The Narrative Fallacy: Building a Story Where There Is Only Data

The narrative fallacy is accepting an account because it fits, when the data was never capable of ruling out the alternatives. A small number of observations is consistent with many stories, and the mind produces one of them, quickly, and then treats the fit as evidence. The story adds no information and subtracts a good deal of doubt.

The fallacy rests on a counting argument that most readers apply happily to equations and never to explanations. Two unknowns and one equation leave a whole line of answers standing, and nobody calls that line a solution. Explanations behave the same way and are never treated the same way. A competent explainer can always make an account fit, so whether an account fits is never the question. The question is how many other accounts fit just as well, and that number is usually large and almost never counted. Everything that follows comes from taking that second number seriously.

What exactly is the narrative fallacy, and is it about stories being false?

No. Nearly everybody starts there, so it is the first thing to get out of the way. The narrative fallacyAccepting an account because it fits data that could not have ruled out the alternatives. is not the claim that stories are usually wrong. The story produced may well be exactly right. The fallacy is in the step where the fit is treated as though it were evidence, when the observations in front of the analyst were never capable of eliminating anything. The term is set out by Taleb in The Black Swan, published in 2007, and the sharp edge of it is that the error survives being right. A true account arrived at by fittingConstructing an account after seeing the observations, so that it cannot fail to match them. was still arrived at badly, and there is no way of telling from the inside which kind is being held.

The example is worth taking out of finance before taking it into it. An electricity bill for the month arrives at nearly twice the usual amount. Within about four seconds an account is in place: the new water heater. It fits. The heater explains the size of the jump, it explains why the jump started this month, and it feels settled enough that thinking stops. Other candidates fit that single observation just as completely. A meter read as an estimate rather than an actual reading. A tariff revision. Somebody at home more hours than usual through an unusually hot fortnight. A neighbour drawing from the same line. A faulty connection nobody has looked at. Six accounts, one observation, and all six fit perfectly. The water heater was not chosen because it beat the other five; it was chosen because it arrived first and nothing then asked it to compete.

Arrival order doing the choosing is the whole mechanism, and it does not get more complicated in a financial setting. A financial setting makes it worse. There the observations are numbers, and numbers carry an authority that makes the account resting on them feel measured rather than produced.

Why does an account that fits feel like understanding?

Because the feeling of understanding is produced by coherence, and coherence is exactly what a fitted account is optimised for. When every observation has a place in the account and nothing is left over, the sensation is of a thing clicking shut. The sensation is real, it is pleasant, and it is not information. Every rival account also leaves nothing over, so the same sensation would arrive from the second-best account, or the fourth-best, or one that happened to be flatly wrong.

Notice which operations the mind is not running while it produces that sensation. The mind is not enumerating the rivals. The mind is not asking what constraintHow much a set of observations narrows the range of possible explanations. the observations actually imposed. The mind is not testing the account against anything it was not built on. Each of those three operations could produce a defeat, and none of them are running. An account earns assent by explaining what was already seen, the one test it was constructed to pass. This is why arguing about whether a story is convincing goes nowhere: being convincing is a property of the telling and not a property of the world.

The related caution is that a good storyteller and a careful analyst produce the same feeling in a listener, and the listener cannot tell them apart from the feeling alone. Honesty is not the issue. The same caution applies just as strongly to the account told silently to oneself, with nobody else in the room and no motive to deceive anyone.

How many accounts fit the same handful of observations?

The arithmetic behind that second number runs as follows. The account in hand matters less than the number of accounts that could have been produced. Counting those properly is not possible, so a crude device stands in: about twenty four divided by the number of observations held, never going below one. The result is roughly how many distinct simple accountsAn explanation using one cause and no special cases bolted on to make it fit. remain consistent with everything observed. The number twenty four carries no authority; it was chosen because it puts the shape of the fall on one screen. The shape is the teaching, not the number.

The progression runs as follows. Three observations leave about eight accounts standing. Six leave about four. Nine leave about three. Twelve leave about two. Twenty four leave about one. Every one of those is the same division worked twice, and each checks in a moment: twenty four over three is eight, twenty four over six is four, twenty four over nine is two point seven and rounds to three, twenty four over twelve is two, twenty four over twenty four is one.

Look at where the steep part of that curve sits. The steep part sits at the left, over the small counts, and that is precisely the region every ordinary decision lives in. Nobody deliberates with twenty four clean observations. People deliberate with four, or six, or nine, and at those counts the record has barely narrowed anything. The reason a confident account is so easy to produce from a short record is not that short records are especially revealing; it is that short records forbid so little that almost any account clears them.

Why do a few observations constrain almost nothing?

Think about what an observation actually does. An observation does not point at an explanation. An observation rules some explanations out and leaves the rest untouched. A record with four entries in it can only rule out accounts that predicted something other than those four entries, and a flexible account predicts almost nothing in particular, so almost nothing rules it out. The accounts that survive longest are therefore usually the vaguest ones, and that is the reverse of how survival is normally read.

Two further things make the constraint weaker than it looks. First, an account can always be repaired. Add a special case, an exception, a one-off, and an account that was about to be eliminated goes back to fitting. A simple account, in the sense used above, is one that has not been repaired in that way, and the counting device above only counts those; allow repairs and the number of surviving accounts is unbounded. Second, the observations in a real record are rarely independent of each other. Nine readings taken from the same quarterly process are not nine separate tests, so nine entries do less eliminating than nine would suggest. Both effects push in the same direction: the record constrains less than its length implies, so the true count of surviving accounts is higher than any device like this one will show.

What happens when three accounts are told about the same nine readings?

The invented Palash 100 index is a set of nine readings written into a record, and it serves one purpose: it is a short record that somebody is trying to explain. The index opens at 100.0 and then carries eight quarter ends, at 118.0, 131.0, 112.0, 104.0, 116.0, 124.0, 121.0 and 127.0. The highest quarter end is Q2 at 131.0 and the lowest is Q4 at 104.0. From the open to Q2 is 31.0 per cent up. Q2 to Q3 falls 14.5 per cent and Q3 to Q4 falls a further 7.1 per cent, so Q2 to Q4 is 20.6 per cent down. Whether any one of these readings implies anything about a later one is a separate question.

Nine readings, on the device above, leave about three simple accounts standing. Here are three, and each is one of several that fit rather than the explanation. The first: enthusiasm built into the Q2 reading and then unwound, and the readings from Q4 onward are that unwinding settling. The second: something arrived between Q2 and Q4, did its work, and then passed, and the readings from Q4 onward are the record after it passed. The third: nothing in particular happened at all, and readings of this kind wander this much as a matter of course, so there is no episode in the record to find.

All three fit every one of the nine readings completely, so the readings do not choose between them. The sense of having understood the record comes from having produced one account rather than from having eliminated two. Anybody preferring the first over the third is preferring it on grounds that are not in the record.

What does an account do to memory of the observations?

Memory is where a harmless habit turns into an expensive one. An account does not sit politely on top of the record. An account reaches into it. Once an account is in place, the observations it uses become easy to recall and the observations it does not use quietly become a detailAn observation an account does not use, which stops being recalled once the account is in place., and a detail is something that stops being reproduced.

One account holds that the readings from Q4 onward are a recovery. The recovery account is perfectly reasonable and it fits. Four readings are what the account needs: Q4 at 104.0, Q5 at 116.0, Q6 at 124.0 and Q8 at 127.0. The account does not need Q7 at 121.0. Q7 sits below Q6 and interrupts the rise. A recovery is entirely compatible with an interruption in it, so Q7 is not evidence against the account. Q7 is simply not used. And an observation that is not used stops being rehearsed, and an observation that is not rehearsed is not there the next time the record is reproduced from memory.

Why is an account with a cause preferred to one with a coincidence?

Offer somebody two accounts of the same record. The first names a cause. The second says the pattern is a coincidenceA pattern with no cause behind it, which explanations are reluctant to accept even where it fits. and there is nothing behind it. Both fit the record equally. The first wins almost every time. The reason is worth being precise about, and it is not that causes are more probable.

A cause makes what happened feel as though it had to happen. The feeling of necessity is the whole of it. An account with a cause converts a set of readings from a list of things that occurred into a sequence of things that followed, and following is what understanding feels like from the inside. Coincidence offers no such conversion. Coincidence explains the record exactly as well and leaves the sense that nothing has been said, so it loses the contest even on the occasions when it is right. The preference for causes is a preference about how an account feels rather than about how likely it is, and the counting device above does not care which kind of account is in a slot.

The cost is one-sided and easy to state. Because coincidence never wins the contest, records that genuinely contain no episode get an episode attached to them anyway, and the person then holds a firm account of something that did not occur. Holding a firm account of something that did not occur is worse than holding no account at all. Holding no account leaves the analyst looking; holding a firm one stops the looking.

What single test separates a useful account from a fitted one?

The question to put is what the account forbids. An account explains everything it was built on, so what it explains settles nothing. The forbidden observation is the one the account says will not appear. The next step is to check whether that observation is one that could actually be looked for. An account that forbids something has stuck its neck out and can be beaten; an account that forbids nothing has described the record in different words and called it an explanation.

Run it on the electricity bill. The water heater account forbids something: it forbids the next bill returning to the usual amount while the heater is still running the same way. The prohibition is checkable, it is out of sampleA test against observations the account was not built on, so the account can fail it., and the next bill settles it. Compare the account that says charges have simply been running higher lately. Such an account forbids nothing at all: whatever the next bill says, it survives. Whether an account is true cannot be known, so the test does not ask it. The test asks whether the account is the kind of thing that could turn out to be false, and that question can be answered in about a minute.

Most accounts fail this. Failing it is not a reason to despair, it is the finding. Once it is clear that most accounts produced forbid nothing, the confidence they generate stops being treated as though it had been earned.

Where is an account genuinely the right tool?

Everywhere that an account is being used to carry a decision to somebody else, or to a later self, rather than being used as evidence. Accounts are how a reason gets remembered at all. A record of nine readings with no account attached to it is not neutral and pure; it is unusable. In eight months nobody will recall why anything was done about it. The Palash decision log records that a written reason was attached to only 84 of its 240 decisions, being 35.0 per cent. The shortfall is not a case for fewer accounts but a case for more of them, written down at the time.

So the correction is not scepticism about accounts, a discipline nobody has ever managed to sustain. The correction is a division of labour. Accounts do the work of carrying reasons forward. Records do the work of holding what actually happened. The failure comes only where the two jobs get merged, and the account is allowed to become the store of the observations. Kept in separate places, the account can be revised as often as necessary at no cost. The record it would otherwise have edited is sitting somewhere it cannot reach.

How are the observations kept where an account cannot reach them?

The correction turns out to be a filing decision rather than an intellectual one, and a filing decision is achievable. The observations are written down once, at the time, with the date on them, and never re-derived from the account later. Reconstructing what the readings were from what is believed to have happened means the record is already lost and the account is being read back in its place.

Three rules make it work. The record is written before the account is produced, or at least independently of it. The record includes the observations the account does not use, exactly the ones that will disappear otherwise. And the record is never updated to agree with a later account: a revised understanding gets written as a new dated line, alongside the old one, not over it. Applied to the nine readings, that means all nine get filed, including Q7 at 121.0, and especially Q7 at 121.0.

How does an adviser use this, and how does somebody deciding alone?

Meera Sundaram, Devika Rao, Palash Advisory Services Private Limited, the Palash decision log, the Palash 100 index, Suvarna Chemicals Limited and Kesari Logistics Limited are invented.
Educational material. Not advice on any investment, tax, budget or market position.