3 ms·
I'm going to present a critique similar to this one ( https://news.ycombinator.com/item?id=31568047 https://news.ycombinator.com/item?id=31568047) but I'll try
by civilized 4y ago
I'm going to present a critique similar to this one (
https://news.ycombinator.com/item?id=31568047 https://news.ycombinator.com/item?id=31568047) but I'll try to slightly rephrase.
Suppose the amount in the envelope you choose is $100. If your amount is the smaller one, the other one has $200. If your amount is the larger one, the other one has $50. So the expectation supporting the switching argument is computed over two different scenarios, where the amounts in the envelopes are {50, 100} and {100, 200} respectively.
This calculation seems to violate a hidden logical constraint: the set of amounts in the two envelopes must be the same no matter what conditional branches we consider for the expectation.
Another related issue - if you switch, the argument for switching back assumes the amount in your original envelope is 4x what you originally said it was.
- one-more-minute 4y agoTo expand on this, the switching argument is actually correct if you happen to know that the envelopes contain either {x, 2x} or {2x, 4x} dollars (where x = 50 or whatever), and you observe that A=100. These are effectively hidden assumptions of the argument. If you wanted to, you could explicitly model all possible values of the envelopes, and all possible observations of A – and you'd get the right answer again, including in the case above. You just can't define A in a path-dependent way, and then treat it as having the same value in all paths.
- phkahler 4y agoSo the issue is assigning the value A to the selected envelope and then doing conditional calculations for only the other envelop.