Strongly upvoted. This post does a good job at highlighting a fundamental confusion about probability theory and principle of indifference, which, among other things, make people say silly things about anthropic reasoning.
The short answer is: empty map doesn’t imply empty territory.
Consider an Even More Clueless Sniper:
You know absolutely nothing about shooting from a sniper rifle. To the best of your knowledge you simply press a trigger and then one of the two outcomes happens: either Target Is Hit or Target Is Not Hit and you have no reason to expect that one outcome is more likely than the other.
Should you be the one making the shot in such circumstances? After all, acording to POI you have 50% chance to hit the target while less clueless snipers estimate is a mere epsilon. Will someone be doing a disservice by educating you about sniper rifles and telling you what is going on, therefore updating your estimate to hit the target to nearly zero?
I guess one could object that in you’re even more clueless sniper example, applying the POI between Hit and Not Hit is just as arbitrary as applying it between, e.g., Hit, Hit on his right, and Hit on his left. This is what Greaves (2016) -- and maybe others? -- called the “problem of multiple partitions”. In my original scenario, people might argue that there isn’t such a problem and that there is only one sensible way to apply POI. So it’d be ok to apply it in my case and not in yours.
I don’t know what to make of this objection, though. I’m not sure it makes sense. It feels a bit arbitrary to say “we can apply POI but only when there is one way of applying it that clearly seems more sensible”. Maybe this problem of multiple partitions is a reason to reject POI altogether (in situations of what Greaves call “complex cluelessness” at least, like in my sniper example).
Well obviously when you know that there are such options as Hit on his right, and Hit on his left you will apply POI to be indifferent between all the options.
But according to Even More Clueless Sniper experiment you don’t know that. All that you know is that there are two options Hit or No Hit. And then POI gives you 50% to hit.
In other words, the problem of multiple partitions happens only when you know about all this multiple options. And if you don;t know—then there is no problem.
Maybe this problem of multiple partitions is a reason to reject POI altogether
What we need to is to properly understand where does POI even comes from. That it’s not some magical principle that allows totally ignorant people to shoot better than trained snipers. That there is some systematic reason that allows to produce correct maps of the territory and POI is derived from it. If we understand the reason, such situations will cease to be mysterious.
Strongly upvoted. This post does a good job at highlighting a fundamental confusion about probability theory and principle of indifference, which, among other things, make people say silly things about anthropic reasoning.
The short answer is: empty map doesn’t imply empty territory.
Consider an Even More Clueless Sniper:
You know absolutely nothing about shooting from a sniper rifle. To the best of your knowledge you simply press a trigger and then one of the two outcomes happens: either Target Is Hit or Target Is Not Hit and you have no reason to expect that one outcome is more likely than the other.
Should you be the one making the shot in such circumstances? After all, acording to POI you have 50% chance to hit the target while less clueless snipers estimate is a mere epsilon. Will someone be doing a disservice by educating you about sniper rifles and telling you what is going on, therefore updating your estimate to hit the target to nearly zero?
Interesting, thanks!
I guess one could object that in you’re even more clueless sniper example, applying the POI between Hit and Not Hit is just as arbitrary as applying it between, e.g., Hit, Hit on his right, and Hit on his left. This is what Greaves (2016) -- and maybe others? -- called the “problem of multiple partitions”. In my original scenario, people might argue that there isn’t such a problem and that there is only one sensible way to apply POI. So it’d be ok to apply it in my case and not in yours.
I don’t know what to make of this objection, though. I’m not sure it makes sense. It feels a bit arbitrary to say “we can apply POI but only when there is one way of applying it that clearly seems more sensible”. Maybe this problem of multiple partitions is a reason to reject POI altogether (in situations of what Greaves call “complex cluelessness” at least, like in my sniper example).
Well obviously when you know that there are such options as Hit on his right, and Hit on his left you will apply POI to be indifferent between all the options.
But according to Even More Clueless Sniper experiment you don’t know that. All that you know is that there are two options Hit or No Hit. And then POI gives you 50% to hit.
In other words, the problem of multiple partitions happens only when you know about all this multiple options. And if you don;t know—then there is no problem.
What we need to is to properly understand where does POI even comes from. That it’s not some magical principle that allows totally ignorant people to shoot better than trained snipers. That there is some systematic reason that allows to produce correct maps of the territory and POI is derived from it. If we understand the reason, such situations will cease to be mysterious.