After recent events in Ukraine, Samotsvety convened to update our probabilities of nuclear war. In March 2022, at the beginning of the Ukraine war, we were at ~0.01% that London would be hit with a nuclear weapon in the next month. Now, we are at ~0.02% for the next 1-3 months, and at 16% that Russia uses any type of nuclear weapon in Ukraine in the next year.
Expected values are more finicky and more person-dependent than probabilities, and readers are encouraged to enter their own estimates, for which we provide a template. We’d guess that readers would lose 2 to 300 hours by staying in London in the next 1–3 months, but this estimate is at the end of a garden of forking paths, and more pessimistic or optimistic readers might make different methodological choices. We would recommend leaving if Russia uses a tactical nuclear weapon in Ukraine.
Since March, we have also added our track record to samotsvety.org/track-record, which might be of use to readers when considering how much weight to give to our predictions.
Update 2022-10-04: Changed our estimates as a result of finding an aggregation error. You can see the previous version of our post here. We also noticed that because of the relatively low number of estimates, they are fairly sensitive to each forecasts, so we are working on incorporating more forecasts.
Update 2022-10-19: These estimates seem a bit out of date now; see this comment and these forecasts from the Swift Institute.
We have updated our decomposition to the following:
- What is the probability that Russia will use a nuclear weapon in Ukraine in the next MONTH?
- Conditional on Russia using a nuclear weapon in Ukraine what is the probability that nuclear conflict will scale beyond Ukraine in the next MONTH after the initial nuclear weapon use?
- Conditional on the nuclear conflict expanding to NATO, what is the chance that London would get hit, one MONTH after the first non-Ukraine nuclear bomb is used?
For each of those questions, we also asked forecasters for their yearly probabilities. Following up on previous feedback, we also asked forecasters for their core reasons behind their forecasts, and we’ll present those alongside their probabilities.
We also asked a range of questions about counterfactuals:
- Conditional on Russia NOT using a nuclear weapon in Ukraine, what is the probability of a nuclear conflict outside Ukraine in the next MONTH?
- Conditional on Russia NOT using a nuclear weapon in Ukraine what is the probability that nuclear conflict will scale beyond Ukraine in the next YEAR?
- Conditional on Russia NOT dropping a nuclear weapon in Ukraine in October, what is the probability that London will be hit with a nuclear weapon in October?
As well as a sanity check:
- What is the unconditional probability of London being hit with a nuclear weapon in October?
For ≤ 1 month staggering times between each step
|Event||Conditional on previous step||Unconditional probability|
|Russia uses a nuclear weapon in Ukraine in the next month|
|Nuclear conflict scales beyond Ukraine in the next month after the initial nuclear weapon use|
|London gets hit, one month after the first non-Ukraine nuclear bomb is used?|
For ≤ 1 year staggering times between each step
|Event||Conditional on previous step||Unconditional probability|
|Russia uses a nuclear weapon in Ukraine in the next year|
|Nuclear conflict scales beyond Ukraine in the next year after the initial nuclear weapon use|
|London gets hit, one year after the first non-Ukraine nuclear bomb is used?|
This time, we are also experimenting with providing a few visualizations. Their advantage is that they may be more intuitive; the disadvantage is that they may gloss over the shape of our uncertainty, and thus mislead. Reader beware.
For the forecast with one month between each escalation step, we have:
A forecaster’s perspective
In order to understand at what level we are forecasting here, we are providing forecasters’ comments. One forecaster provided his comments in a more self-contained form—rather than question by question—so I’m presenting those comments here, lightly edited:
In general, nuclear rhetoric has been used extensively before and it seems that it was fairly successful at achieving its intended goals without having to use the weapons (e.g., Germany was hesitant to send weapons to Ukraine). I think such bluffing might be wearing off but Moscow is very good at maintaining ambiguity.
- Nonetheless, previously stated “red lines” have already been crossed in this war without nuclear escalation. E.g., cross-border raids into Belgorod and strikes against Crimea.
Being ambiguous about one’s willingness to use these weapons is what we have seen in the past and is what we see now. E.g., Zvi previously summarizes, when discussing a recent Putin's speech:
> What I heard were several instances of drawing a distinction between Russia and its territorial integrity, and the territories under occupation. He said that the call-ups would be ‘sufficient for the operation.’ He declared his intention to keep the territory, if he can maintain physical control. Then, he went back to saying that Ukraine was getting weapons that could ‘threaten Russia,’ explicitly including Crimea as part of Russia but not Donbass, whereas Ukraine’s normal forces can obviously already threaten Donbass or Kherson. He framed his threats of nuclear use in response to claimed Western nuclear blackmail and what he says are Western attempts to get Ukraine to invade clearly Russian territories.
Using nukes doesn’t feel like a good choice.
- Using one on a battlefield can’t be all much helpful. The frontline is ~1,000 km; troops are not concentrated. I guess the main benefits can come from “scaring troops,” “being credibly nuclear,” and maybe destroying key infrastructure.
- Breaking the nuclear taboo is likely to alienate parties that are ~neutral right now — most of all India. This effect is greater the more damage is done with nukes (e.g., “just testing” vs. using a very small nuke on a battlefield vs. attacking key infrastructure vs. endangering civilians).
- Using nuclear weapons would also alienate various parties in Russia:
- IIRC, most people disapprove of the use of nuclear weapons.
- Likewise, elites might be legitimately more scared: it’s one thing to be cut off from EU/US: you can still live lavishly in Russia. It’s another thing to endanger yourself and your loved ones with the salient possibility of nuclear war.
- Even military planners, I think, would not be happy about stretching the nuclear doctrine that far.
Consider what will happen if the Ukrainian offensive continues. Russia is losing cities in Lugansk. I feel that Ukrainians are calling Putin’s nuclear bluff. And this gives Putin few good options to work with.
- It seems like the most likely option is Russia just trying to sustain the conflict by pouring more resources and will into it. But it also might just lose in the end. I think “partial mobilisation” can be seen through that lens.
- Maybe Putin’s move is just to wait until the winter, when the European energy crisis will be most acutely felt?
- I think the nuclear pretext might be important for Western leadership, because they can’t just make a deal with Putin right now, he is far beyond redemption. But making deals to “avoid nuclear holocaust” — while also giving citizens cheaper gas — might be manageable.
If things go nuclear:
- I think it might be with the “least” scary nuke, because every escalation step, every credibly ambiguous situation could be turned into concessions, pauses, etc. Giving up intermediate steps is not wise.
- Other forecasters discussed, just “testing” or nuking a small island or just dumping it in the Black sea.
- I am worried about the multi-step conditional probabilities we are using here. While I think we have some ability to model the present situation, if the nuclear taboo were to be broken, we would be in unchartered land.
- In this case, people would still push for de-escalation and would try to avoid a Russia–NATO conflict (and especially a full-out Russia–NATO nuclear war). It's just hard to think about.
- (A) Because evidently previous diplomatic efforts would have failed catastrophically, and it’s unclear if there would be any remaining diplomatic tricks in their sleeves;
- (B) we haven’t been at this level of tension for a while, and we just don’t know how everyone would react;
- (C) the situation is likely to worsen for Putin (both internally and externally), and Putin might be likely to increase risk-taking as his likelihood of attaining a “win” diminishes.
I feel uncomfortable about my estimation process for a few reasons:
- We are in the territory where the “proven technique” of carefully crafting base-rates is less applicable.
- There is a good GJOpen “rule of thumb:” if a decision depends on one person, don’t go below 5%. This is because other people are not transparent to us, we don’t know their constraints and we don’t know the bulk of their incentives. In this case:
- It's not inconceivable that the decision to invade Ukraine in late February was misinformed (and ~unilateral). Relevant actors might be misinformed now, and they might be misinformed in surprising-to-us ways due to Putin being partly “siloed.”
Forecaster probabilities and comments
See a later section for a comment on our aggregation method.
Russia using a nuclear weapon in Ukraine
What is the probability that Russia will use a nuclear weapon in Ukraine in the next MONTH?
- Aggregate probability: 0.053025 (5.303%)
- All probabilities: 0.27, 0.04, 0.02, 0.001, 0.09, 0.08, 0.07
What is the probability that Russia will use a nuclear weapon in Ukraine in the next YEAR?
- Aggregate probability: 0.16388 (16%)
- All probabilities: 0.38, 0.11, 0.11, 0.005, 0.42, 0.2, 0.11
Conditional on Russia using a nuclear weapon in Ukraine in the next year, will it be a tactical nuclear weapon?
- Aggregate probability: 0.96356 (96%)
- All probabilities: 0.97, 0.93, 0.97, “Yes”, 0.98, 0.95, 0.8
These have been lightly edited. Reading them is probably indicative of the level at which we are thinking, which has the flavor of “we have a lot of uncertainty about this.”
This is a particularly dangerous time. Many of the gambles Putin has taken so far have gone badly and now he stands a real risk of losing power as the war drags on and he has nothing to show for it. Even still, for Putin, even without moral guardrails, the risks of using nuclear weapons of any kind should still outweigh the benefits if he is seeing things clearly. If things continue to deteriorate, the situation may change, but for now, it seems that although Putin has been weakened, he still has a very good chance of remaining in power if he can simply get to a stalemate in the territories he now controls. Although I've frontloaded a lot of the risk into the next month, if a nuclear weapon is going to be used, there will probably be some build-up before it is deployed with warning signs along the way. It is likely Putin will try to prepare his population, and, while declaring territories within Ukraine to be part of Russia may provide some pretense of a justification, each stage of escalation brings heightened risk. At each stage, it makes sense to escalate slowly to attempt to extract the maximum possible concessions a before taking on the increased risk of further escalation. I would expect to see nuclear tests or warning shots before seeing nuclear attacks, and for the first nuclear attack, tactical nuclear weapons would be the most logical starting point.
I think the use of nuclear weapons tactically would be a lot easier for Putin to explain to the Russian people. Perhaps strategic use could come afterwards, if he is in a desperate situation.
I think that Putin is 100% committed to conquering Ukraine. His "special military action" has largely failed so far, so he is expanding his military efforts with a "partial" mobilization. If that fails, or perhaps in combination with increased military mobilization, it looks possible to me that he could detonate a tactical nuclear weapon in the mistaken belief that it would make NATO countries back off at least from territory that Russia currently controls. In reality, I think detonating a tactical nuclear weapon would have the opposite effect, though.
[My uncertainty is] primarily methodological and from skewing to uncertainty. The main errors in the Superforecaster post-mortem for predicting invasion were overreliance on certain base rates and underestimating Putin’s willingness to take major risks. I’m hesitant to make the same mistakes twice.
I also think Putin and Kremlin officials are less analyzable than most seem to think. I still don’t have a compelling explanation for why Putin wants Ukraine so bad and why he’s taken so much risk up until this point, which to me says my mental model of their decision-making isn’t good enough to do much with.
Plausible scenarios exist where Putin uses a tactical nuke, probably to scare Ukraine, divide NATO, etc.
I would be higher with my first two estimates if they included an attack on a nuclear plant that could lead to a radiation disaster. This might be Putin's preferred method because he could keep a level of ambiguity as to Russia being responsible. That said, Putin's reason for using a tactical nuclear weapon might precisely be to let Ukraine and the world know how serious he is about not backing down. I think Putin wants to win the Ukraine War at pretty much any cost.
> […] I think Putin would almost definitely use a tactical nuke instead of a strategic one because it would make Ukraine and America/NATO more fearful of the situation without as high of a chance of a nuclear apocalypse (when compared to a strategic nuke being detonated in Ukraine).
Putin has established a land bridge to Crimea, which is a major strategic goal for Russia. In recent speeches, he has explicitly said that Russia will use everything it has on the table to protect the newly annexed region.
Using nuclear weapons would drastically upend the current geopolitical order. But I don't have enough confidence to confidently reject that outcome.
Nuclear conflict escalating beyond Ukraine after Russia uses a nuclear weapon in Ukraine
Conditional on Russia using a nuclear weapon in Ukraine what is the probability that nuclear conflict will scale beyond Ukraine in the next MONTH after the initial nuclear weapon use?
- Aggregate probability: 0.0254 (2.5%)
- All probabilities: 0.15, 0.09, 0.0013, 10^(-5), 0.01, 0.3, 0.05
Conditional on Russia using a nuclear weapon in Ukraine, what is the probability that nuclear conflict will scale beyond Ukraine in the next YEAR after the initial nuclear weapon use?
- Aggregate probability: 0.095685 (9.6%)
- All probabilities: 0.2, 0.15, 0.0151, 10^(-5), 0.15, 0.4, 0.1
I think nuclear war happening as a result of Russia using a tactical nuke in Ukraine is not extremely unlikely because the world would be in somewhat unprecedented territory, so this could make for a catastrophe as a result of miscalculations on one or both sides.
If Russia uses a nuclear weapon, the west probably would not respond with a nuclear strike, but would probably try to use other channels which I won't speculate about publicly. Depending on the type, scale, and impact of the attack, a nuclear response is possible. If there is no Russian nuclear attack there is a minuscule chance of either a preemptive strike (based on intelligence that Russia is likely to launch a nuclear attack) or a false signal based on something that looks like an attack triggering a nuclear strike against Russia. The fact of heightened tensions makes these kinds of accidents more likely than they would otherwise be.
I don't think Russia nuking Ukraine raises the global nuclear risk by much. I think most of the risk still comes from accidental launches due to false alarms, which I think is probably at an elevated risk currently.
I think that the MAD precludes nuclear conflict scaling up. And I think that if nuclear conflict were to expand following Russia detonating a nuclear weapon in Ukraine (or elsewhere), then that would likely happen close to immediately.
Payload and target of tactical nukes are all widely variable, if one is used I’d imagine those parameters would be chosen to minimize the risk of a nuclear response.
NATO isn’t currently personally involved in the war, its hard to imagine them deciding to send troops or especially to send nukes in response to a hit on a military target or a demonstration blast on Snake Island or the Black Sea.
It’s possible Putin miscalculates or actually wants nuclear war, but to me the most likely outcome is negotiations (for better or for worse).
I have high confidence that nuclear weapons will not be used outside this conflict.
I don't have high confidence that nuclear weapons will not be used in areas close to the strategic landscape (e.g., areas supporting either side in NATO, Belarus, inner Russia, etc.)
No one wants it to escalate. Escalating to NATO is suicidal, just clearly a loss for Putin and folks.
Also, I expect revolt of elites or something. As they would feel that this is totally suicidal, not worth it. I expect a lot of people to fear that nuclear war would mean guaranteed death or misery for their families etc.
London being hit with a nuclear weapon, conditional on nuclear conflict escalating beyond Ukraine
Conditional on the nuclear conflict expanding to NATO, what is the chance that London would get hit, one MONTH after the first non-Ukraine nuclear bomb is used?
- Aggregate probability: 0.1424 (14%)
- All probabilities: 0.4, 0.15, 0.9985, 0.05, 0.02, 0.002, 0.5
Conditional on the nuclear conflict expanding to NATO, what is the chance that London would get hit, one YEAR after the first non-Ukraine nuclear bomb is used?
- Aggregate probability: 0.232015 (23%)
- All probabilities: 0.45, 0.3, 0.9985, 0.05, 0.12, 0.01, 0.5
What is the unconditional probability of London being hit with a nuclear weapon in October?
- Aggregate probability: 0.00066 (0.066%)
- All probabilities: 0.01, 0.00056, 0.001251, 10^-8, 0.000144, 0.0012, 0.001
If nuclear conflict expands outside of Ukraine, it seems quite likely that London would get hit because I think that the UK would be the second choice of a Russian nuclear attack—the first choice being America. I also think that in the case of a nuclear war, it is a likely scenario that Russia launches a general nuclear attack on most, if not all of, NATO.
Barring accidents nd other unlikely circumstances, London will only be a target in the event of full-scale nuclear war. At each stage of escalation, prior to full-scale war, there would be attempts to take off ramps. But, it is possible, even if unlikely, that predetermined nuclear response protocols could kick in, or, in the fog of war mistakes and miscalculations could result in rapid escalation.
If there is a nuclear exchange between NATO and Russia, London will be hit very quickly.
If a nuclear conflict does expand to NATO, I would still hold out some hope that it doesn't turn into an all-out nuclear war. Thus, my forecast for London getting hit in the event of nuclear conflict with NATO is relatively low. And, if the nuclear conflict expanded to NATO, I'd expect that if London were to get hit, then it would happen within a month. My forecast for the unconditional chance of London getting hit in October is about 10% of my forecast for any nuclear conflict in October and is barely above my forecast conditional on Russia not dropping a nuclear weapon in Ukraine.
Conflict likely wouldn’t expand to the exchange of strategic nukes after a tactical nuke exchange. Large cities are where the leaders making decisions are. Its one thing to kill soldiers and civilians but it's another to put your own life on the line. Unlike other questions, we have a fairly strong historical track record here for mutually assured destruction during the cold war. Time has passed and tactical nukes are a key difference, but I think the core concept still applies.
London getting targeted is also a very foreseeable scenario, I’d be surprised if NATO’s military systems aren’t ready and sophisticated enough to detect and shoot down a missile or submarine.
There are also layers of complication from assassination, coups, and civil unrest. The risk to Putin feels much more personal than in other scenarios.
Escalation is still possible, e.g. maybe Putin just really hates the West and that’s his true motivation, or maybe conflict simply keeps escalating once nukes are exchanged. But that type of dramatic escalation feels unlikely.
Escalation beyond Ukraine doesn't help Russia achieve its strategic goals.
hard to see intermediate escalation
Comparison vs other sources
A few other sources which have forecasts on this are:
- Back in 2019, Luisa Rodríguez’s analysis put the chance of a US/Russia nuclear exchange at 0.38%/year (if taking the arithmetic mean of her samples), or a 0.13%/year if taking the geometric mean of odds.
- Back in March, we gave a 0.067%/month to a “NATO/Russia nuclear exchange killing at least one person in the next month”, and an 18% probability of London being hit with a nuclear weapon after that, for an implied 0.012% monthly probability.
- Back at the end of March, Peter Scoblic gave a heavily caveated 5% to a “NATO/Russia nuclear exchange killing at least one person in the next month”, and a likewise heavily caveated 65% probability to London being hit with a nuclear weapon after that, for an implied 3.2% probability
- Zvi and Daniel Filan also gave their probabilities using our decomposition.
- Metaculus has several questions on nuclear weapons, such as:
- Will there be at least one fatality due to deliberate nuclear detonation by 2024? (7%)
- Will there be an offensive nuclear detonation on a nation's capital by 2024, if an offensive nuclear detonation occurs anywhere by 2024? (20%)
- Will the first offensive nuclear detonation by 2024 be against a battlefield target, if there's an offensive detonation by then? (53%)
- Will at least one nuclear weapon be detonated in Ukraine before 2023? (7%)
- Will a Russian nuclear weapon be detonated in the US before 2023? (<1%; note that Metaculus doesn’t accept probabilities below 1%)
- Will a non-test nuclear detonation cause at least 1 fatality before 2024? (12%)
- Will >2 countries offensively detonate nuclear weapons by 2024, if any offensive detonation of a country's nuclear weapon occurs by then? 35%
- Will >2 countries have nuclear weapons offensively detonated on or over their territories by 2024, if any country offensively detonates a nuclear weapon by then? (49%)
- Manifold Markets also has a few markets on this, such as:
There is internal discord within Samotsvety about the degree to which the magnitude of the difference between our current and former probabilities is indicative of a lack of accuracy. We Samotsvety updated our endline monthly probability of London being hit with a nuclear weapon by ~2 (~0.02% vs 0.067 * 0.18 = 0.012%). The difference was higher before correcting an aggregation error, so I've moved discussion to a footnote.
In addition, a former senior U.S. government official previously gave me a 20% probability of Russia using nuclear weapons by the end of the year, and at the time I thought that this was too high, but now think that this was a reasonable belief to have, and I regret not having deferred more to him.
Estimating the value of leaving London or other major cities
Here is a template for calculating risk, given one’s probabilities (also saved here and here).
If we input the full range of our forecasters’ probabilities together with some default values, we get the following estimate of how many lost hours one loses in expectation as a result of staying in London in the medium term—where, because of the way we prompted forecasters, the “medium term” can range from one to three months:
If we instead input the forecasters’ aggregate, rather than the range, we arrive at:
A mixture of both estimates gives a 90% confidence interval of ~2 to 300 hours lost. Personally, I would use this second estimate, but it's hard to say why: maybe because I think that taking the minimum and maximum out of each question does a good job of filtering the least accurate forecasts.
Compare with a previous estimate back in March:
So, the danger of staying in London has increased by ~1-10x since March. We’d guess for most people reading this post moving out of the city for 1-3 months would still cause more value in lost productivity than the updated estimates of expected lost life hours, but it might be a closer call than it was previously.
For personal purposes, we probably don’t have a better decision rule than “leave major cities if any tactical nukes are dropped in Ukraine” (as this will ~10x risk).
A sanity check
We can compare the directly elicited probability of nuclear war reaching London in October with the conditional steps multiplied directly:
The conditional steps are:
- What is the probability that Russia will use a nuclear weapon in Ukraine in the next MONTH? 0.053025 (5.303%)
- Conditional on Russia using a nuclear weapon in Ukraine what is the probability that nuclear conflict will scale beyond Ukraine in the next MONTH after the initial nuclear weapon use? 0.0254 (2.5%)
- Conditional on the nuclear conflict expanding to NATO, what is the chance that London would get hit, one MONTH after the first non-Ukraine nuclear bomb is used? 0.1424 (14%)
And if we multiply these together, we get 0.053025 * 0.0254 * 0.1424 = .00019178930400 (0.019% ~ 0.02%), versus 0.00065 (0.066%) when elicited directly.
I think that the conditionals multiplied directly should be higher. Because the directly elicited probability assumes a scenario where escalation happens within one month, whereas the conditionals multiplied directly would include that scenario, but also scenarios where each escalation step is more staggered.
One way to think about this difference is that a ~3x difference when eliciting unlikely, <1% events is relatively normal. Personally, I (Nuño) would give more weight to the conditionals multiplied directly.
Counterfactual baseline risk
Forecasters also predicted on these counterfactual questions.
- Conditional on Russia NOT using a nuclear weapon in Ukraine, what is the probability of a nuclear conflict outside Ukraine in the next MONTH? (0.036%)
- Conditional on Russia NOT using a nuclear weapon in Ukraine what is the probability that nuclear conflict will happen beyond Ukraine in the next YEAR? (0.132%)
- Conditional on Russia NOT dropping a nuclear weapon in Ukraine in October, what is the probability that London will be hit with a nuclear weapon in October? 0.006%
- All probabilities: 0.1%, 0.002%, 0.125%, 0.000001%, 0.001%, 0.01%, 0.005%.
The first two probabilities are dwarfed by the probabilities in the Russian conflict. The third probability indicates a very low baseline risk, but is also very sensitive to the individual forecasts.
A brief note on the aggregation method
We used the geometric mean of the samples with the minimum and maximum removed to better deal with extreme outliers, as described in our previous post. Note that the minimum (resp. maximum) do matter. For example, in [0.1, 1, 10, 100, 1000], the aggregate would be (1 * 10 * 100) ^ (1/3) = 10. But if we remove 0.1, that aggregate would become (10 * 100) ^ (1/2) = 31.6.
This is a project by Samotsvety. Thanks to Jared Leibowich, Jonathan Mann, Tolga Bilge, belikewater, Greg Justice (@slapthepancake), Misha Yagudin and Nuño Sempere for providing updates. Thanks as well to Eli Lifland for comments and suggestions, and to Daniel Kokotajlo and Bhuvan Singla for their probability mass app.
Dropping into the first person, I (Nuño) felt that the degree to which we updated, or at least the degree to which I personally updated, is indicative that our/my probability wasn’t a martingale, i.e., that it didn’t accurately price the likelihood of future movements. See some discussion about this here, in the context of Nassim Taleb criticizing Nate Silver. Overall, that update to me suggests we should give probabilities closer to 50%, to better adjust for future unknowns, which we maybe aren’t pricing in.
On the other hand, other proud Samotsvety forecasters point out that our previous forecast was only for March, even though we presented the risk in annualized units. It’s also just straight-out possible that we are in the bottom 10-20% of scenarios. So overall we are not done with our post-mortem, which would also include personal updates in April &c.
These numbers seem pretty all-over-the-place. On nearly every question, the odds given by the 7 forecasters span at least 2 orders of magnitude, and often substantially more. And the majority of forecasters (4/7) gave multiple answers which seem implausible (details below) in ways that suggest that their numbers aren't coming from a coherent picture of the situation.
I have collected the numbers in a spreadsheet and highlighted (in red) the ones that seem implausible to me.
Odds span at least 2 orders of magnitude:
Another commenter noted that the answers to "What is the probability that Russia will use a nuclear weapon in Ukraine in the next MONTH?" range from .001 to .27. In odds that is from 1:999 to 1:2.7, which is an odds ratio of 369. And this was one of the more tightly clustered questions; odds ratios between the largest and smallest answer on the other questions were 144, 42857, 66666, 332168, 65901, 1010101, and (with n=6) 12.
Other than the final (tactical nuke) question, these cover enough orders of magnitude for my reaction to be "something is going on here; let's take a closer look" rather than "there are some different perspectives which we can combine by aggregating" or "looks like this is roughly the range of well-informed opinion."
Individual extreme outlier answers:
Two forecasters gave an estimate on one of the component questions that was more than 2 orders of magnitude away from the next closest estimate (odds ratio over 100).
On the question "Conditional on Russia using a nuclear weapon in Ukraine, what is the probability that nuclear conflict will scale beyond Ukraine in the next YEAR after the initial nuclear weapon use?", one forecaster gave the answer 10^-5. The next smallest answer was 0.0151, an odds ratio of 1533. On the MONTH version of this question, the ratio was 130. So the 10^-5 answer differs wildly from each of the other answers, and also (IMO) seems implausibly low.
On the question "Conditional on the nuclear conflict expanding to NATO, what is the chance that London would get hit, one MONTH after the first non-Ukraine nuclear bomb is used?", the largest answer was .9985 and the 2nd largest was 0.5, an odds ratio of 666. The ratio was the same for the YEAR version of this question. This multiple-orders-of-magnitude outlier from all the other forecasts also seems implausibly high to me.
Implausible month-to-year ratios:
We can compare the answers to "Conditional on Russia using a nuclear weapon in Ukraine, what is the probability that nuclear conflict will scale beyond Ukraine in the next MONTH after the initial nuclear weapon use?" to the YEAR version of this question to see how likely each forecaster thought that the escalation would happen within a month, conditional on it happening within a year. From smallest to largest, these probabilities for p(escalation within a MONTH | escalation within a YEAR) are .067, .086, .5, .6, .75, .75, 1. Probabilities below 10% seem implausible here, both considering the question (nuclear escalation will very likely take more than a month if it happens?) and considering the other estimates, but 2 forecasters are in that range. (A probability of 1 would be implausibly high if forecasters were estimating it directly, but given that this is calculated from 2 probabilities and many answers only had 1 sigfig I guess it's not a major issue.)
Similarly, the implied estimates for p(London hit within a MONTH of a non-Ukraine nuke | London hit within a YEAR of a non-Ukraine nuke) are, from smallest to largest, .17, .2, .5, .89, 1, 1, 1. Again, low probabilities (.2 or smaller) seem implausible.
Conjunction vs. direct elicitation:
One sanity check in the original post is comparing the implied probability for a London nuke (based on p(London within a month | escalation), p(escalation within a month | Ukraine nuke), and p(Ukraine nuke within a month)) with the directly elicited p(London nuke in October). The implied probability covers a longer time period (since the monthlong window resets with each event), but the directly elicited probability covers all paths to London being nuked (not just the path via escalation from Russia nuking Ukraine), so it's not obvious which should be larger, but I think they should be close (and Nuño thought the conjunction should be larger).
Looking at each forecaster, the ratio of p(London nuke in October) to the conjunction, from smallest to largest, is .57, .62, 1.04, 8, 20, 25, 48. Five of seven forecasters gave estimates which imply that the direct estimate (shorter timeframe, more pathways) is larger. Four of them gave estimates which imply a ratio of 8 or higher, which seems implausible.
And all four of those forecasters gave at least one of the other implausible forecasts mentioned above (an outlier individual estimate and/or an implausible month:year ratio). The three forecasters who have plausible ratios here (.57, .62, 1.04) did not give any of the implausible answers according to my other two sanity checks.
3 of the 7 forecasters passed all three of these sanity checks. The other 4 forecasters each failed at least 2 of these sanity checks.
Aggregation which treats all this as noise and tries to find the central tendency helps keep the final estimate in a plausible range (and generally within the range of the 3 forecasters who passed the sanity checks), but it still seems possible to do significantly better.
IMO the epistemic status here is not seven good generalist forecasters who have thought carefully enough about these questions to give well-considered estimates, aggregated with some math that helps combine their different perspectives. Instead, the math is mainly just helping to filter out the not-carefully-considered answers.
Hey, thanks for the analysis, we might do something like that next time to improve consistency of our estimates, either as a team or as individuals. Note that some of the issues you point out are the cost of speed, of working a bit in the style of an emergency response team, rather than delaying a forecast for longer.
Still, I think that I'm more chill and less worried than you about these issues, because as you say the aggregation method was picked this up, and it doesn't take the geometric mean of the forecasts that you colored in red, given that it excludes the minimum and maximum.
I also appreciated the individual comparison between chained probabilities and directly elicited ones, and it makes me even more pessimistic about using the directly elicited ones, particularly for <1% probabilities
Hey Dan, thanks for sanity-checking! I think you and feruell are correct to be suspicious of these estimates, we laid out reasoning and probabilities for people to adjust to their taste/confidence.
I agree outliers are concerning (and find some of them implausible), but I likewise have an experience of being at 10..20% when a crowd was at ~0% (for a national election resulting in a tie) and at 20..30% when a crowd was at ~0% (for a SCOTUS case) [likewise for me being ~1% while the crowd was much higher; I also on occasion was wrong updating x20 as a result, not sure if peers foresaw Biden-Putin summit but I was particularly wrong there].
I think the risk is front-loaded, and low month-to-year ratios are suspicious, but I don't find them that implausible (e.g., one might expect everyone to get on a negotiation table/emergency calls after nukes are used and for the battlefield to be "frozen/shocked" – so while there would be more uncertainty early on, there would be more effort and reasons not to escalate/use more nukes at least for a short while — these two might roughly offset each other).
Yeah, it was my prediction that conjunction vs. direct wouldn't match for people (really hard to have a good "sense" of such low probabilities if you are not doing a decomposition). I think we should have checked these beforehand and discussed them with folks.
It would be interesting whether the forecasters with outlier numbers stand by those forecasts on reflection, and to hear their reasoning if so. In cases where outlier forecasts reflect insight, how do we capture that insight rather than brushing them aside with the noise? Checking in with those forecasters after their forecasts have been flagged as suspicious-to-others is a start.
The p(month|year) number is especially relevant, since that is not just an input into the bottom line estimate, but also has direct implications for individual planning. The plan 'if Russia uses a nuclear weapon in Ukraine then I will leave my home to go someplace safer' looks pretty different depending on whether the period of heightened risk when you will be away from home is more like 2 weeks or 6 months.
Thanks for this! It was really useful and will save 80,000 Hours a lot of time.
There is a real-money market on Russia offensively using a nuclear weapon in 2022 on Polymarket with good liquidity. Currently it is trading at 0.06
Do you know what is the cheapest way to convert fiat into USDC? Because if I get charged 2% on the conversion in and out it changes the payout dramatically
It's free on Coinbase and FTX.
Coinbase wants to charge me 3% to buy USDC with a debit card (the only option I'm given) and according to Polymarket's deposit page FTX does not support Polygon transfers of USDC
Deposits from FTX should be possible, though. They recently started to support USDC on MATIC (Polygon). Another option is to use crypto.com
What is the probability that Russia will use a nuclear weapon in Ukraine in the next MONTH?
Sorry if it sounds rude but If one person gives 0.001 and the other gives 0.27 shouldn't it mean that at least one of the two is not good at forecasting?
No, if an individual forecast would prove to be off, that wouldn't entail they're not good at forecasting.
So I agree that having a wide spread is worrying. At the same time, I'd expect the aggregate to be better if it incorporates different perspectives, even if they don't come to agree.
I don't see how that's consistent with:
I get that the first of those should be 0.053. Haven't run the numbers on the latter, but pretty sure the geometric mean should be smaller than 23% from eyeballing it. (I also haven't run the numbers on other aggregated numbers in this post.)
Geometric mean of the odds.
Aaand, you are right, I was missing the last estimate. Will change, though probably after the next hour.
Now fixed. The exercise also make me realize that these numbers are very sensitive to individual forecasters' estimates, so we are looking to add more forecasters to our aggregate.
A forecast from Swift Center: https://www.swiftcentre.org/will-russia-use-a-nuclear-weapon/
Upd: seems important to note that we have an overlap of ~2 forecasters, I think.
Another follow-up forecast from Swift: https://www.swiftcentre.org/what-would-be-the-consequences-of-a-nuclear-weapon-being-used-in-the-russia-ukraine-war/
Thanks for the post. I appreciate your effort to attach your reasoning to the forecasts - I think the reasoning is much more informative, especially given the huge amount of uncertainty.
A small suggestion for improvement would be to number the probabilities and quoted reasoning, so as to make it easier to match between them.
Thanks for doing this!
In this squiggle you use "ableToEscapeBefore = 0.5". Does that assume that you're following the policy "escape if you see any tactical nuclear weapons being used in Ukraine"? (Which someone who's currently on the fence about escaping London would presumably do.)
If yes, I would have expected it to be higher than 50%. Do you think very rapid escalation is likely, or am I missing something else?
I was just using 0.5 as a default value. In our March estimate, we were at 0.75, a critic was at 0.3; Zvi Moskovitz was at solomonic 0.5. This time this wasn't really the focus of our estimate, because I was already giving forecasters many questions to estimate, and the situation for that sub-estimate doesn't seem to have been changed as much.
Thanks for the links! (Fyi the first two points to the same page.)
The critic's 0.3 assumes that you'll stay until there's nuclear exchanges between Russia and NATO. Zvi was at 75% if you leave as soon as a conventional war between NATO and Russia starts.
I'm not sure how to compare that situation with the current situation, where it seems more likely that the next escalatory step will be a nuke on a non-NATO target than conventional NATO-Russia warfare. But if you're happy to leave as soon as either a nuke is dropped anywhere or conventional NATO/Russia warfare breaks out, I'm inclined to aggregate those numbers to something closer to 75% than 50%.
On the other hand, the critic updated me towards higher numbers on p(nuke london|any nuke). Though I assume Samotsvety have already read it, so not sure how to take that into account. But given that uncertainty, given that that number only comes into play in confusing worlds where everyone's models are broken, and given Samotsvety's 5x higher unconditional number, I will update at least a bit in that direction.
Really helpful. I'd love to hear a quick and dirty analysis of a) what qualifies as a 'major' city? (eg lesser UK/US cosmopolitan areas or capitals of less involved European countries, Amsterdam, Paris, etc), and b) how physically far from a city you'd need to move to be safe from the fallout of a modern nuke detonated there.
you can play with the interactive maps ok NukeMap
Disclaimer: I don't have any expertise in bombs and I can't tell whether the information provided by the site is realiable or not. It would be good to have the opinion of someone who spent some time in researching whether the NukeMap assumptions are correct
I wish there was a way to do granular disagreement on this. While this is a clear case for forecasting and estimation, all issues boil down to how big quantities are.
There is no way for me to comment on specific lines or specific numbers. And technically speaking I don't think this can be too difficult since LessWrong has a docs-style editor. I suggest that inline comment threads are hidden by default and users can turn them on if they want to. Perhaps they get brighter the more upvoted they are.
Secondly, I wish estimation was a first-class citizen of the forum. Imagine if for each of these models, users could add their own numbers and we could see a community median across all supplied values. For many articles, I think that would be really valuable/game-changing.
I reckon that it's gonna happen by 2030 and I'm happy to bet to that effect
I'm willing to bet* the forum will support it - and I think it's a bad idea.
*Not, like, on the actual platform
Why do you think it's a bad idea?
Because I think crowdsourced forecasts without any incentives are basically random. It's going to give a wrong semblance of information.
Same for estimations that are forced to be numerical even when that's not appropriate. I think EA should have less forecasting and estimation, and not more.
(I do appreciate the group making this post - see my top level comment)
I unironically think that almost everything in EA should be numerical somewhere. Maybe we have a text layer to explain the numbers, but deep down everything is about the sizes of quantities.
If you think crowdsources forecasts without incentives are random, what do you think about crowdsourced discussions?
I down x-ed your post. I get that feels harsh, but I strongly think you are wrong.
Much more informative - in accordance with what my other comment saying I find the reasoning in the OP much more informative than the numbers.
Feels honest rather than harsh. But thanks for the sympathy, and it's nice to know where the votes come from.
Obviously, I also strongly disagree with you :)
Update 2022-10-19: These estimates feel a bit dated right now. The Swift Center has some slightly more recent estimates here, though they ask about the next six months, rather than the next month.
Overall I'd say that since these estimates were published, our uncertainty has gone a bit down.
I've polled a few more forecasters these past few weeks and they are lower than our initial aggregate. But aggregation doesn't feel as meaningful given that each forecast was at slightly different times.
Does anyone have comments on how the huge degree of uncertainty should change our actions?
My intuition is that high uncertainty is argument in favour of leaving town, since it seems like it's worse to underestimate the risks (death) than overestimate them (some inconvenience).
Or another idea might be that if the risk turns out to be lower than the best guess, you can just return to town. Whereas if it was higher, then you're dead. So leaving town is a more robust strategy.
But I could also imagine this is totally the wrong way of thinking about it. E.g. maybe if we're thinking about hours of EA work (instead of personal hours), we should be pretty risk neutral about them, and just go with expected hours lost vs. gained.
Expected hours lost vs gained seems the most intuitive + rational model.
If thinking time was free, the appropriate theoretical way to handle uncertainty of course is to have multiple plausible distributions with different weights and multiply though the area-under-the-curve for each of them.
You probably want to include some discounting for future hours as well (since 1h now probably matters more than 2h 10 years from now), and another multiplier on the distribution for how much more vs less important your time after a large-scale catastrophe will be.
(Have I actually done this? No. But hopefully somebody else will).
Isn't there a similar argument to covid – the best case scenario is bounded at zero hours lost, while the bound on the worst case is very high (losing tens of thousands of hours), so increasing uncertainty will tend to drag up the mean?
The current forecasts try to account for a bunch of uncertainty, but we should also add in model uncertainty – and model uncertainty seems like it could be really high (for the reasons in Dan's comment). So this would suggest we should round up rather than down.
This seems wrong to me? It doesn't take risk into account at all. I may be willing to pay some price to make sure dying is not a probable option.
In other words, plain expected value is just one metric. Conditional value at risk (with some risk tolerance) could be another, for example.
I was thinking altruistically, as was Ben. I agree that there are also the usual personal reasons to want to be alive, which pushes in favor of sacrificing expected work hours to increase the probability of survival.
I am lower on use in Ukraine the next month (~4%) and much lower in the next year (6%).
I guess I sense it's just still a big norm we need reasons to push us away from this. What's more, even if Putin does want to launch a nuke, which I guess I think is unlikely (10?%) it still needs to happen soon and the chain of command need to agree with him. And his lieutenants need to think that this is a situation that gains them something rather than thinking that NATO will support Ukraine with conventional weapons.
What I find more compelling is that they might launch/detonate a low-megaton nuke on the battlefield where they are losing. But again, that has to go off without a hitch, via some chain of command, it has to happen in the next month. And again, what does Russia gain from this, other than showing that their bluff wasn't a bluff.
I am happy to bet here.
I'm not sure whether this is included in your 4%?
It is. I guess I just sense this is still really quite unlikely.
In the row for "Nuclear conflict scales beyond Ukraine in the next month after the initial nuclear weapon use" it says that the probability is 0.36%. I think that is a typo and should say 0.386%.
Thank you! It's such a pleasure to read high quality work in this forum.
Thanks, though your complement seems oddly double-sided against the rest of the forum's content
That was not my intention. I just wanted to communicate the ideas that 1. this is high quality work 2. I appreciate it more when I read high quality work here, instead of somewhere else. Makes me happier about the community.
This number is before you made the correction, is that right? Can you edit this to highlight the fact that it (aiui) does not apply any more?
This is a fantastic forecast, thank you.
I understand why this would be beyond the scope of this forecast, and maybe it's simply too chaotic to forecast reasonably, but I think from the perspective of making a personal decision what I wish there were here is a forecast on the likely regional outcome of a nuclear weapon detonating on London (or any other major city). Something like a forecast, conditional of a nuclear weapon detonating on London, that an escaped Londoner stays alive >1 year somewhere not directly hit in the UK vs >1 year in New Zealand, given baseline but minimal disaster prep.
Mostly I just bring this up because the cost of leaving the direct blast/fallout zone of a major city by travelling an hour or two is significantly lower than the cost of say, moving a family back and forth from New Zealand each time there is an escalatory step taken. If the only reasonable escape option is a significant trip to the Southern Hemisphere then it changes the cost side of the calculus pretty drastically for a personal decision (vs. just getting out of the immediate danger radius).
Israel - any chance you could help me find some kind of prior to whether we'd be bombed?
(For example, "Israel doesn't interest anyone, you're ok", or "Israel will only need a one bomb since it's so small, probably worth it in case of war", or "use the London numbers as priors")
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