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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’ve put this on Chit Chat 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’ve put this on Chit Chat 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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Patra
"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."
With five bullets they'd all be dead. The only way they survive pulling the trigger five times is by having one bullet in the chamber.
"Now, if you asked the surviving prisoners to estimate the number of bullets per chamber, they would never say five"
True, they wouldn't say anything, they're dead.
"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."
With five bullets they'd all be dead. The only way they survive pulling the trigger five times is by having one bullet in the chamber.
"Now, if you asked the surviving prisoners to estimate the number of bullets per chamber, they would never say five"
True, they wouldn't say anything, they're dead.
No problem, mate. It's not the simplest question in the world!
The Chit Chat thread has had more replies, so if any general bettors feel a sudden urge to discuss selection bias with respect to possible past apocalyptic events, it might be better to do it over there.
The Chit Chat thread has had more replies, so if any general bettors feel a sudden urge to discuss selection bias with respect to possible past apocalyptic events, it might be better to do it over there.
With this kind of problem you would start with a guess. The risk has to remain to make sense of it though (you're example seems like a one off event).
Let's say it's 1962, and the chance that a nuclear bomb will be dropped on a major city in the next 12 months is deemed to be 3%.
As time passes and nothing happens, the risk would drop so that a year later the risk for the next 12 months might be 1.5%, then 0.85%, then 0.5%, 0.35%, 0.25%, 0.2%, 0.18%, 0.17% etc. where it gets smaller over time, but doesn't reach zero.
I don't think selection bias comes into it. All you can do (given a lack of further information) is to make an assumption in order to come up with a probability, then adjust that probability over time given what actually occurs. The whole thing is largely guesswork. One key thing to remember, though, is that given enough time (centuries perhaps), the probability of another nuclear bomb being dropped on a major city (or some other equivalent man made disaster) approaches one.
Berkshire Hathaway is big in 'Super-Cat insurance' so they deal with working out this kind of stuff.
http://www.intelligentinvestorclub.com/bonds/super-cat-insurance-2
.
http://www.fool.com/investing/general/2007/08/29/how-berkshire-built-a-super-cat-powerhouse.aspx
Let's say it's 1962, and the chance that a nuclear bomb will be dropped on a major city in the next 12 months is deemed to be 3%.
As time passes and nothing happens, the risk would drop so that a year later the risk for the next 12 months might be 1.5%, then 0.85%, then 0.5%, 0.35%, 0.25%, 0.2%, 0.18%, 0.17% etc. where it gets smaller over time, but doesn't reach zero.
I don't think selection bias comes into it. All you can do (given a lack of further information) is to make an assumption in order to come up with a probability, then adjust that probability over time given what actually occurs. The whole thing is largely guesswork. One key thing to remember, though, is that given enough time (centuries perhaps), the probability of another nuclear bomb being dropped on a major city (or some other equivalent man made disaster) approaches one.
Berkshire Hathaway is big in 'Super-Cat insurance' so they deal with working out this kind of stuff.
http://www.intelligentinvestorclub.com/bonds/super-cat-insurance-2
.
http://www.fool.com/investing/general/2007/08/29/how-berkshire-built-a-super-cat-powerhouse.aspx
TheInvestor2,
Quite an interesting link. I doubt that Berkshire underwrite truly apocalyptic events though - ones with a significant drop in population.
Question: Would you agree that the probability of having been born in the 10th century is lower than the probability of having been born in the 20th century, by virtue of the lower population in the former? If so, I'm positing that the logic could be extended to different versions of the universe we inhabit - or different universes within the multiverse, if that's your kind of thing.
I'll be happy to be proven wrong, btw. Just trying to understand the world a little better.
Quite an interesting link. I doubt that Berkshire underwrite truly apocalyptic events though - ones with a significant drop in population.
Question: Would you agree that the probability of having been born in the 10th century is lower than the probability of having been born in the 20th century, by virtue of the lower population in the former? If so, I'm positing that the logic could be extended to different versions of the universe we inhabit - or different universes within the multiverse, if that's your kind of thing.
I'll be happy to be proven wrong, btw. Just trying to understand the world a little better.
I like Investor2's post but have a quibble:
There are many probability series that never reach 1 when totalled over the series.
As an example: the series 3% + 1.5% + 0.75% + 0.375% + . . . will never approach 100%. It might approach 6% but never more.
And this might reflect real life as species that show attributes like mutual cooperation, will have reduced chances of self-destruction every instance they can cooperate for mutual benefit.
Alternatively a species that continually conquers new lands may never self-destruct: there have been total annihilations before such as the Arawaks, the Easter Islanders, and certain North American tribes afaik. Apocalyptic events then of course to those concerned, but imagine a species that colonises 100 different planets one day - the parent planet could be obliterated, and in relative terms it wouldn't even rank, tragic though it may be, as it would be a loss of just 1% of the total pool of that species.
At a more mundane level, imagine a betting company that has stopped growing and continually mugs off new clients to in-play betting by permitting courtsiders to operate on the site, a policy which is against the company's own rules regarding cheating and betting in good faith. The extent of this practice means that the new client loses at a rate of say 5% more than expectation. An intelligent company would eventually work out that this is not a good policy as new clients stop coming and sets policies that protect new customers for mutual benefit. These companies survive in the market. The stupid companies that protect their mates and don't protect new customers will eventually wither and die, like 99+% of the species that have ever existed on this earth.
There are many probability series that never reach 1 when totalled over the series.
As an example: the series 3% + 1.5% + 0.75% + 0.375% + . . . will never approach 100%. It might approach 6% but never more.
And this might reflect real life as species that show attributes like mutual cooperation, will have reduced chances of self-destruction every instance they can cooperate for mutual benefit.
Alternatively a species that continually conquers new lands may never self-destruct: there have been total annihilations before such as the Arawaks, the Easter Islanders, and certain North American tribes afaik. Apocalyptic events then of course to those concerned, but imagine a species that colonises 100 different planets one day - the parent planet could be obliterated, and in relative terms it wouldn't even rank, tragic though it may be, as it would be a loss of just 1% of the total pool of that species.
At a more mundane level, imagine a betting company that has stopped growing and continually mugs off new clients to in-play betting by permitting courtsiders to operate on the site, a policy which is against the company's own rules regarding cheating and betting in good faith. The extent of this practice means that the new client loses at a rate of say 5% more than expectation. An intelligent company would eventually work out that this is not a good policy as new clients stop coming and sets policies that protect new customers for mutual benefit. These companies survive in the market. The stupid companies that protect their mates and don't protect new customers will eventually wither and die, like 99+% of the species that have ever existed on this earth.
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