Naive Probabilism



  1. Mehmet UrcuMarch 27th, 2020 at 12:10 pm

    Turkish Translation of Naive Probabilism by Mehmet Urcu, Scientist

    Kumar oynarken, olasilik dusun.

    Hedge ederken, olumlu dusun.

    Hazirlik yaparken, makul olani dusun.

    Bunlar calismazsa dusunmeyi birak. Hayatta kal.

    Bircok teknokrat ve akademisyen tarafindan benimsenen Naif Olasilikcilik; rasyonel dusuncenin olasilik hesaplamalarina indirgendigi bir gorustur. Bu trend hayranlik derecesinde artan ve bilim, yari-bilim, bilim disinin yerini almakta olan veri tabanli methodlarin varligina isaret etmektedir. Politika, toplum ve is dunyasina sizmis bir akimdir. Bu ayni zamanda epistemoloji, karar verme mekanizmasi ve davranissal ekonominin calisma motorudur. Cunku cogunlukla dusuk veya sifir risk alan akademik arastirmalarda ve felsefi dolambacli yollarda kullanilmistir. Naif Olasilikcilik gercek hayatta orantisiz riskler olusturur ki, bunlar taraflar acisindan ustel olarak artan risklerdir ki bunlar akademik baglamda zararsizla savas ve pandemi gibi uc noktalarda yikici olabilen olgulardir.

    2019-2020 Koronavirus (Covid19) pandemisi naif olasilikcilarin karsilasmis oldugu zor kosullara guzel bir ornek teskil eder. 13 Mart 2020’de yazdigim uzere alti kitayi kapsayan, dunya ekonomisini cokerten ve gelecege gecmisten farkli bakmamiza neden olan bir epideminin ortasindayiz. Covid-19’un yayilmasinin getirdigi ana zararin nedeni ; hizli hareket etmekte gecikmek ve acik ortada gorunen dogrulara itiraz etmis olmaktir. Sozkunusu paylasilmis vurdumduymazlik naif olasilikciliga gozu kapali bagliliktan ve dunya ile yerel liderlerin ve genel kamuoyunun sagduyu ile hareketi reddetmesinden kaynaklanmaktadir.

  2. David CorfieldMarch 17th, 2020 at 11:23 am

    As a recovering probabilist, interesting article, but I’m not sure about your argument in point 2. Won’t you have to say that the situation where a coin has already been tossed but is covered by a hand is like your case (ii) - 100% H or 100% T, and so to be avoided? So long as I have the freedom which outcome to pick, why should I care whether the outcome is determined or not? In fact, I may prefer this situation to one where I call mid-toss, giving the tosser the opportunity to change the height of the catch and perhaps control the outcome.

    Of course, this freedom to choose is vital for me, and if someone is only offering me heads as an outcome, I should run in any scenario, fair coin or otherwise.

  3. Walter VanniniMarch 15th, 2020 at 06:53 pm

    Extremely interesting article

    There is GREAT need for papers on this issue addressed to the general public, rather than to cognoscenti or (god forbid) IYIs. Public awareness, and the public action that follows it, are needed now more than ever.

    but my 2c regards a potential LIMIT: as it is (very usefully) addressed to lay people, it's ok to bash (AND please bash some more) on dumb economists and IYIs etc. but you risk missing one point: the overall level of innumeracy equally common among the lay people and the (apparently) educated IYIs.

    It's innumeracy that allows people to shrug off alerts with a "pff, it's only a 2% mortality rate" (neglecting that 2,5% was the mortality rate of the Spanish flu). It's also innumeracy that leads public commentators to rely on absolute numbers that bring no information whatsoever but are "big, really big".

    This is not to say that some are not playing dumb for heir own political gain. Still, this is not the  problem addressed here.

    Also, innumeracy plays a role in which figures are used in dailiy sitreps. Why should I care how many new cases there are today? It brings no information whatsoever! If they want to inform math-aware people, they should tell us how distant we are (if at all) from a 33% daily increase /6-day doubling time exponential.
    And if they want to represent the situation, they should tell us how above-average we are with respect to hospital and ICU occupancy. At least those numbers relate to something people can genuinely understant.

    Let me know if you I can help you with a couple paragraphs to this effect.



  4. Mehmet UrcuMarch 15th, 2020 at 02:58 pm

    Very interesting article. To summarize my comments short, l am closer to A. Farrington. You could have been harsher on Sunstein. Your criticism sounds like it is just a mental and modeling mistake but I think it is more than that. You could have criticized his comments more rigorously. Left-tail risk can not be eliminated with a lot of verbal nonsense. We all know this.

    The second point I wanted to mention here is regarding quantification. You tend to prefer a hybrid approach rather than a strong quantification. I could not understand why hybrid approach would work better in this spesific problem. There is not enough evidence. Technical points are not addressed here as you put in your comments. I look forward to seeing more detailed technical stuff worked into it.

  5. Tarek MilleronMarch 14th, 2020 at 10:32 pm

    I can't take credit for Suhansanu Kumar's made qualitative/quantitative comment.

    But now having read it, it leads me back to my point: how do we measure wasted time and resources? The "true" cost of over-preparation? You lay up 2x wood in November because the almanac forecasts an extra cold winter while Sunstein laughs at your sweat. In fact you end up using 1.125x wood. Assuming you don't sell the excess wood, but keep it, what was the true cost of being overprepared? What weren't you doing that Sunstein insists you should have been? More to the point now, if we had ramped up mask production domestically x10 normal supply, and then didn't need them, what's the downside if they last 10 years?

  6. Harry CraneMarch 14th, 2020 at 05:35 am

    Mike Saunders, Allen Farrington, Suhansanu Kumar and Tarek Milleron, Thank you all for your helpful comments.  I've posted a revision that takes some (thought not all) of your thoughts into account.  Some of your comments will be address in a future version, after further research.

    Tarek, your question about qualitative and quantitative gets to the heart of the matter, which I don't address fully here. For some thoughts on this, also in progress, you might look at  Comments would be much appreciated.  In a nutshell, I don't believe quantification is necessary, desirable or even possible in most cases.  That is why I advocate for the multiple-tiered approach ranging from qualitative (common sense, possibility), to a hybrid (plausibility), to quantitative (probability).  They range from vague and of broad scope in the qualitative case to precise and of limited scope in the quantitative case.  I don't address these more technical points in this article, but could probably work them into the article linked above.  I'll think more about it.

    I appreciate any additional comments anyone has. I apologize for the typos.  Please don't worry about typos in these versions, as the article will be undergoing continual re-writing in the coming weeks and months.

  7. Tarek MilleronMarch 14th, 2020 at 12:21 am

    Absorbing and important essay, thanks.


    Minor comments on text:

    For one-off or non-repeatable events, naive probabilists settle on a subjective ‘degree of belief’, i.e., a value p at which one lacks a preference between the options of either buying or selling a contract for $p in exchange for either a payment or obligation if the event occurs.

    With COVID, for example, focusing on the possibility (small according to Sunstein) of a global pandemic instead of the more likely MISSING WORD (again, according to Sunstein) that the disease is about on par with the flu, is an example of probability neglect.

    Behavioral economists like Sunstein VIEW probability neglect as a cognitive flaw,
    which ought to be corrected if possible.

    The gambler’s priorities are the reverse of the naive probabilist’s caricature of the ‘rational agent’:

    The same priorities apply, only much, much more so, in the case of COVID-19.

    General comments:

    Sunstein's conceit seems to be that there is a zero sum game in attention allocation which is tightly coupled to action and investment. In fact the human animal is designed to rest and observe for much of the time. So the general cost of his perceived probability neglect is not what he makes it out to be. This doesn't mean we sit and wait on the virus - it means that we have the time and resources to act and the cost of doing so is actually low...frontside. You covered this well.

    The concluding sentence is good but you could make more of the fact that if it's not  massive now this is a dress rehearsal for the next wave of this virus or the next pandemic. Also, after 911 everyone was yacking about bioterrorism. Maybe Sunstein was downplaying it then, too, but the point is people were in fact paying a great deal of attention to a "low probability" event. That didn't get us prepared for COVID-19 in 2020. We didn't even hedge with domestic mask manufacturing, i.e., with plans that require low resources until needed but which cannot absorb resources without being seeded early. So, is it basic incompetence over 3 Administrations that matters most in the end?

  8. Suhansanu KumarMarch 13th, 2020 at 10:39 pm

    Very interesting article!

    I agree with your point that we should be 'prepare for the worst-case by considering all the possibilities'. However, this makes sense qualitatively, there is a lack of quantitative support behind it according to me. If we over-prepare and are safe, we often don't see the effect of over-preparation in a quantitative way or when we see the effect it is very delayed. If we under-prepared and we are safe, we reinforce our beliefs for under-preparation. If we prepare well and are safe, we don't have often not enough feedback leading us to a belief that we over-prepared.  In other words, the feedback either doesn't come or it comes very late. I am assuming every one of us wants to prepare just enough that the worst-case scenario is avoided. Thereafter, we may want to maximize our profits. We use our past experience (or wisdom) to make this tradeoff. Also, we give more weight to the recent past (like Ebola, SARS, Mers) where preparation of this case was not needed. In such a scenario, I was wondering if there is a concrete quantitative way of describing the effect of preparation?

  9. Allen FarringtonMarch 13th, 2020 at 07:49 pm

    1 – Be Harsher on Sunstein - Sunstein needs to be taken down more rigorously on logical grounds. Your criticism gives the impression he just used the wrong mental model and that this was an easy enough mistake to make. In fact, there are several logical contradictions in that article – both explicit and implicit. The two sentences you quote include an explicit fallacy, so you shouldn’t let him off so easy! He didn't just 'have the wrong idea', he was literally talking nonsense.

    I suggest you address (at least) these three mistakes of his, and consider stressing that they are not innocent, but are stupid and dangerous. A reminder of his claim:

    “At this stage, no one can specify the magnitude of the threat from the coronavirus. But one thing is clear: A lot of people are more scared than they have any reason to be.”

    i. Modal Logic**:** Set some arbitrary threat magnitude as “x-dangerous.” Then, “we know that the threat is not x-dangerous” is completely different to, “we do not know that the threat is x-dangerous.” Even if you assume that ‘rationality’ can be defined, you can only specify what is or is not “reasonable” based on what you know to be the case or what you know not to be the case. Yet Sunstein tells us that we should define reasonableness on the basis of what we do not know, which is nonsensical.

    ii. Tail-risk/Kurtosis Sensitivity: If you assume, in addition, that it is meaningful to define an ‘expectation’ of the magnitude of the danger of the threat, then we face the problem of how to assess the parameters of such a distribution. The fact that we know very little (as Sunstein is more than happy to admit) is precisely what makes this very difficult. There is grossly insufficient data to do so with any reasonable confidence. And so, even if, as he suggests, the probability of a truly extreme magnitude of danger is very small, the fact that we do not know enough to rule this out means that, never mind the acknowledged extremes of the distribution, but even the expectation could be an extreme magnitude of danger. His claims about what is ‘reasonable’ are once again shown to be highly suspect.

    Recall the following additional quote from the article, which can only sensibly be interpreted as implying can meaningfully define an expectation:

    “If so, there is an excellent chance that you will focus on it -- and pay far less attention than you should to a crucial question, which is how likely it is to occur.”

    iii. Ergodicity: You can’t assume it is meaningful to define an expectation because we do not have a million societies from which to extract an average. We have one. Our assessment of the threat magnitude is a purely epistemological metric with no real world meaning. We need to act with an awareness that whatever happens will happen in real life, not in a statistical model.

    2 – Explain ‘long/short indifference’ fallacy – You come close several times to articulating a specific refutation of naïve probabilism but never quite reach it. When you put forward the naïve probabilist interpretation of a ‘degree of belief’, you let them get away with the idea that there is a binary choice between buying and selling such a contract. There is not; one can buy, sell, or do nothing at all.

    The root of this fallacy lies deeper still, in the implicit idea that “everything has a probability” and your “degree of belief” is as correct as it is close to the true value. But the logic here is backwards: the true probability does not determine your willingness to bet, but rather your willingness to bet determines what probabilities (i.e. odds) you will deem attractive. Of course, you may simply to be unwilling to bet because you lack knowledge to assess the attractiveness of the odds on offer. In the real world, the vast majority of available bets are not taken by those in a position to do so, because they lack the knowledge required to assess the attractiveness of the bet. This is a sign of rationality, not irrationality.

    Neglect of this distinction – not just long or short, but long, short, or out the market – makes Sunstein’s stance highly susceptible to (at least) the following two criticisms:

    First, he assumes he needs to pick a probability in the first place. The whole article is full of allusions to the existence of an ‘expectation’ in which it is rational to believe. I covered above why an expectation is meaningless in this realm, but it is interesting to note in this context that the reason he doesn’t realise this is because he thinks that some value must exist. He doesn’t realise that the statistic he has in mind can only be given meaning in the epistemological sense as the odds of a bet he deems to be fair. But since he has no knowledge, he has no idea what he deems fair. He is not really short the virus, he is just out the market.

    Second, HE IS NOT REALLY SHORT THE VIRUS! He claims to be (wrongly) and yet he has not exposed himself to the potential downsides of being wrong in this claim. If he really thought he had identified the odds of a fair bet, he would have taken the other side of it. Subsequently he would have been financially ruined given how comically wrong he was about the magnitude of the threat. But of course, he entered no such contract: he just gave his readers the impression that the rational thing to do was to be short the virus, when, really, he was out the market.

    This second point is worth re-emphasising on moral grounds rather than just logical grounds. Almost everybody is involuntarily short the virus, with some people more short than others: i.e. those who die. What Sunstein did was therefore a kind of abstract securities fraud: he encouraged people to make an investment that he gave the impression of having made himself, but in fact had not. Needless to say, the investment was a catastrophically poor one.

    The ‘long/short indifference fallacy’ refutes naïve probabilism in general, but is also devastating in Sunstein’s particular case.

    3 – It wouldn’t hurt to quote Warren Buffett. Everybody likes Warren Buffett. “in order to succeed, you must first survive.”

    4 - typo on pg 2: “Behavioural economists like Sunstein views probability neglect …”

  10. Mike SaundersMarch 13th, 2020 at 07:24 pm

    Discussing the COVID-19 pandemic with friends and colleagues over the past few weeks, I've continued to fall back on the following example: if you're kitchen was on fire, the last thing you'd do is try to calculate the probability of the fire spreading to the rest of the house. You'd either try to put it out if you could, or grab your family and pets, get out fast and call the fire department.

    Thank you for this extremely important piece of work! It explains in an incredibly articulate way what I, and I can only assume many others, have been trying to since this whole thing kicked off.

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When gambling, think probability.
When hedging, think plausibility.
When preparing, think possibility.
When this fails, stop thinking. Just survive.

Naive probabilism is the (naive) view, held by many technocrats and academics, that all rational thought boils down to probability calculations. This viewpoint is behind the obsession with `data-driven methods' that has overtaken the hard sciences, soft sciences, pseudosciences and non-sciences. It has infiltrated politics, society and business. It's the workhorse of formal epistemology, decision theory and behavioral economics. Because it is mostly applied in low or no-stakes academic investigations and philosophical meandering, few have noticed its many flaws. Real world applications of naive probabilism, however, pose disproportionate risks which scale exponentially with the stakes, ranging from harmless (and also helpless) in many academic contexts to destructive in the most extreme events (war, pandemic). The 2019--2020 coronavirus outbreak (COVID-19) is a living example of the dire consequences of such probabilistic naivet\'e. As I write this on March 13, 2020, we are in the midst of a 6 continent pandemic, the world economy is collapsing and our future is bound to look very different from the recent past. The major damage caused by the spread of COVID-19 is attributable to a failure to act and a refusal to acknowledge what was in plain sight. This shared negligence stems from a blind reliance on naive probabilism and the denial of basic common sense by global and local leaders, and many in the general public.



➤  Version 1 (2020-03-13)


Harry Crane (2020). Naive Probabilism. Researchers.One,

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