But if I’m blindfolded and asked which one colour you’ve given me then I’m going to say blue. I can’t say “not blue”, because I’ve been asked to pick a particular colour.

I would say a reasonable assumption is information. It’s certainly something we can reason from.

No it doesn’t contain information about humanity’s demise. It’s the mathematical reasoning that shows we’re most likely close to that demise. — AJJ

Mathematical reasoning, being a deductive process, cannot generate information though.

The probability does change if you divide the rooms into groups. If I say you’re either in rooms 1 or 2 or in any of the rest, then it’s most likely you’re in the second “any of the rest” group. — AJJ

If those are the groups you are given by some outside source. But if no outside source provides you with any groupings, and you're just standing alone in a room, you cannot reason yourself into rooms 3 to 100 by arbitrarily deciding on these groups. Given arbitrary groups, one can make any sequence of rooms the most likely one. No such thought experiment tells you where you actually are though.

It's even worse when, as is the case with future generations, you don't even know how many rooms there are. If you simply know there are n rooms and you are in one of them, there is no way to tell what number your room is. Yet the logic of the "doomsday argument" would have you believe that you can.

But if I’m blindfolded and asked which one colour you’ve given me then I’m going to say blue. I can’t say “not blue”, because I’ve been asked to pick a particular colour. — AJJ

If you're asked to pick a colour then, yes, you should say blue -- although you're more likely to be wrong than right, and so if you're asked if it's more likely to be blue or not-blue you should say not-blue.

And if you're asked to pick a generation then, yes, you should say the last generation -- although you're more likely to be wrong than right, and so if you're asked if you're more likely in the last generation than not in the last generation then you should say not in the last generation.

Mathematical reasoning, being a deductive process, cannot generate information though. — Echarmion

Well sure, I guess reasoning doesn’t generate information, but it does discover it.

If those are the groups you are given by some outside source. But if no outside source provides you with any groupings, and you're just standing alone in a room, you cannot reason yourself into rooms 3 to 100 by arbitrarily deciding on these groups. Given arbitrary groups, one can make any sequence of rooms the most likely one. No such thought experiment tells you where you actually are though. — Echarmion

The groups we’re using in the thought experiment are real though: Generations, with the assumption that each is larger than the last, which so far has actually been the case.

It's even worse when, as is the case with future generations, you don't even know how many rooms there are. If you simply know there are n rooms and you are in one of them, there is no way to tell what number your room is. Yet the logic of the "doomsday argument" would have you believe that you can. — Echarmion

That we don’t know how many generations there will be is entirely the point though. If we knew there’d be no room for the probabilities we’re establishing.

What you’re actually saying is you have more chance of being within generations 1-4. What you actually have to do is pick one; the one most likely for you to be in. — AJJ

I don't have to pick one. It is true that I'm more likely of being within generations 1-4 (66.7% chance) than being in generation 5 (33.3% chance). Therefore it's less likely that my generation is the last generation.

Well sure, I guess reasoning doesn’t generate information, but it does discover it. — AJJ

So are you claiming that information concerning the timing of the end of humanity is encoded in a) the fact that humans exist right now and b) the assumption that the living human population will be highest shortly before it's demise?

The groups we’re using in the thought experiment are real though: Generations, with the assumption that each is larger than the last, which so far has actually been the case. — AJJ

Generations aren't real. they are more or less arbitrary groupings of people who were born in the same time period. But regardless, the generations are the rooms in the hotel. You want to know which room you're in.

So let's set up a proper thought experiment: The entire human population that will ever have lived is grouped into 100 hotel rooms. Every room represents the same amount of time between humanity's evolution and it's demise, but you don't know how long that is. Every room is an incredibly vast extradimensional space, and it is completely dark, so you don't know how many other people are in your room and you have no way of communicating with them.

Now a voice tells you that you will go to heaven if you can guess which room you're in. You can choose any range of 5 rooms as your guess, as long as you're in any one of them, you win. Which range do you choose?

And if you're asked to pick a generation then, yes, you should say the last generation -- although you're more likely to be wrong than right, and so if you're asked if you're more likely in the last generation than not in the last generation then you should say not in the last generation. — Michael

You seem to be saying you’re more likely to be in a generation other than the one you’re in.

Once you’re in a generation there is no chance you’re in the other four. So the question is which particular generation is yours, and the best answer is “the last one”.

So let's set up a proper thought experiment: The entire human population that will ever have lived is grouped into 100 hotel rooms. Every room represents the same amount of time between humanity's evolution and it's demise, but you don't know how long that is. Every room is an incredibly vast extradimensional space, and it is completely dark, so you don't know how many other people are in your room and you have no way of communicating with them.

Now a voice tells you that you will go to heaven if you can guess which room you're in. You can choose any range of 5 rooms as your guess, as long as you're in any one of them, you win. Which range do you choose? — Echarmion

Assuming population growth (and an abrupt rather than gradual end), you're more likely to win if you select the last 5 rooms (assuming the rooms are numbered according to the time period).

But you're more likely to be wrong than right (unless >= 50% of humanity lived during the final 1/10th of humanity's total time). This is where I think AJJ is going wrong.

You seem to be saying you’re more likely to be in a generation other than the one you’re in. — AJJ

No I'm not. I'm saying that if you have to pick a generation then you're more likely to be right if you pick the final generation, but that you're more likely to not be in the final generation than to be in the final generation.

Consider again the example with 1 red ball, 2 orange balls, 3 yellow balls, 4 green balls, and 5 blue balls.

If you have to guess which ball you will be given your chances of winning are:

1. Guess red - 6.7%
2: Guess orange - 13.3%
3: Guess yellow - 20%
4: Guess green - 26.7%
5: Guess blue - 33.3%

Guessing blue gives you the best odds, but you're more likely wrong (66.7% chance) than right (33.3% chance).

Once you’re in a generation there is no chance you’re in the other four. So the question is which particular generation is yours, and the best answer is “the last one”.

There's a difference between an answer being the best answer and that answer being more likely right than wrong. The best answer has < 50% chance of being right, so it's wrong to say that we're most likely in the last generation. We're most likely not in the last generation.

So are you claiming that information concerning the timing of the end of humanity is encoded in a) the fact that humans exist right now and b) the assumption that the living human population will be highest shortly before it's demise? — Echarmion

Yes.

Generations aren't real. they are more or less arbitrary groupings of people who were born in the same time period. But regardless, the generations are the rooms in the hotel. You want to know which room you're in. — Echarmion

Sure, but those arbitrary groupings are real and that’s what we’re using.

So let's set up a proper thought experiment: The entire human population that will ever have lived is grouped into 100 hotel rooms. Every room represents the same amount of time between humanity's evolution and it's demise, but you don't know how long that is. Every room is an incredibly vast extradimensional space, and it is completely dark, so you don't know how many other people are in your room and you have no way of communicating with them.

Now a voice tells you that you will go to heaven if you can guess which room you're in. You can choose any range of 5 rooms as your guess, as long as you're in any one of them, you win. Which range do you choose? — Echarmion

Whatever the last five are, because that will be the range with the most people in it. That’s assuming we go extinct quickly, but whatever the choice you’d choose a range towards the end of all the rooms.

There's a difference between an answer being the best answer and that answer being more likely right than wrong. The best answer has < 50% chance of being right, so it's wrong to say that we're most likely in the last generation. We're most likely not in the last generation. — Michael

I haven’t said the answer is more likely right than wrong. For whichever generation we might be in you can say we’re most likely not in that generation, but we can’t not be in whichever generation is ours so I don’t see why that’s a factor.

So the question I’ve been answering is which generation carries the best likelihood of being ours. And the answer is the last one; the last one is the most likely to be ours; of all the generations we can be in we’re most likely (but not more likely than not) to be in the last one. It seems to me that last part is only a contradiction if you allow the chance that we are not in whichever our generation is.

I haven’t said the answer is more likely right than wrong. — AJJ

What you originally said is "Whoever/whenever you are it’s always most likely that yours is the final generation. The rationale being that if the final generation is the largest one, and if a random person is always most likely to be among the largest generation/group, then it follows that you (a random person) are most likely among the final generation." That's wrong. I am not most likely among the final generation. Just as in my example with the coloured balls you're not most likely to have a blue ball.

You're most likely to not have a blue ball and you're most likely to not be among the final generation.

The particular claim of yours which is wrong is "a random person is always most likely to be among the largest generation/group". This is only true if there's > 50% chance of being in the largest generation. In our example there's a 33.3% chance of being in generation 5, so you're not most likely to be among the largest generation. You're most likely to be among one of the other generations (even though no individual generation is more likely than the largest).

It seems to me what you’re doing is selecting an option and reasoning that you’re most likely not to have selected that option. You’ve chosen a ball but you’re most likely not to have chosen that ball. You’re in a generation but you’re most likely not in that generation.

I’m saying that if you have to bet on a colour then bet on blue because it has the best odds, but if you can choose to not bet then don’t because you’re more likely to get a not-blue ball and lose than to get a blue ball and win.

And if you have to bet on a generation then bet on the last because it has the best odds, but if you can choose to not bet then don’t because you’re more likely to be in an earlier generation and lose than to be in the last generation and win.

I am most likely in the last generation only if there’s > 50% chance that I’m in the last generation, and this is only true if > 50% of every human who will ever live is in the last generation.

Assuming population growth (and an abrupt rather than gradual end), you're more likely to win if you select the last 5 rooms (assuming the rooms are numbered according to the time period). — Michael

Whatever the last five are, because that will be the range with the most people in it. That’s assuming we go extinct quickly, but whatever the choice you’d choose a range towards the end of all the rooms. — AJJ

So, the argument here is the last five presumably have the most people, and presumably we're in the largest group.

But we're assuming population growth as well. So if humanity stays around after us, the chance that we are in the last 5 rooms drops dramatically. So to answer the last 5 rooms is presuming - and not proving - that humanity's demise will come relatively soon. If the demise isn't soon - and we have no prior information on that - the chances might be completely different.

Our ignorance here is such that even betting on being in the largest (and therefore last) group doesn't work, because the way we've set the thought experiment (assuming population growth and a rapid decline) the question we are asking is actually "are we in the largest group". The argument thus ends up circular.

Yes. — AJJ

That seems to me an utterly fantastical claim. It would imply that the laws of physics somehow base humanity's demise on the first person who is formulating this doomsday argument in their heads.

If the chances are 3-1 and you’re getting 3-1 on your money then you can bet all you want since you’ll break even. Does “best odds” not mean most likely to win?

You’re still in check as far as I’m concerned. What you’re doing it picking a ball and saying, “whatever ball this is, it’s more likely another one.”

So to answer the last 5 rooms is presuming - and not proving - that humanity's demise will come relatively soon. — Echarmion

I don’t think it is. The only presumption is population growth until an abrupt demise. It then follows that the final X years will have a greater population than any earlier X-year range, and so therefore that betting on the final X years will give us the best odds of winning.

However, contrary to AJJ’s claim, unless more than half of humanity lives in the final X years then it doesn’t follow that we’re most likely living in the final X years.

If the chances are 3-1 and you’re getting 3-1 on your money then you can bet all you want since you’ll break even. Does “best odds” not mean most likely to win? — AJJ

If the chances are 3-1 then you’re not most likely to win (be in the last generation). You’re 3 times more likely to lose (not be in the last generation). This discussion has nothing to do with payouts.

You’re still in check as far as I’m concerned. What you’re doing it picking a ball and saying, “whatever ball this is, it’s more likely another one — AJJ

No I’m not. I’m saying “I’m going to bet that it’s blue but it’s more likely not blue” - which is true if there are 15 balls and only 5 are blue. Two-thirds of the time I lose. It’s better odds than betting on any other colour, but it’s still losing odds.

I don’t think it is. The only presumption is population growth until an abrupt demise. It then follows that the final X years will have a greater population than any earlier X-year range, and so therefore that betting on the final X years will give us the best odds of winning. — Michael

That is if we are in fact living in the final years. If we're not, then betting on the last rooms gives you no better chance of winning. Your position in the rooms is determined by time, not population number, so you can only be in the largest group (given continuous population growth) by being in the last group. So, the question ends up circular.

If the 3-1 is the best chance available then the 3-1 is the most likely to win. Most likely to win is what “best odds” means right? Payouts come into this if you say you shouldn’t bet in a spot; payouts are essential to consider there.

I’m saying “I’m going to bet that it’s blue but it’s more likely not blue” - which is true if there are 15 balls and only 5 are blue. — Michael

But of all the balls blue is the most likely one you’re holding. You can say it’s more likely to not be that colour about any of them, but it has to be one, and one of them is going to be most likely.

That is if we are in fact living in the final years. If we're not, then betting on the last rooms gives you no better chance of winning. Your position in the rooms is determined by time, not population number, so you can only be in the largest group (given continuous population growth) by being in the last group. So, the question ends up circular. — Echarmion

That’s not right. Take my example with the coloured balls. 1 red is given out at T1, then 2 orange at T2, then 3 yellow at T3, then 4 green at T4, and then 5 blue at T5. There’s nothing circular in saying that if I have to bet on which Tn my ball was given to me then T5 gives me the best odds (1/3). It doesn’t make sense to say that if I was given my ball at T4 then T5 doesn’t give me the best odds. That’s like saying that if my ball is red then betting on blue doesn’t give me the best odds. That’s not how probabilities are calculated.

That’s not right. Take my example with the coloured balls. 1 red is given out at T1, then 2 orange at T2, then 3 yellow at T3, then 4 green at T4, and then 5 blue at T5. There’s nothing circular in saying that if I have to bet on which Tn my ball was given to me then T5 gives me the best odds (1/3). It doesn’t make sense to say that if I was given my ball at T4 then T5 doesn’t give me the best odds. That’s like saying that if my ball is red then betting on blue doesn’t give me the best odds. That’s not how probabilities are calculated. — Michael

That's true, but in your example, you know you're already after T5. That is to say all balls are in the game. With the doomsday argument, this is not the case. In your example, you'd have to account for the probability that there are no blue balls at all yet.

That's true, but in your example, you know you're already after T5. That is to say all balls are in the game. With the doomsday argument, this is not the case. In your example, you'd have to account for the probability that there are no blue balls at all yet. — Echarmion

Sorry if I wasn't clear. I'm just told the rules and then given a hidden ball. I don't know if my ball is blue and I don't know if the time I was given the ball (say 12:00pm) is T5.

If the 3-1 is the best chance available then the 3-1 is the most likely to win. Most likely to win is what “best odds” means right? Payouts come into this if you say you shouldn’t bet in a spot; payouts are essential to consider there. — AJJ

But of all the balls blue is the most likely one you’re holding. You can say it’s more likely to not be that colour about any of them, but it has to be one, and one of them is going to be most likely. — AJJ

This is ambiguous, so perhaps this will better explain what I'm saying:

Let's say 98 people have 1 lottery ticket and you have 2 lottery tickets. Of everyone playing, you have the best chance of winning (1/50 compared to their 1/100). However, it is most likely that someone other than you wins (98/100).

Of each generation, you have the best chance of being in generation 5 (1/3 compared to 1/15 for generation 1, 2/15 for generation 2, 1/5 for generation 3, and 4/15 for generation 4). However, it is most likely that you're in some other generation (2/3).

So this really depends on what you're trying to say. If it's "you're probably in the final generation" then you're wrong. That would be like saying "you're the most likely to win the lottery, therefore you're probably going to win the lottery" – which is wrong; you're probably going to lose even though you have better odds of winning than any other individual.

Sorry if I wasn't clear. I'm just told the rules and then given a hidden ball. I don't know if my ball is blue and I don't know if the time I was given the ball (say 12:00pm) is T5. — Michael

So what are the probabilities P(it is at most T4) and P(it is T5 or later)? If they aren't equal, this changes the probability to have a blue ball.

So what are the probabilities P(it is at most T4) and P(it is T5 or later)? If they aren't equal, this changes the probability to have a blue ball. — Echarmion

P(T1) = 1/15
P(T2) = 2/15
P(T3) = 1/5
P(T4) = 4/15
P(T5) = 1/3

So, if we have to bet on a time then betting on T5 gives us the best odds. This is where I agree with AJJ. However, given that P(T1-T4) = 2/3, it's most likely not T5. This is where I disagree with AJJ.

And, as I said before, there's no circular reasoning here, and it's the same reasoning as used in the case of which time period we're living in (it's just "people being born at time" rather than "balls being given out at time").

The question(s) goes as follows: In which scenario are we most likely to live? Or rather, can we make a statement about this? — Mind Dough

The likelihood to live now...compared to living in history or in the future is very low. Now if we assume humans have been around for 100 000 years, it's totally possible for us to be around for another 100 000 year. No, we won't go extinct in a couple of decades or continue on an upward trend (as Peak Human Population) will come likely in 100 years or so. Yet if there are 10 billion people for the next 100 000, do the math.

(Actually demographics is something that is very precise. The simple fact is that those who will have children 20 years or so from now have already been born. I've seen some very accurate forecasts made of population growth and demographic change done in the early 1900's, which predicted correctly the next 100 years.)