= 27d567bc2d48d9f40e9ccc20ea370b15)
Vladimir_M comments on Beauty quips, "I'd shut up and multiply!" - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (335)
How about the following scenario? Say instead of Omega, it's just a company doing a weird promotional scheme. They announce that they'll secretly flip a coin in their headquarters, and if it's tails, they'll hand out prizes to a million random people from the phone directory tomorrow, whereas if it's heads, they'll award the same prize to only one lucky winner. The next day, you receive a phone call from them. Would you apply analogous reasoning in this case (and how, or why not)?
I think that's very different... in the original scenario, heads and tails both result in you experiencing the same thing. In this case, if it comes up heads, it is a million times more likely that you will receive the prize, so getting a phone call from them is very significant Bayesian evidence.
Yes, you're right (as are the other replies making similar points). I tried hard once more to come up with an accurate analogy of the above problem that would be realizable in the real world, but it seems like it's impossible to come up with anything that doesn't involve implanting false memories.
After giving this some more thought, it seems to me that the problem with the copying scenario is that once we eliminate the assumption that each agent has a unique continuous existence, all human intuitions completely break down, and we can compute only mathematically precise problems formulated within strictly defined probability spaces. Trouble is, since we've breaking one of the fundamental human common sense assumptions, the results may or may not make any intuitive sense, and as soon as we step outside formal, rigorous math, we can only latch onto subjectively preferable intuitions, which may differ between people.
In the situation you state, then yes, of course I place high probability on the coin having come up tails. However, in order for your situation to be truly analogous to the Sleeping Beauty problem, you would have to be guaranteed to get the phone call either way, which destroys any information you gain in your version.
The probability for the head is still the same.
On the additional information, that you got the call, it becomes more likely that it was the head this time.