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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.

See in context

21 ... And Everyone Loses Their Minds

by Ritalin

16th Jan 2015

1 min read

21

Chris Nolan's Joker is a very clever guy, almost Monroesque in his ability to identify hypocrisy and inconsistency. One of his most interesting scenes in the film has him point out how people estimate horrible things differently depending on whether they're part of what's "normal", what's "expected", rather than on how inherently horrifying they are, or how many people are involved.

Soon people extrapolated this observation to other such apparent inconsistencies in human judgment, where a behaviour that once was acceptable, with a simple tweak or change in context, becomes the subject of a much more serious reaction.

I think there's rationalist merit in giving these inconsistencies a serious look. I intuit that there's some sort of underlying pattern to them, something that makes psychological sense, in the roundabout way that most irrational things do. I think that much good could come out of figuring out what that root cause is, and how to predict this effect and manage it.

Phenomena that come to mind, are, for instance, from an Effective Altruism point of view, the expenses incurred in counter-terrorism (including some wars that were very expensive in treasure and lives), and the number of lives said expenses save, compared with the number of lives that could be saved by spending that same amount into improving road safety, increasing public helathcare expense where it would do the most good, building better lightning rods (in the USA you're four times more likely to be struck by thunder than by terrorists), or legalizing drugs.

What do y'all think? Why do people have their priorities all jumbled-up? How can we predict these effects? How can we work around them?

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[-]Daniel_Burfoot10y240

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.

[-]emr10y200

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.

[-]gwern10y120

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.

[-]Daniel_Burfoot10y20

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.

[-]JoshuaZ10y10

Ok. Now I want a President to declare the "War Against Lightning."

[-]gwern10y50

"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."

[-]IlyaShpitser10y70

http://sharpwriter.deviantart.com/art/Ben-Franklin-VS-Zeus-271337266

[-]Ben Pace10y50

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...

[-]see10y90

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.

[-]spencerth10y60

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?"

[-]see10y20

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.

[-]satt10y40

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.

[-]Daniel_Burfoot10y100

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 :-)

[-]satt10y40

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.

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.

[-]JoshuaZ10y70

In the terrorism case, the relevant biases are well-known and well-studied. The primary two biases in question are that humans take threats from intent or agencies much more seriously than threats from random chance. The second bias is that people pay more attention to threats which get a lot of coverage or which involve a large number of deaths at the same time. Tversky and Kahneman did studies on this (back when Tversky was still alive), and there's been followup by others since then.

[-]Pentashagon10y70

Is there also a bias toward the illusion of choice? Some people think driving is safer than flying because they are "in control" when driving, but not when flying. Similarly, I could stay inside a well-grounded building my whole life and avoid ever being struck by lightning, but I can't make a similar choice to avoid all possible threats of terrorism.

[-]Ritalin10y50

The primary two biases in question are that humans take threats from intent or agencies much more seriously than threats from random chance.

Could you refer me to the relevant bibliography?

[-]JoshuaZ10y70

I'm not an expert on this, but my understanding is that one of the first papers on this subject was Johnson, Hershey, Meszaros, Kunreuther, "Framing, probability distortions, and insurance decisions" the Journal of Risk and Uncertainty in 1993 in the in which showed that roughly that people were willing to pay less for insurance for an airplane crashing for any reason than for insurance for an airplane crashing due to a terrorist attack. That this isn't just a form of the conjunction fallacy is shown by subsequent work that I don't have a citation for where people were willing to pay more for the anti-terrorism insurance than insurance against plane crashes due to specific labeled technical problems (e.g. ice on wings, wiring problems).

[-]nbouscal10y60

Minor nit, but I don't think anyone has ever died from being struck by thunder.

[-]torekp10y40

Trivial Pursuit question (literally): if you're struck by lightning, which of your five senses are you most likely to lose? Being struck by thunder, indeed.

[-]Adam Zerner10y40

One of his most interesting scenes in the film has him point out how people estimate horrible things differently depending on whether they're part of what's "normal", what's "expected", rather than on how inherently horrifying they are, or how many people are involved.

Agreed. I love that scene!

Soon people extrapolated this observation to other such apparent inconsistencies in human judgment, where a behaviour that once was acceptable, with a simple tweak or change in context, becomes the subject of a much more serious reaction.

Indeed. The social psychology experiment about people asking to cut in line with/without a reason is a good example.

I intuit that there's some sort of underlying pattern to them

Check out Thinking Fast and Slow. If I understand you correctly, you're referring to heuristics and biases, which have been studied pretty extensively. I apologize if you're already aware of this and I'm missing your point.

[-]Ritalin10y50

I think most LWers can be expected to know about those. I'm just curious as to which biases are involved specifically.

[-]Gram_Stone10y20

I just don't see how this post is saying anything but: "Irrationality is bad. We should do something about that. Ideas?"

This post summarizes the entire enterprise in which we're engaged, and offers a few examples of manifestations of the problem, and some pop culture references. The answers to your questions are: people have their priorities jumbled for lots of reasons that have been discussed; they jumble their priorities in systematic ways but it's not always obvious which way they'll pull out of the hat, so it's only semi-predictable, and; people have tried to work around them by writing things like the Sequences and the academic material that covers the same ground, but it's hit or miss like most things because we don't always know Exactly What To Say and because knowing about jumbled priorities doesn't unjumble them. This problem has been around long enough to have been sort of broken up into subproblems, so if you want to help, you should probably offer new insight on an existing subproblem or come up with a whole new subproblem. I don't see how fallaciously generalizing from the Joker's half-baked commentary on society's tendency to insulate people from anxiety-provoking uncertainty is tangibly helpful in that regard. I don't see what this post contributes.

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[-]Ritalin10y70

Indeed, I have very little to contribute on my own. I'm mostly here to learn.

I'm not generalizing from the Joker's reflection. Rather, I'm using it as a springboard to talk about an issue that concerns me; namely, what triggers fear and warth and outrage in people and what doesn't. I think this is a different kind of bias from just scope insensitivity or fundamental attribution error or overconfidence bias or anything like that. Those can be overcome by just explaining the facts. This one, however, can't; explaining stuff and putting numbers forth will only get you accused of sophistry. I find that very frustrating.

[-]RomeoStevens10y60

This seems a bit harsh. I expect it to result in OP taking the actions you outline in fewer universes compared to a positive framing of the same info.

If every single discussion post is highly useful it means we are erring on the side of posting too few things.

[-]Gram_Stone10y30

Good point. I just feel like this is really basic. But I also dislike it when people chastise me for thinking that something is non-obvious when it's obvious to them.

I guess this is what karma's for.

[-]Gunnar_Zarncke10y10

the expenses incurred in counter-terrorism and the number of lives said expenses save, compared with the number of lives that could be saved by spending that same amount into improving road safety, increasing public helathcare expense

I'm fully with you but it also implies that we adjust our reaction to the losses due to terrorism or in general to losses due to not selected interventions.

One example from parenting is choosing between

giving children a chance to experience life and to become autonomous
protecting children from all possible emotional and physical harm

I judge the first to have higher utility (and hedons) to the child and future adult even despite the risks implied. But I can already hear the accusations should anything happen during the time the child is not fully protected.

Should anything happen - say a serious accident - how do I deal emotionally with that? Do I accept it as a sad but acceptable consequence of my decision or do I resort to guilt and change my future decision on this issue?

We should make clear that the positive effects of experience and autonomy actually derive from the decision for them. Otherwise the much stronger corrective guilt - or even the fear of guilt alone - will out-compete such approaches.

Your proposal or this approach in general implies that we develop a capability to suffer in certain cases - and sometimes I think that our society is headed more toward a minimization of suffering than toward a maximization of happiness.

[-]Ritalin10y10

It is time for man to fix his goal. It is time for man to plant the seed of his highest hope.

His soil is still rich enough for it. But that soil will one day be poor and exhausted, and no lofty tree will any longer be able to grow there.

Alas! there comes the time when man will no longer launch the arrow of his longing beyond man -- and the string of his bow will have unlearned to whiz!

I tell you: one must still have chaos in oneself, to give birth to a dancing star. I tell you: you have still chaos in yourselves.

Alas! There comes the time when man will no longer give birth to any star. Alas! There comes the time of the most despicable man, who can no longer despise himself.

Lo! I show you the Last Man.

"What is love? What is creation? What is longing? What is a star?" -- so asks the Last Man, and blinks.

The earth has become small, and on it hops the Last Man, who makes everything small. His species is ineradicable as the flea; the Last Man lives longest.

"We have discovered happiness" -- say the Last Men, and they blink.

They have left the regions where it is hard to live; for they need warmth. One still loves one's neighbor and rubs against him; for one needs warmth.

Turning ill and being distrustful, they consider sinful: they walk warily. He is a fool who still stumbles over stones or men!

A little poison now and then: that makes for pleasant dreams. And much poison at the end for a pleasant death.

One still works, for work is a pastime. But one is careful lest the pastime should hurt one.

One no longer becomes poor or rich; both are too burdensome. Who still wants to rule? Who still wants to obey? Both are too burdensome.

No shepherd, and one herd! Everyone wants the same; everyone is the same: he who feels differently goes voluntarily into the madhouse.

"Formerly all the world was insane," -- say the subtlest of them, and they blink.

They are clever and know all that has happened: so there is no end to their derision. People still quarrel, but are soon reconciled -- otherwise it upsets their stomachs.

They have their little pleasures for the day, and their little pleasures for the night, but they have a regard for health.

"We have discovered happiness," -- say the Last Men, and they blink.

Friedrich Nietzsche Thus Spoke Zarathustra,

I read this from the comfort of my couch, and I blink. Isn't that the right way to live, the model of polite society? Is it wrong to want to live that way?

EDIT: I have no idea how this weird formatting thing happened or how to undo it.

[-]kpreid10y70

You used a monospace block instead of a quote block. Remove leading spaces, and add leading “> ”.

[-]Salemicus10y60

I read this from the comfort of my couch, and I blink. Isn't that the right way to live, the model of polite society? Is it wrong to want to live that way?

Nietzsche's point is not so much that it's wrong to want to live that way, as small and pathetic. If their supreme values are comfort and health, are these people any better than domesticated pets? Where is the drive to excel? Where is the drive to exceed yourself? They have reduced their desires to match their limited capacities, rather than striven to increase their capacities to meet their boundless desires. Are these people actually happy, or are they merely content?

To quote Nietzche elsewhere:

For believe me! — the secret for harvesting from existence the greatest fruitfulness and the greatest enjoyment is: to live dangerously! Build your cities on the slopes of Vesuvius! Send your ships into uncharted seas! Live at war with your peers and yourselves! Be robbers and conquerors as long as you cannot be rulers and possessors, you seekers of knowledge! Soon the age will be past when you could be content to live hidden in forests like shy deer! At long last the search for knowledge will reach out for its due: — it will want to rule and possess, and you with it!

[-]Ritalin10y30

"Beyond good and evil, there is awesome and lame. Don't be lame."?

[-]Gunnar_Zarncke10y20

Probably the space at the beginning.

[-]FeepingCreature10y00

I think what Nietzsche is saying is that there doesn't seem any point to this society.

[-]JQuinton10y00

Seems like the same sort of bias reference class as the status quo bias.

[-]Elo10y00

I think its worth considering the causes of death that are in our control; vs out of our control.

in control - i.e. managing your health, road safety, not being out in lightning.

out of control - all the civillians in the 9/11 events were under the assumption that they were just going to work on a normal day of the week. Where those who drove to work were under the understanding that they took normal road risks, and therefore predicted they would get to work safely when doing so.

An extremist-type attack is more unpredictable and less within personal control. there will be nearly no way to know (without investing massive amounts) if you will be victim of a terrorism event; however not standing outside during lightning storms will be pretty helpful to prevent lightning strikes to your person.

[-][anonymous]10y-20

How about the line between words and actions.

The idea is (The Interview, Charlie Hebdo), you can say absolutely any thing you like, and the right to do so, makes it right.

But if someone punches you in the face for mouthing off, they've crossed the line that everyone believes in, but is ultimately imaginary.

Ethics, Freedom, Seth Rogen, and Charlie Hebdo

[-]JoshuaZ10y70

This is at best deeply confused. There are a lot of things that we consider unethical or just stupid that we still think people have a right to do and their basic right to do so should be protected. Focusing on "is this speech ethical" misses almost the entire issue at hand.

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