I’m curious if your 1⁄2 intuition still holds in this situation?
I’d still say 1⁄2 is the right answer, yes.
But I’m trying to avoid using intuition here; when I do, it tends to find the arguments on both sides equally persuasive (obvious, even). If there is a right answer at all, then this is truly a case where we have no choice but to shut up and do the math.
Suppose you’re a member of a large exploratory team on an alien planet colonized by humans. As a part of the standard equipment, each team member has an intelligent reconnaissance drone that can be released to roam around and explore. You get separated from the rest of your team and find yourself alone in the wilderness. You send out your drone to explore the area, and after a few hours it comes back. When you examine its records, you find the following.
Apparently, a local super-smart creature with a weird sense of humor—let’s call it Omega—has captured several drones and released (some of?) them back after playing with them a bit. Examining your drone’s records, you find that Omega has done something similar to the above described false memory game with them. You play the drone’s audio record, and you hear Omega saying: “I’ll toss a coin now. Afterwards, I’ll release your drone back in any case. If heads come up, I’ll destroy the other ten drones I have captured. If it’s tails, I’ll release them all back to their respective owners, but I’ll also insert this message into their audio records.” Assume that you’ve already heard a lot about Omega, since he’s already done many such strange experiments on the local folks—and from what’s known about his behavior, it’s overwhelmingly likely that the message can be taken at face value.
What would you say about the expected coin toss result now? Would you take the fact that you got your drone back as evidence in favor of tails, or does your 1⁄2 intuition still hold? If not, what’s the difference relative to the false memory case above? (Unless I’m missing something, the combined memories of yourself and the drone should be exactly equivalent to the false memory scenario.)
I’d still say 1⁄2 is the right answer, yes.
But I’m trying to avoid using intuition here; when I do, it tends to find the arguments on both sides equally persuasive (obvious, even). If there is a right answer at all, then this is truly a case where we have no choice but to shut up and do the math.
Hm.. let’s try pushing it a bit further.
Suppose you’re a member of a large exploratory team on an alien planet colonized by humans. As a part of the standard equipment, each team member has an intelligent reconnaissance drone that can be released to roam around and explore. You get separated from the rest of your team and find yourself alone in the wilderness. You send out your drone to explore the area, and after a few hours it comes back. When you examine its records, you find the following.
Apparently, a local super-smart creature with a weird sense of humor—let’s call it Omega—has captured several drones and released (some of?) them back after playing with them a bit. Examining your drone’s records, you find that Omega has done something similar to the above described false memory game with them. You play the drone’s audio record, and you hear Omega saying: “I’ll toss a coin now. Afterwards, I’ll release your drone back in any case. If heads come up, I’ll destroy the other ten drones I have captured. If it’s tails, I’ll release them all back to their respective owners, but I’ll also insert this message into their audio records.” Assume that you’ve already heard a lot about Omega, since he’s already done many such strange experiments on the local folks—and from what’s known about his behavior, it’s overwhelmingly likely that the message can be taken at face value.
What would you say about the expected coin toss result now? Would you take the fact that you got your drone back as evidence in favor of tails, or does your 1⁄2 intuition still hold? If not, what’s the difference relative to the false memory case above? (Unless I’m missing something, the combined memories of yourself and the drone should be exactly equivalent to the false memory scenario.)