in the USA you’re four times more likely to be struck by thunder than by terrorists
Our minds are actually picking up on a valid statistical issue here, which is that the number of people killed by terrorists is much more variable than the number of people killed by lightning. Since lightning strikes are almost completely uncorrelated random events, the distribution of deaths by lightning is governed by the Central Limit Theorem and so is nearly Gaussian. If X people died from lightning in 2014, then it is very unlikely that 2X people will die from lightning in 2015, and astronomically unlikely that 100X people will so die.
In contrast, if X people die from terrorism in 2014, you cannot deduce very much about the probability that 100X people will die from terrorism in 2015. Nassim Taleb would say that lightning deaths happen in Mediocristan while terrorism deaths happen in Extremistan.
During the initial coverage of the ebola outbreak, there were several comparisons to the malaria death toll, with the conclusion that paying so much attention to the (much, much smaller) death toll from ebola was irrational. This was wrong, because the ebola outbreak was undergoing exponential growth, and so the early death toll had huge importance as evidence about the long-term growth rate, and because arresting the exponential process in the early stages might be very cost effective. At the time, there were credible predictions that we might see 1.5 million cases in a relatively small region (with perhaps .75 million deaths), compared to a rate of 0.5 million global deaths from malaria. Thankfully, these predictions now look unlikely, but it is very much rational to care about possible early evidence for something that might be on track for substantial growth.
which is that the number of people killed by terrorists is much more variable than the number of people killed by lightning.
High or low variation does not mean easy or hard to control. Estimates of the cost of the War on Terror since 9/11 are going to be upwards of $6 trillion at this point. That’s a lot of money.
How much would it cost to install a few million more lightning rods? Install giant wires to draw lightning strikes? Develop a mandatory early warning system tied into all smartphones’ GPSes to warn people? Researching better medical treatments to deal with the long-term cognitive & psychological damage? Banning kites and taxing umbrellas? Subsidizing cardiac arrest kits? Relocating millions of people to less lightning-strike-prone regions?
(None of this sounds more costly or intrusive than spending $6t+, requiring millions of travelers to shed shoes annually for decades, invading multiple countries and creating millions of refugees, maintaining continuous drone strikes on multiple continents, running a global network of torture sites, etc etc etc.)
Since lightning strikes are almost completely uncorrelated random events, the distribution of deaths by lightning is governed by the Central Limit Theorem and so is nearly Gaussian.
True (perhaps), yet almost completely irrelevant to the question of how to allocate resources.
I entirely agree with you about what a calamity the war on terror has been (heres a comment I wrote a while back suggesting that the negative impact of the WoT might be about as big in magnitude as the positive impact of the tech revolution).
I was just observing that there is a meaningful statistical difference between the two types of events and therefore it isn’t wildly irrational to be more concerned with one type than the other, even if a naive expected loss calculation suggests the opposite.
“Friends, countrymen, lend me your ears! Too long have we suffered under the blows of indifferent fate. I meet you today to propose a War on Lightning, against the axis of electrons—a strike on the Mount (Olympus).
Its conquest deserves the best of all mankind, But why, some say, the Mount? Why choose this as our goal? And they may well ask why climb the highest mountain? Why, 88 years ago, fly the Atlantic? Why does Rice play Texas?
We choose to go to the Mount. We choose to go to the Mount in this decade and do the other things, not because they are easy, but because they are hard, because that goal will serve to organize and measure the best of our energies and skills, because that challenge is one that we are willing to accept, one we are unwilling to postpone, and one which we intend to win.
Further, of course, we know that lightning strikes are not controlled by intelligent beings, while terrorist strikes are.
If there’s a major multi-fatality lightning strike, it’s unlikely to encourage weather phenomena to engage in copycat attacks. Nor will all sorts of counter-lightning measures dissuade clouds from generating static electricity and instead dumping more rain or something.
Right. I think this is one of the key issues. When things like ‘natural’, ‘random’ (both in where, when, and how often they happen) or are otherwise uncontrollable, humans are much keener to accept them. When agency comes into play, it changes the perspective on it completely: “how could we have changed culture/society/national policies/our surveillance system/educational system/messaging/nudges/pick your favorite human-controllable variable” to have prevented this, or prevent it in the future? It’s the very idea that we could influence it and/or that it’s perpetuated by ‘one of us’ that makes it so salient and disturbing. From a consequentialist perspective, it’s definitely not rational, and we shouldn’t (ideally) affect our allocation of resources to combat threats.
Is there a particular bias that covers “caring about something more, however irrelevant/not dangerous, just because a perceived intelligent agent was responsible?”
Well, there are definitely forms that are irrational, but there’s also the perfectly rational factor of having to account for feedback loops.
We don’t have to consider that shifting resources from lightning death prevention to terrorism prevention will increase the base rate of lightning strikes; we do have to consider that a shift in the other direction can increase (or perhaps decrease) the base rate of terrorist activity. It is thus inherently hard to compare the expected effect of a dollar of lightning strike prevention against a dollar of terrorism prevention, over and above the uncertainties involved in comparing the expected effect of (say) a dollar of lightning strike prevention against a dollar of large asteroid collision protection.
If X people died from lightning in 2014, then it is very unlikely that 2X people will die from lightning in 2015,
This doesn’t actually follow from (annual?) lightning strikes being nearly Gaussian. A Gaussian distribution can have a standard deviation not much smaller than its mean, in which case a fall of 50% or a rise of 100% from one year to the next wouldn’t be so unlikely. Indeed the last 8 counts of annual US lightning fatalities vary over a range of a factor of 2.
A Gaussian distribution can have a standard deviation not much smaller than its mean
That’s true of Gaussians in general, but Gaussians obtained as the limiting distribution of binomial random events will have a standard deviation roughly equal to the square root of the mean. In this case, looking at the data you linked to, the mean would be about 30 for a stdev=5.5, so an observation of X=60 would be a 5-sigma Black Swan.
Indeed the last 8 counts of annual US lightning fatalities vary over a range of a factor of 2.
You’re misinterpreting this data. What’s happening is a overall decrease in the probability of getting struck by lightning, (which probably has to do with urbanization), not statistical fluctuation. If you don’t believe me, I’ll give you 10:1 odds that the number of lightning deaths in 2015 is less than 60 :-)
That’s true of Gaussians in general, but Gaussians obtained as the limiting distribution of binomial random events will have a standard deviation roughly equal to the square root of the mean.
Good point.
In this case, looking at the data you linked to, the mean would be about 30 for a stdev=5.5, so an observation of X=60 would be a 5-sigma Black Swan.
True enough, though the factor-of-2 fluctuation I had in mind was more like a jump from 23 to 45 (2013′s & 2007′s numbers respectively), and those values are more like 2.2-sigma & 1.7-sigma events (using the observed 2006-2013 average as the parameter of a Poisson distribution). Still pretty unlikely, of course.
You’re misinterpreting this data. What’s happening is a overall decrease in the probability of getting struck by lightning, (which probably has to do with urbanization), not statistical fluctuation.
Yeah, you’re right. (Well, I disagree about the urbanization explanation, the dip looks too sudden. But other than that.) If I take the 2006-2013 figures, subtract their mean μ from each of them and divide the results by √μ, that should give me z-scores (if the data are IID & Poisson). The sum of those z-scores’ squares should then be roughly χ²-distributed with n − 1 = 7 degrees of freedom, but the actual χ² statistic I get is too far in the tail for that to be plausible (χ² = 17.9, hence p = 0.012). So the lightning deaths are unlikely to be IID from a Poisson (or, nearly equivalently, Gaussian) distribution.
Our minds are actually picking up on a valid statistical issue here, which is that the number of people killed by terrorists is much more variable than the number of people killed by lightning. Since lightning strikes are almost completely uncorrelated random events, the distribution of deaths by lightning is governed by the Central Limit Theorem and so is nearly Gaussian. If X people died from lightning in 2014, then it is very unlikely that 2X people will die from lightning in 2015, and astronomically unlikely that 100X people will so die.
In contrast, if X people die from terrorism in 2014, you cannot deduce very much about the probability that 100X people will die from terrorism in 2015. Nassim Taleb would say that lightning deaths happen in Mediocristan while terrorism deaths happen in Extremistan.
During the initial coverage of the ebola outbreak, there were several comparisons to the malaria death toll, with the conclusion that paying so much attention to the (much, much smaller) death toll from ebola was irrational. This was wrong, because the ebola outbreak was undergoing exponential growth, and so the early death toll had huge importance as evidence about the long-term growth rate, and because arresting the exponential process in the early stages might be very cost effective. At the time, there were credible predictions that we might see 1.5 million cases in a relatively small region (with perhaps .75 million deaths), compared to a rate of 0.5 million global deaths from malaria. Thankfully, these predictions now look unlikely, but it is very much rational to care about possible early evidence for something that might be on track for substantial growth.
High or low variation does not mean easy or hard to control. Estimates of the cost of the War on Terror since 9/11 are going to be upwards of $6 trillion at this point. That’s a lot of money.
How much would it cost to install a few million more lightning rods? Install giant wires to draw lightning strikes? Develop a mandatory early warning system tied into all smartphones’ GPSes to warn people? Researching better medical treatments to deal with the long-term cognitive & psychological damage? Banning kites and taxing umbrellas? Subsidizing cardiac arrest kits? Relocating millions of people to less lightning-strike-prone regions?
(None of this sounds more costly or intrusive than spending $6t+, requiring millions of travelers to shed shoes annually for decades, invading multiple countries and creating millions of refugees, maintaining continuous drone strikes on multiple continents, running a global network of torture sites, etc etc etc.)
True (perhaps), yet almost completely irrelevant to the question of how to allocate resources.
I entirely agree with you about what a calamity the war on terror has been (heres a comment I wrote a while back suggesting that the negative impact of the WoT might be about as big in magnitude as the positive impact of the tech revolution).
I was just observing that there is a meaningful statistical difference between the two types of events and therefore it isn’t wildly irrational to be more concerned with one type than the other, even if a naive expected loss calculation suggests the opposite.
Ok. Now I want a President to declare the “War Against Lightning.”
“Friends, countrymen, lend me your ears! Too long have we suffered under the blows of indifferent fate. I meet you today to propose a War on Lightning, against the axis of electrons—a strike on the Mount (Olympus).
Its conquest deserves the best of all mankind, But why, some say, the Mount? Why choose this as our goal? And they may well ask why climb the highest mountain? Why, 88 years ago, fly the Atlantic? Why does Rice play Texas?
We choose to go to the Mount. We choose to go to the Mount in this decade and do the other things, not because they are easy, but because they are hard, because that goal will serve to organize and measure the best of our energies and skills, because that challenge is one that we are willing to accept, one we are unwilling to postpone, and one which we intend to win.
Good night, and gods bless America.”
http://sharpwriter.deviantart.com/art/Ben-Franklin-VS-Zeus-271337266
And with the ominous resolution spoken, a deep thunder was heard, as if echoing the importance of what had just been said,
Then everyone dived for cover...
Further, of course, we know that lightning strikes are not controlled by intelligent beings, while terrorist strikes are.
If there’s a major multi-fatality lightning strike, it’s unlikely to encourage weather phenomena to engage in copycat attacks. Nor will all sorts of counter-lightning measures dissuade clouds from generating static electricity and instead dumping more rain or something.
Right. I think this is one of the key issues. When things like ‘natural’, ‘random’ (both in where, when, and how often they happen) or are otherwise uncontrollable, humans are much keener to accept them. When agency comes into play, it changes the perspective on it completely: “how could we have changed culture/society/national policies/our surveillance system/educational system/messaging/nudges/pick your favorite human-controllable variable” to have prevented this, or prevent it in the future? It’s the very idea that we could influence it and/or that it’s perpetuated by ‘one of us’ that makes it so salient and disturbing. From a consequentialist perspective, it’s definitely not rational, and we shouldn’t (ideally) affect our allocation of resources to combat threats.
Is there a particular bias that covers “caring about something more, however irrelevant/not dangerous, just because a perceived intelligent agent was responsible?”
Well, there are definitely forms that are irrational, but there’s also the perfectly rational factor of having to account for feedback loops.
We don’t have to consider that shifting resources from lightning death prevention to terrorism prevention will increase the base rate of lightning strikes; we do have to consider that a shift in the other direction can increase (or perhaps decrease) the base rate of terrorist activity. It is thus inherently hard to compare the expected effect of a dollar of lightning strike prevention against a dollar of terrorism prevention, over and above the uncertainties involved in comparing the expected effect of (say) a dollar of lightning strike prevention against a dollar of large asteroid collision protection.
This doesn’t actually follow from (annual?) lightning strikes being nearly Gaussian. A Gaussian distribution can have a standard deviation not much smaller than its mean, in which case a fall of 50% or a rise of 100% from one year to the next wouldn’t be so unlikely. Indeed the last 8 counts of annual US lightning fatalities vary over a range of a factor of 2.
That’s true of Gaussians in general, but Gaussians obtained as the limiting distribution of binomial random events will have a standard deviation roughly equal to the square root of the mean. In this case, looking at the data you linked to, the mean would be about 30 for a stdev=5.5, so an observation of X=60 would be a 5-sigma Black Swan.
You’re misinterpreting this data. What’s happening is a overall decrease in the probability of getting struck by lightning, (which probably has to do with urbanization), not statistical fluctuation. If you don’t believe me, I’ll give you 10:1 odds that the number of lightning deaths in 2015 is less than 60 :-)
Good point.
True enough, though the factor-of-2 fluctuation I had in mind was more like a jump from 23 to 45 (2013′s & 2007′s numbers respectively), and those values are more like 2.2-sigma & 1.7-sigma events (using the observed 2006-2013 average as the parameter of a Poisson distribution). Still pretty unlikely, of course.
Yeah, you’re right. (Well, I disagree about the urbanization explanation, the dip looks too sudden. But other than that.) If I take the 2006-2013 figures, subtract their mean μ from each of them and divide the results by √μ, that should give me z-scores (if the data are IID & Poisson). The sum of those z-scores’ squares should then be roughly χ²-distributed with n − 1 = 7 degrees of freedom, but the actual χ² statistic I get is too far in the tail for that to be plausible (χ² = 17.9, hence p = 0.012). So the lightning deaths are unlikely to be IID from a Poisson (or, nearly equivalently, Gaussian) distribution.