Black swans from the future

“I’m the Doctor,” he said, stepping out of his time machine and ogling the young ladies. “I know your future.”

You react as any full-blooded, rational de-biaser must react when confronted by the impossible: you invite him out for a drink. 

Several bottles later, he confides in you that an extremely unlikely event – a “black swan” – is going to happen within the next few days. “Not only is it going to be a total outlier, like September the 11th,” he slurs, “but also like then, all your probability estimates are going to be up in the air for several weeks after.” 

He stumbles back to his machine and vanishes – to crash soon after as he tries to drive between our two suns – and leaves you with a pair of important questions: as a dedicated de-biaser, how do you add this information to your estimates? And, more importantly, how do you make money out of it? 

I’ll argue that there isn’t much you can do in practice. Let’s assume he’d confided that the black swan was an event on the stock markets. Your first instinct might be to increase your estimate of a dramatic crash or a huge upswing. But those aren’t the only sort of outliers that can happen; and arguably, they’d be the least effective at messing up all your probability estimates. 

What if there’s an hour of trading where no-one buys or sells a stock? What if the market were to stay constant for a full day – every price increase balanced by a price decrease, so that the total value never moves. What if instead the fluctuations of the market that day spell out, in Morse code, the first chapter of the Koran – or Moby Dick? 

In order to update your estimates, you’d need to know, in advance, everything that would be an extreme event, and spread an increase of probability over them all.

The comparison with 9/11 might be useful here – suppose you knew in advance that some massive terrorist attack was on its way that day (as some apparently should have). You’d have to imagine everything could be a terrorist attack, and spread an increase in probability among them all. You’d probably end up increasing the probability of an attack on the World Trade Center, or a plane hijacking (correct) but also on attacks on ports, an assassination attempt on the president, and more terrifying events like a dirty bomb or a bacteriological weapon. You probably wouldn’t increase your estimate of the chance of a plane being used to crash into a building – because that wouldn’t occur to you.

To even begin changing your estimates, you’d have to have a feel for how much of these outliers there are out there that you can’t even imagine yet – an impossible task. If you allowed yourself “probabilities about probabilities” you might be tempted to just decrease your certainty of all your estimates. But that, however, is the equivalent of smashing up your telescope because a friend told you it had an unspecified flaw.

I think the best you can do is leave your estimates as they are, bet someone a lot of money that “something financial will make the news in a big way soon” and expect the unexpected. But is there a better way? It’s intensely frustrating to have information we can’t use.

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  • http://profile.typekey.com/sentience/ Eliezer Yudkowsky

    Stuart, please break up this article into the “Introduction” and “Continuation” (I would recommend using the first four paragraphs as the introduction.)

  • Carl Shulman

    “What if there’s an hour of trading where no-one buys or sells a stock? What if the market were to stay constant for a full day – every price increase balanced by a price decrease, so that the total value never moves. What if instead the fluctuations of the market that day spell out, in Morse code, the first chapter of the Koran – or Moby Dick?”

    The priors for these events are far lower than for a large swing in market values. You should buy put and call options on the major indexes to exploit volatility.

    “like September the 11th,” he slurs, “but also like then, all your probability estimates are going to be up in the air for several weeks after.”
    Terrorists crashing some airplanes screwed up your probability estimates to a degree comparable to the NASDAQ spelling out the Koran or some other comprehensible message?

  • http://profile.typekey.com/halfinney/ Hal Finney

    A change in the width of your probability distribution is just as significant as a change in the peak, and foreknowledge of such a change on the part of the market allows profit opportunities. There are investments called “straddles” which bet on an increase in volatility. Basically you buy an option that bets the price will go up and simultaneously one that bets it will go down. If he’s right and the markets are unsettled afterwards, you could make a nice profit there.

  • http://cob.jmu.edu/rosserjb Barkley Rosser

    Given that the historical distribution of returns in most asset markets is skewed downwards, that is many more dramatic crashes than sharp upward movements, a dramatically sharp upward movement would make for more of a “black swan” event, although in fact black swans are hardly all that rare.

  • michael vassar

    Time travel (and personal contact with a time traveler) is sufficiently unlikely that you should simply assume that you dreamed or hallucinated the whole experience. You should slightly increase your probability estimate that you are insane in certain ways which predispose you to such experiences, and consequentially you should try to pull your beliefs slightly towards conformity with the majority of relevant experts or of the general population if you can identify such majorities (but why are your attempts to do this assumed to be any less biased than attempts to do anything else). For the most part though, you should simply acknowledge that human brains are messy error-prone machines, barely good enough to do science, and recognize that a single hallucination is not that uncommon or disturbing an experience, especially if you are composed enough not to believe what is happening at the time, or failing that, immediately afterwards.

    You should probably not even be on the look-out for extreme black-swan events to check your experience for confirmation, as confirmation biases are two powerful, and 9/11 level unlikely and significant events are fairly likely in aggregate. Anything unlikely enough to genuinely confirm something as unlikely as time travel to a meaningful degree will be obvious enough that you will notice without needing to be on the lookout, and is likely to be sufficiently surprising that your expectation that money is highly desirable should be, conditional upon such an event, relatively small.

  • http://rafefurst.wordpress.com/ Rafe Furst

    A sticky wicket for these types of discussions is that in complex systems, feedback loops and self-fulfilling prophecies are rife. The observer is not independent of the outcome. So when you update your predictions based on new information and then do anything at all based on your new predictions, you are changing the relative likelihoods of all the outcomes you just updated your predictions on. We are all butterflies flapping our wings causing hurricanes across the world, and de-biasers have bigger wings than most.

  • Brian

    It’s absolutely hilarious that a post on a blog dedidated to the eradication of bias cites none other than…CBS News!

  • Stuart Armstrong

    Terrorists crashing some airplanes screwed up your probability estimates to a degree comparable to the NASDAQ spelling out the Koran or some other comprehensible message?

    Not quite to that extent, but close. For a few days after, I felt the world was going to change – had no idea what to expect from the point of view of air-travel security, terrorism, the economy, international relations, even the future of the world.

    Of course, I was more impressionable back then. I think that the stock market spelling out the Koran, today, would have only a slighter greater effect than 9/11 did then.

    Time travel (and personal contact with a time traveler) is sufficiently unlikely

    Yes, that’s the easy way out. But you get round that by adding sufficient evidence the story to convince yourself that Time Travel is possible. In fact, Time Travel isn’t needed – you can replace it with an equivalent situation – someone with insider information on, say, a huge upcoming scandal. If he/she doesn’t say anything more than that, doesn’t tell you the nature of the scandal or who’s involved, but just hints that it will demolish a lot of your estimates, then the situation is analogous.

  • Stuart Armstrong

    You should buy put and call options on the major indexes to exploit volatility.

    How do you know that volatility is coming along? Sure, of the options I stated, the most likely were the most volatile. But of all the things that could count as a black swan, why are you confident that volatility will be a feature of the most likely?
    (note: I agree with you, that would be my feeling too. But are our feelings based on anything rational? Or are they just a failure of imagination?).

  • http://profile.typekey.com/halfinney/ Hal Finney

    Stuart, the Doctor said, “all your probability estimates are going to be up in the air for several weeks after”. That is almost a literal description of enhanced volatility in the markets. Even if no other strange things happen, this change in market psychology will make your straddles a winning play.

  • Stuart Armstrong

    “all your probability estimates are going to be up in the air for several weeks after”. That is almost a literal description of enhanced volatility in the markets.

    I don’t really see this. If the stock market were to suddenly change to a situation where increases and decreases were much smaller than before, or to a situation where they were more predictable and less likely to change directions, that would put all your probability estimates up in the air, but would have decreased volatility.

  • Stuart Armstrong

    Found this, eerily close to the example I was using: http://www.wired.com/wired/archive/15.04/play.html?pg=6. On black swans and “expecting the unexpected”.