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Imagine you got 3,600 people and put them into individual isolated cells. Now, imagine that you sent a guard into each cell, each with two revolvers with five bullets each. You asked each guard to fire both revolvers, point blank, at each prisoner’s head. Approximately (1/6)*(1/6) of the prisoners would survive, i.e. 100.
Now, if you asked the surviving prisoners to estimate the number of bullets per chamber, they would never say five. I guess they would say 0, 1 or 2. They would underestimate the number of bullets each gun had been loaded with by virtue of having survived the event. Even if you had sent guards in with three loaded revolvers, the remaining 17 or so wouldn’t realise how lucky they had been.
One commonly stated argument relating to e.g. nuclear war is that it looked very likely in e.g. the 1960s, but it didn’t happen. Therefore there probably won’t be a nuclear war soon, because before lots of people thought there was going to be one, and there wasn’t.
If nuclear wars always killed 100% of the population, an analogy could easily be made with the guard/prisoner example above. You could say that the fact that a nuclear war hadn’t occurred yet had no bearing on the probability of a future nuclear war since the alternate histories in which nuclear war had broken out had left no survivors.
But nuclear wars don’t always kill 100% of the population, so the calculation gets a lot messier.
I have a couple of ideas myself, but does anyone have any theories regarding the underestimation of future apocalyptic events due to selection bias (actually survivorship bias).
I’ll put this on General Betting too. If nobody can help/cares, I’ll probably try a dedicated maths forum. Also, if anything is unclear, please let me know.
Cheers.
Now, if you asked the surviving prisoners to estimate the number of bullets per chamber, they would never say five. I guess they would say 0, 1 or 2. They would underestimate the number of bullets each gun had been loaded with by virtue of having survived the event. Even if you had sent guards in with three loaded revolvers, the remaining 17 or so wouldn’t realise how lucky they had been.
One commonly stated argument relating to e.g. nuclear war is that it looked very likely in e.g. the 1960s, but it didn’t happen. Therefore there probably won’t be a nuclear war soon, because before lots of people thought there was going to be one, and there wasn’t.
If nuclear wars always killed 100% of the population, an analogy could easily be made with the guard/prisoner example above. You could say that the fact that a nuclear war hadn’t occurred yet had no bearing on the probability of a future nuclear war since the alternate histories in which nuclear war had broken out had left no survivors.
But nuclear wars don’t always kill 100% of the population, so the calculation gets a lot messier.
I have a couple of ideas myself, but does anyone have any theories regarding the underestimation of future apocalyptic events due to selection bias (actually survivorship bias).
I’ll put this on General Betting too. If nobody can help/cares, I’ll probably try a dedicated maths forum. Also, if anything is unclear, please let me know.
Cheers.
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Replies: 32
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six out of every four people don't understand statistics.
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Too heavy for a Sunday but I like statistical problems.
The problem is with your question. If a nuclear war were to happen then it would be 100% certain that it happened. It's a true false statement. Either it happens or it doesn't and I don't think your initial question has validity. We don't have any statistical evidence to back up this so we can't use probability. Now other questions to the "End of the World" do have some validity. Asteroid impacts can wipe out the planet once every 250,000,000 years but that could mean it hit's tomorrow or 4 times in row in a billion years. I'm not sure your question has any meaning. |
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Cheers for the response, Ovalman. Appreciate it's a bit heavy for a Sunday, but on the other hand I do have some spare time for once.
What about the original question about the guards and the prisoners. Is that bit valid, do you reckon? |
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Cheers for the response, Ovalman. Appreciate it's a bit heavy for a Sunday, but on the other hand I do have some spare time for once.
What about the original question about the guards and the prisoners. Is that bit valid, do you reckon? |
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Yes there's maths and logic in that although the prisoners would have nothing to back up their reasoning unless they pooled their information.
I think your questions are ambiguous with no clear answers BTW. |
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Patra - there is insufficient information in the first para to accurately predict probability of death.
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Insufficient from whose point of view? From the experimentor's (it's 35/36 per prisoner) or from each surviving prisoner's point of view?
Each surviving prisoner would probably perform the calculation using incorrect assumptions and therefore arrive at the incorrect answer. I'm interested in the possibility that we are using similarly incorrect assumptions to assess the likelihood of apocalyptic events, and thus underestimating it. |
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There is maths and reasoning in the first statement but the prisoners don't have this info and therefore can't presume anything. I think your question is flawed from the start. Not sure where you want to go with this?
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What about misfires and/or bullet/gun malfunction, is that factored in? Or that some of the guards might deliberately miss? It was estimated that up to 70% of WW2 Soldiers never killed anybody in Battle, many deliberately missing targets. Lots of unknown variables here.
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Its sort of possible that a massive sh1tstorm of asteroids ventures our way every few thousand years or whatever and weve just been incredibly lucky they all missed for the last few million years if that helps
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There is maths and reasoning in the first statement but the prisoners don't have this info and therefore can't presume anything. I think your question is flawed from the start. Not sure where you want to go with this?
I certainly haven't expressed myself particularly well thus far. Still trying to get my head properly around the question I want to ask, so anyone is forgiven for being confused. |
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Frank/kellie malony ur man/woman
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big issue - I think we are being asked to ignore all that stuff. We are not told, but are presumably expected to assume that said revolvers are equipped with six chambers, five of which are loaded. The quoted 35/36 odds of first round death assume that the guard fires every possible shot and does not give up or switch revolvers upon "firing" one or other of the two possible blank chambers.
Not many people know that probability is bloody hard to grasp . |
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That's true, similarly there are 10 types of people who understand the binary system, those who do and those who don't.
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Blackbarn. I thought it meant that each guard spins the chamber randomly and then pulls the trigger...ONCE with EACH gun. Effectively, two games of 'Russian roulette'. 5 to 1 against each gun landing on the blank chamber.
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No Naydam, his (1/6)*(1/6) is survival rate, suggesting that all shots are "fired" (except the chambers that are empty of course). God, how have I got myself into explaining this plonk... poster's personal indulgences. No more. Off to bed
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it is a bit much to comprehend Patra
Even if you had sent guards in with three loaded revolvers, the remaining 17 or so wouldn’t realise how lucky they had been. but i liken this very much to making it to the final table of a big poker tournament , which is why they often look unbeatable & v top heavy prize pools |
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I think the OP should also take into account whether the likely outcome had been tipped up in a free munny thread by one of the resident experts on the football forum.
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I like the cut of Patra's jib.
Consider abortion - it's said that about 150,000 a year foetuses a year were being aborted in the UK at one point, the exact number isn't important. That's a lot of selection pressure against childen that would otherwise be born unloved and not really wanted deep down where it counts. It's also a lot of selection pressure in favour of children who are definitely loved and wanted coming into this world, and also selection pressure in favour of children of thicker parents who only see the benefits and not the downside of having a child as somebody else will be paying. Those who are born in the abortion era which is pretty much everyone born from about 1966 to now, will not see themselves as 'selected for' but they undoubtedly have been considering the numbers of foetuses who have been exterminated. Consider also eugenics in Sweden say - huge numbers of potentially bad parents were sterilised after having one child or having no children at all. Those who were born in the eugenics era, when they were competing at school as children naturally do, won't have considered that they were selected for at birth and so competing to be top of the class against a selective cohort group. You could be average intelligence in Sweden and not realise you're probably well brainy by global standards. It's all a kind of selection bias really. History written by the how the winners see it etc. Thank goodness for the scientific method, control groups, peer review etc. Because if we only allowed perception as the basis of enquiry we'd be truely fukked. |
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MCM: welcome back. Bongo: good to have you on board. Everyone else: cheers for taking some sort of interest.
I hope to have some free time soon so that I may address this important topic. |
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Let’s say the guard tells each prisoner that there is a random number of bullets in each gun, from 0 to 6, and that the number of bullets is the same in each gun, before firing*. This makes the situation a bit unrealistic, but you’ve got to start somewhere.
The surviving prisoners will have faced two clicks, and any mathematicians amongst them will use Bayes Theorem to estimate the number of bullets per gun. If there had been 0 bullets per gun, the probability of not being shot would have been (6/6)*(6/6) = 36/36 If there had been 1 bullets per gun, the probability of not being shot would have been (5/6)*(5/6) = 25/36 If there had been 2 bullets per gun, the probability of not being shot would have been (4/6)*(4/6) = 16/36 If there had been 3 bullets per gun, the probability of not being shot would have been (3/6)*(3/6) = 9/36 If there had been 4 bullets per gun, the probability of not being shot would have been (2/6)*(2/6) = 4/36 If there had been 5 bullets per gun, the probability of not being shot would have been (1/6)*(1/6) = 1/36 If there had been 6 bullets per gun, the probability of not being shot would have been (0/6)*(0/6) = 0/36 He will therefore estimate the probability of there having been n bullets in each gun as follows: n prob 0 39.6% 1 27.5% 2 17.6% 3 9.9% 4 4.4% 5 1.1% 6 0% The initial assumption (*) was a bit of a jump, but it’s clear that if someone shot you with two different guns and you heard two clicks, you be unlikely to guess that there had been five bullets in each. The difficult part is how to apply this to catastrophic global events. I’m trying to avoid having to use the multiverse theory, as that will put a lot of people off. |
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might be worth reading, not sure if I am understanding correct what you are looking for
. http://www.ritholtz.com/blog/2013/11/the-wyatt-earp-effect/ Wyatt Earp Effect. Earp is famous largely for one simple reason: he quite remarkably survived a lot of duels. We only calculate the odds in these highly improbable situations when we already know what happened and are surprised by it. Thus, in terms of predictive value, these instances don’t mean very much at all. |
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Yeah im struggling. You can only calculate odds of things you know and even then you dont know how much you dont know so you never really know. A coin flip may have true odds of 1000/1 tails for reasons unknown to us and there has just been a ridiculous freakish run of them since people have been flipping. I would guess this isnt the case and we know almost 100% of the story with a coin flip but your prisoners dont know plenty and we dont know even more about catastrophic global events.
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we dont know even more
often said as 'we know less'  |
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bongos post removed
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What did it say?
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something about mugs and non mugs and betting on betfair and not betting on betfair
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While I still can, I'd like to reply to Bongo's post saying that it gives an example of survivorship bias (like Brendan's). Think a few of us are on the same page as far as that's concerned.
The question is, can I get anyone onto my page regarding the apocalypse thing? Does anyone think that our presence in this universe has benefitted from a bias towards universes that haven't had apocalypses thus far? I reckon you're more likely to exist on an Earth whose Cuban Missile Crisis didn't escalate into nuclear war because that universe had a lower population thereafter. You can't exist on an Earth where the Cuban Missile Crisis brought about the end of everything, because nobody exists in those universes. Seriously, I reckon I'm right. We're underestimating the chance of an future apocalypse by not taking this important factor into account. I'm not doing this purely to make money. I love thinking about stuff like this. Plus, occasionally it can help you make money. |
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bongos gone again
 http://en.wikipedia.org/wiki/Human_extinction John Von Neumann said he was "absolutely certain (1) that there would be a nuclear war; and (2) that everyone would die in it" We're all going to die . http://www.nature.com/news/2007/071221/full/news.2007.384.html |
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I reckon you're more likely to exist on an Earth whose Cuban Missile Crisis didn't escalate into nuclear war because that universe had a lower population thereafter. You can't exist on an Earth where the Cuban Missile Crisis brought about the end of everything, because nobody exists in those universes. Seriously, I reckon I'm right. We're underestimating the chance of an future apocalypse by not taking this important factor into account.
To be clear, is the factor you’re talking about us failing to take into account this: That there could be many worlds for each event of which ours is but one. And though in this world the CMC never escalated to nuclear war, in many of the other many worlds it did escalate. And in those worlds where it escalated either the population will have been so reduced as to eventually fade from existence, or have been wiped out altogether in pretty much one go. And that overall these ‘extinct world versions’ far outnumber the one (or few) where nuclear war didn’t escalate? And in failing to take into account that imbalance, we are underestimating the likelihood of a future natural or manmade disaster wiping us out? I like to get this clear because you’ve been veering a bit easily between maths, philosophy and quantum physics such that it is hard (for me at least) to understand what the real question is that you’re interested in. |
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You've pretty much got it! What you said, except that:
I wouldn't say that the extinct world versions necessarily outnumber the non-escalating ones; it's more that they could do and we'd be unappreciative of how lucky we are not living in one of them. Sorry about the veering about between maths, philosophy and quantum physics. I'm hoping to be able to cut out the many worlds part at some point as I think that it is just one valid method of interpreting probability. E.g. I toss a coin for a fiver: Multiverse approach: Half of Patras in the multiverse win and half lose. They cancel each other out, so EV = 0. Probability approach: EV = 0.5*5 + 0.5*(-5) = 0 |
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Sorry didn't see this here have put a reply on General Betting.
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