not sure which of JeffJo's examples you're referring to. — Srap Tasmaner
As for my "tree" and what it predicts -- You face a choice at the beginning between two values, and the same choice at the end between those same two values. If you flip a coin each time, then your expectation is the average of those two values both times and it is unchanged.
Opening an envelope changes things somewhat, but only somewhat. It gives more substance to the word "switch", because having opened one envelope you will never be allowed to open another. You are now choosing not between two envelopes that can be treated as having equal values inside, although they do not, but between one that has a known value and another that cannot be treated as equal in value.
But it is, for all that, exactly the same choice over again, and however many steps there are between beginning and end, your expected take is the average of the values of the two envelopes. If there's an example in which that is not true, I would be surprised.
But it is, for all that, exactly the same choice over again, and however many steps there are between beginning and end, your expected take is the average of the values of the two envelopes. If there's an example in which that is not true, I would be surprised. — Srap Tasmaner
Suppose the initial distribution is, unbeknownst to you, ((5,10), (10,20), (20,40)). In that case, if you are being dealt 5, the expected value of sticking is 5. You don't know what the expected gain of switching is. But it's not the case that it is therefore zero. That would only be zero if you knew for a fact that (5, 10) is half as likely as (5, 2.5) in the prior distribution. — Pierre-Normand
I am not sure why you are saying that I am facing a choice rather than saying that I simply don't know whether my envelope is smallest or largest (within the pair that was picked). — Pierre-Normand
This makes no sense to me. Initial distribution of what? If these are pairs of envelopes from which will be chosen the pair that the player confronts, then not only is this sample space unknown to the player, she never interacts with it. She will face the pair chosen and no other. — Srap Tasmaner
A further perspective is held by those who know the chosen amount and also know the initial distribution but not which envelope pair was initially selected. — Andrew M
There are values in envelopes. How they got there can be discussed, and that can be interesting when the player has, say, partial knowledge of that process, but it is not the source of the paradox, in my opinion. — Srap Tasmaner
Whereas, on my view, it is the source of the paradox ;-) — Pierre-Normand
Conversely, the expected gain that the player calculates will still be the unconditional gain of zero since she doesn't know the initial distribution or both amounts in the selected envelope pair. — Andrew M
Why would your ignorance preclude you from facing a choice and making a decision? In the OP, you make at least two choices: which envelope to claim, and whether to keep it or trade it for the other. Whether you end up with the most or the least you could get depends on those two decisions and nothing else. What the amounts are depends on someone else. — Srap Tasmaner
Yes, absolutely, and this is specifically beyond the OP. The distributions we've been talking about have almost always been (or should have been) unknown to the player. — Srap Tasmaner
The player doesn't even know that there is some selection process. There are values in envelopes. How they got there can be discussed, and that can be interesting when the player has, say, partial knowledge of that process, but it is not the source of the paradox, in my opinion. — Srap Tasmaner
On the assumption, of course, that the player takes this initial distribution to be bounded above by M for some (possibly uncknown) M; or [...] — Pierre-Normand
I like this explanation. And I thought of a possibly better way explain how "unknown" is used in the TEP, by analogy:n the case of the two envelopes paradox, the case is similar. The player never has the opportunity to chose which branch to take at the first node. So, the player must treat this bifurcation as occurring within a black box, as it were, and assign each branch some probability. But, unlike my example with two equally biased dice, those probabilities are unknown. — Pierre-Normand
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.