Lobstrosity

Now I do see this as being analagous to the urn example offered in the OP. As an isomorphic condition, say you have two urns, one containing three balls that are all the same color and one containing 5000 balls that are all the same color as each other but not the same color as the three balls in the other urn. You randomly select an urn, pick out a ball, and see that it's blue. Can you make any conclusions as to whether there are 5000 blue balls or only 3? In my mind it's still a 50-50 toss-up.

Or would the isomorphic condition be that you have only one urn in which you have 5000 balls of one color and three balls of another? Then if you draw a blue ball you could make a prediction as to whether there were 5000 blue or only three blue. That's the key, I believe. Is it one urn or two?

Jesse

I think the latter. In the first case, there's no analogy to idea that "if everyone guesses that their sex is the sex of the majority batch, 5000 will have guessed right and only 3 will have guessed wrong". In the second case, if everyone guesses the color they picked was the majority color, 5000 will be right and 3 will be wrong.

edit: actually, this might hold in the first case too if each person picking replaced their ball after making their choice...but I think one ball to one person is a closer analogy to the "two batches" thought-experiment.

edit edit: no, I was right the first time...in the two-urn scenario each person has a 50% chance of choosing urn #1 and a 50% chance of choosing urn#2, and once they choose the color they'll get is determined...so replacement or not, if each person guesses their color is the majority color, only half of them will have guessed right.

Hans

Sure, make me answer!

I don't see where finding myself to be male would change the original 50/50 odds. Seems to me that I still have a 50/50 chance of being right no matter which I guess, whether I know I'm a male or not.. But what the hell do I know?

Friar Bellows

Again, the Doomsday Argument would not simply say that extinction at 61 billion is more likely than extinction at 100 billion. It would say that all things being equal, extinction at 61 billion is more likely than extinction at 100 billion. But of course, all things are not equal. This is how prior probabilities can affect the argument. You will probably reason that it's extremely unlikely that we will go extinct tomorrow, or the next day, or the next year, or the next decade. But next century, next millenium, who knows? So, include that sort of reasoning in your prior probabilities. Then apply the Doomsday Argument and you'll likely find that our posterior probability for going extinct tomorrow is less than the probability for going extinct next millenium, which in turn might be greater than the probability for going extinct in a million years time.

To summarise: the Doomsday Argument tells you how to adjust the probability of human extinction when taking into account the fact that roughly 60 billion humans have lived so far. It does not tell you how to calculate the probability of human extinction from scratch. It is not rendered false by the fact that we have more than two possible models, or that stone-age men could have reasoned in the same way, or that as I typed this sentence another human was born, and gee we're still alive! But it does rest on (at least) one assumption: that we can each consider ourselves to be a random sample from the list of all humans who will ever live. That, I think, is the tough nut to crack.

Bumble Bee Tuna

Lobstrosity destroyed the argument in his first post, so I'm having trouble understand why people are still discussing. The situation is not analogous. The end.

-B

Jesse

But for the analogy to work, you can't have been sitting around watching the balls come out in order from the beginning--your existence only started once a particular ball popped out, and you have no reason to think it started on an earlier ball as opposed to a later one.

As another analogy, suppose the entire sequence of balls is videotaped, then a random point in the sequence is selected by the experimenter, and then they start rolling the tape for you starting from that point. Of course from whatever ball was popping out at the point you started watching the tape, all future balls will come out in sequence--if the first ball you see is #7690, then you can expect the sequence will continue with #7691, #7692, etc., until the last ball pops out. But if you know that the starting point was randomly selected from the entire sequence, then if you find that your starting point was ball #3, you should expect that as you continue watching, the sequence is likely to end sooner than if you found that your starting point was ball #3,000,000.

Of course, whether I should really reason as if the point at which my life starts is "randomly selected" from the entire sequence of all humans is an open question (that's what the self-sampling assumption is all about), but we can at least say that your analogy, where I start watching the sequence from the beginning, is false.

Lobstrosity

You don't have to watch from the beginning for my analogy to be appropriate. You can start anywhere. The point of the analogy is that you know for a fact that you are starting somewhere that is represented by both urns.

Look, in the urn analogy you reason that should you draw from the one containing the large number of balls, there is a very slim chance that you will come up with a ball that could be in the urn containing the small number of balls (i.e. if urn A has 1,000,000 balls and urn B has 10, if you are drawing from urn A the chance is tiny that you will get a ball labeled with something from one to ten). Therefore, if you get a ball that could be in both urns, you reason probability dictates it came from the small urn (urn B in my example). This scenario of randomly drawing from one of two urns is fundamentally different from the doomsday scenario, in which one of the two urns (you know not which) is guaranteed to crap out a ball contained by both urns. My argument does not hinge upon the fact that the numbers are in numerical order starting from one, it hinges upon the fact that there is no random draw in the sense that there is no possibility of drawing a number from the big urn that is not in the little urn. Your urns by design both contain whatever number you claim to have. This makes distinguishing between the two impossible. You can say nothing probabalistically speaking. My analogy was just an attempt to present this idea in a way that would be trivially obvious.

Jesse

I don't understand your argument Lobstrosity--could you give an example of what you're talking about, showing why seeing the number on the ball would tell us nothing about which urn we had picked from?

Here's how it would work in my analogy--you have two urns which are dribbling out a constant series of balls in numerical order, and videos are taken of each from start to finish. Then you randomly pick one of the two (unlabeled) videos, and the experimenter picks a random point in the video and starts playing.

Let's say one urn contains 100 balls, the other 10,000. If the experimenter starts the video playing at the randomly-selected moment, and the first thing I see is ball #73 popping out, followed by #74, #75, etc., shouldn't that increase my subjective estimation of the odds that I picked the urn containing only 100 balls?

Lobstrosity

The problem I see with your analogy is that the experimenter does not pick a random point in the video to start playing in the sense that he is constrained to pick a point that is contained by both urns. If he did then yes, you could do a probability analysis and say something meaningful. It isn't valid for the experimenter to pick a starting point that would instantly rule out the urn with fewer balls, however. You know he's going to pick a starting point that could come from either urn because in the Doomsday argument you're defining both urns to satisfy this criteria. What I see as the true analogy is everything you've said so far with the added caveat that the experimenter picks at random a starting point less than min(# balls in urn 1, # balls in urn 2) in order to conform with how the "urns" are defined in the doomsday problem (the smaller one is always greater than the current population size being used as a "random" draw). This added constraint makes your ability to determine which urn you are looking at a crap shoot (i.e. 50-50). I don't have enough time at the moment to go into more detail (and I could very well be thinking about this incorrectly) but I'll try to post later on with a better example.

Jesse

How would that be analogous? If a priori there were only two possible lengths that civilization could last, there'd be no reason I couldn't find myself born after the smaller of the two possible lengths, and thus would have 100% certainty that my civilization will last the longer amount of time. So, to be analogous, the experimenter should definitely not limit himself to picking numbers smaller than the maximum number in the smaller of the two urns.

Of course, in real life the doomsday argument does not assume there are only two possible civilization-length--it's more like a probability distribution which is higher for some lengths and lower for others. So instead of two urns, assume a huge collection of urns, where the relative frequencies of urns are equivalent to the ratios of the probabilities--if the prior probability of civilization ending at the 100 billionth person was twice as high as the probability of it ending on the 500 billionth person, then there'd be twice as many urns with 100 billion balls as 500 billion balls in the collection. Then a tape would be made for each urn, you would pick a tape at random and see where the experimenter starts the tape, knowing he picked the starting point randomly.