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An article in The Atlantic makes following claim:

Human Extinction Isn't That Unlikely

“A typical person is more than five times as likely to die in an extinction event as in a car crash,” says a new report

This is all based on assuming that there is annualized 0.1% chance of a global extinction event. However that number seems to be just trumped up.

Is there any hard scientific evidence for these estimates?

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    @Oddthinking yeah, they're mixing up “people” with “Americans” in few places. – vartec May 13 '16 at 17:01
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    Given that it's been millions of years since the last global extinction event, an average of 1 global extinction every 1000 years seems, uh, high. – BlueRaja - Danny Pflughoeft May 14 '16 at 0:01
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    @BobJarvis You've just committed the Gambler's fallacy. If you flip a coin 10 times and get 10 heads, you still have a 50/50 chance of getting tails the next flip. The idea that we're "due" assumes a causal link between extinction events, or that by not having one we're "building up". – Schwern May 14 '16 at 17:52
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    @Schwern: I think Bob was joking, but it's not implausible that there might be a causal link between extinction events, or "building up" (e.g. several-million-year-period galactic orbital mechanics bringing us together with rogue objects; some sort of accretion process in the core; who knows.) – Nick Matteo May 14 '16 at 19:49
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    The title should probably be changed to "die in a global extinction event". It doesn't make sense to say "die from extinction". Extinction is not the cause of death. Rather "Extinction" is caused by the cumulative effect of the deaths, or specifically the last death that makes the species extinct. – Martin Smith May 15 '16 at 18:05
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Summary. There's no factual basis to the claim that there is a 0.1% annual risk of human extinction. What happened is that this figure was used by the authors of the Stern Review as a conservative assumption in their calculation of a discount rate for future costs and benefits, but a game of whispers has caused this context to be lost.

Details. Let's chase down the references and see where this came from, starting with the source given in the OP:

  1. Robinson Meyer (2016). "Human Extinction Isn't That Unlikely". The Atlantic.

    The Stern Review, the U.K. government’s premier report on the economics of climate change, assumed a 0.1-percent risk of human extinction every year.

    It looks as if Meyer based this sentence on:

  2. Cotton-Barratt et al. (2016). "Global Catastrophic Risks". The Global Priorities Project.

    The UK’s Stern Review on the Economics of Climate Change suggested a 0.1% chance of human extinction each year.

    Notice that this is not quite the same as the claim in Meyer. Meyer wrote "assumed" but this only says "suggested".

    Cotton-Barratt et al. cite this claim to:

  3. Nick Bostrom (2013). "Existential Risk Prevention as Global Priority". Global Policy 4:1 15–31.

    The UK’s influential Stern Review on the Economics of Climate Change (2006) used an extinction probability of 0.1 per cent per year in calculating an effective discount rate.

    Note that, again, this is quite not the same as the claim in Cotton-Barratt et al. Bostrom says that the Stern review "used an extinction probability ... in calculating an effective discount rate". Using a probability in a technical calculation is not the same as suggesting its truth.

    Bostrom cites this to:

  4. Nicholas Stern (2006). "Stern review on the economics of climate change". H.M. Treasury.

    Section 2A.2 is a technical discussion of "Intertemporal appraisals and discounting". The problem under discussion is how to compare costs and benefits across long periods of time:

    Different strategies for climate change will yield different patterns of consumption over time. We assume that a choice between strategies will depend on their consequences for households now and in the future.

    The approach taken is to use a "discount rate" — costs and benefits are accorded lower utility the further they are in the future. The discount rate takes into account various forms of uncertainty about the future, and one of these factors is:

    uncertainty about existence of future generations arising from some possible shock which is exogenous to the issues and choices under examination (we used the metaphor of the meteorite).

    Some illustrative figures are drawn up (see table 2A.1) to show the effect of various values for the extinction rate δ, and it is at this point that the authors write:

    For δ=0.1 per cent there is an almost 10% chance of extinction by the end of a century. That itself seems high – indeed if this were true, and had been true in the past, it would be remarkable that the human race had lasted this long.

    It's clear that this figure is just plucked out of the air: no basis is given for it. It's not a serious attempt to estimate the risk of extinction. The point is that unless δ is really high (much bigger than 0.1%) it is dominated by the other contributions to the discount rate in the model (namely elasticity of marginal utility and growth rate) and so the Stern Review's conclusions don't depend on its exact value, and so there is no need for them to make a serious estimation.

Update. After the problems with the Atlantic article (see this article by nostalgebraist) were brought to their attention, the Global Priorities Project issued an erratum:

We were aware that the Stern Review used this figure merely as a modelling assumption, and were trying to give a concise accurate statement. Our intention in using the figure from the Stern Review was not to try to pin down an accurate estimate of the likelihood of global catastrophe, but to demonstrate that existing serious analysis treats the 0.1% probability as a plausible modeling assumption, which would have consequences that are interesting and non-intuitive. [...]

The car crash comparison was picked up in The Atlantic, which reported it as an unconditional claim and emphasised it in their article. We did not intend to argue that the 0.1% figure was an accurate estimate of extinction risk (as we did not plan to offer an estimate of extinction risk), so this was inadvertently misleading to Atlantic readers.

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    +1 for tracing so many steps! Joined this particular SE site just to upvote this :) – MPeti May 13 '16 at 20:34
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    @DavidMulder: In this answer I only looked at the "0.1%" claim. (You'll see that there was plenty there for one answer!) If you want to write another answer about some of the other claims in the Atlantic article, that would be great. – Gareth Rees May 13 '16 at 21:45
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    That 'correction' still shows a fundamental misunderstanding of the point of the statistic; namely that it is an unrealistic upper bound used to show the irrelevance of the event to the analysis in question. It's like me saying even if there was a 50% of dying from skydiving I would still do it; I'm not saying 50% is an accurate number, I'm saying that I really want to skydive and no reasonable estimate on the probability of a catastrophic outcome would dissuade me. – Adam Martin May 13 '16 at 23:20
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    Echoes of: internetjournalofcriminology.com/… – aepryus May 14 '16 at 3:46
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    "For δ=0.1 per cent there is an almost 10% chance of extinction by the end of a century. That itself seems high – indeed if this were true, and had been true in the past, it would be remarkable that the human race had lasted this long." You can't really use use the data from before nuclear weapons, biological warfare, climate change and industrial scale farming to conclude anything about the present chances of survival. Of course we didn't wipe ourselves out in 1342, how could we have? – Scott May 16 '16 at 0:25
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It depends what you mena by "hard scientific evidence". If you mean empirical evidence that has been verified in the field and can be reliably reproduced in the lab. Then the answer is no, it is impossible to gather "hard scientific evidence" about the extinction of our species because we would need to, as extinct persons, observe the extinction of our species to gather this evidence

Here is a quote from a relevant text (http://www.globalchallenges.org/reports/Global-Catastrophic-Risk-Annual-Report-2016.pdf)

When dealing with global catastrophic risks we cannot generally rely on historical experience or trial and error. Given the severity of global catastrophes, learning from experience would be extremely costly or, in the event of human extinction, impossible.

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