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polymathwannabe comments on Open thread, Oct. 27 - Nov. 2, 2014 - Less Wrong
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Assume that Jar S contains just silver balls, whereas Jar R contains ninety percent silver balls and ten percent red balls.
Someone secretly and randomly picks a jar, with an equal chance of choosing either. This picker then takes N randomly selected balls from his chosen jar with replacement. If a ball is silver he keeps silent, whereas if a ball is red he says “red.”
You hear nothing. You make the straightforward calculation using Bayes’ rule to determine the new probability that the picker was drawing from Jar S.
But then you learn something. The red balls are bombs and if one had been picked it would have instantly exploded and killed you. Should learning that red balls are bombs influence your estimate of the probability that the picker was drawing from Jar S?
I’m currently writing a paper on how the Fermi paradox should cause us to update our beliefs about optimal existential risk strategies. This hypothetical is attempting to get at whether it matters if we assume that aliens would spread at the speed of light killing everything in their path.
Before I actually do the math, "you hear nothing" appears to affect my estimate exactly in the same way as "you're still alive."
This seems like the obvious answer to me as well. What am I missing?
Now that I see this problem again, my thoughts on it are slightly different.
In the version with no bombs, there's a possible scenario where the picker draws a red ball but lies to you by keeping silent. So, there's a viable way for "you hear nothing" AND "Jar R" to happen.
But in the version with bombs, the scenario with "you are alive" AND "Jar R" can never happen. So, being alive in the with-bomb version is stronger evidence for Jar S than hearing nothing in the no-bomb version.
Okay, sure. The picker could be lying or speaking quietly; the bomb could be malfunctioning or have a timer that hasn't gone off yet. (Note to self: put down the ball as soon as you find out that it could be a bomb.) These things don't seem like they should be the point of a thought experiment.