Rationality: What It Is, Why It Seems Scarce, Why It Matters

by Steven Pinker

A communal outrage inspires what the psychologist Roy Baumeister calls a victim narrative: a moralized allegory in which a harmful act is sanctified, the damage consecrated as irreparable and unforgivable.29 The goal of the narrative is not accuracy but solidarity. Picking nits about what actually happened is seen as not just irrelevant but sacrilegious or treasonous.

But the history of public outrages suggests they can also empower demagogues and egg impassioned mobs into quagmires and disasters. Overall, I suspect that more good comes from cooler heads assessing harms accurately and responding to them proportionately.

Even when journalists don’t whip readers into a jingoistic lather, intemperate public reactions are a built-in hazard. I believe journalists have not given enough thought to the way that media coverage can activate our cognitive biases and distort our understanding.

The press is an availability machine. It serves up anecdotes which feed our impression of what’s common in a way that is guaranteed to mislead. Since news is what happens, not what doesn’t happen, the denominator in the fraction corresponding to the true probability of an event—all the opportunities for the event to occur, including those in which it doesn’t—is invisible, leaving us in the dark about how prevalent something really is.

As the economist Max Roser points out, news sites could have run the headline 137,000 People Escaped Extreme Poverty Yesterday every day for the past twenty-five years.33 But they never ran the headline, because there was never a Thursday in October in which it suddenly happened.

Pollsters repeatedly find that while people tend to be too optimistic about their own lives, they are too pessimistic about their societies.

global trends in most educated people is exactly backwards: they think that longevity, literacy, and extreme poverty are worsening, whereas all have dramatically improved.

The result can be a paralyzing fatalism or a reckless radicalism: a call to smash the machine, drain the swamp, or empower a demagogue who promises “I alone can fix it.”

And a special place in Journalist Hell is reserved for the scribes who in 2021, during the rollout of Covid vaccines known to have a 95 percent efficacy rate, wrote stories on the vaccinated people who came down with the disease—by definition not news (since it was always certain there would be some) and guaranteed to scare thousands from this lifesaving treatment.

Consumers of news should be aware of its built-in bias and adjust their information diet to include sources that present the bigger statistical picture: less Facebook News Feed, more Our World in Data.38 Journalists should put lurid events in context. A killing or plane crash or shark attack should be accompanied by the annual rate, which takes into account the denominator of the probability, not just the numerator.

the next step in understanding probability: how to calculate the probabilities of a conjunction, a disjunction, a complement, and a conditional. If these terms sound familiar, it’s because they are the probabilistic equivalents of and, or, not, and if-then from the previous chapter.

The probability of a conjunction of two independent events, prob(A and B), is the product of the probabilities of each: prob(A) × prob(B).

Statistical independence is tied to the concept of causation: if one event affects another, they are not statistically independent

gambler’s fallacy is a fallacy. One spin of a roulette wheel cannot impinge on the next, so the high roller who expects a run of blacks to set up a red will lose his shirt: the probability is always a bit less than .5 (because of the green slots with 0 and 00).

Let’s turn to the probability of a disjunction of events, prob(A or B). It is the probability of A plus the probability of B minus the probability of both A and B. If the Browns have two children, the probability that at least one is a girl—that is, that the first is a girl or the second is a girl—is .5 + .5 – .25, or .75.

The probability that a child is either a boy (.5) or a girl (.5) is their sum, 1, since the child must be either one or the other

The probability of the complement of an event, namely A not happening, is 1 minus the probability of it happening.

Finally we get to a conditional probability: the probability of A given B, written as prob(A | B). A conditional probability is conceptually simple: it’s just the probability of the then in an if-then. It’s also arithmetically simple: it’s just the probability of A and B divided by the probability of B.

A and B are independent if, for all Bs, the probability of A given B is the same as the overall probability of A

Forgetting to condition a base-rate probability by special circumstances in place—the lightning storm, the bomb you bring aboard—is a common probability blunder.

Nicole Simpson was not just any old victim of battering. She was a victim of battering who had her throat cut. The relevant statistic is the conditional probability that someone killed his wife given that he had battered his wife and that his wife was murdered by someone. That probability is eight out of nine.

The other common error with conditional probability is confusing the probability of A given B with the probability of B given A, the statistical equivalent of affirming the consequent (going from If P then Q to If Q then P).

Irwin confused the probability of no symptoms given liver disease, which is high, with the probability of liver disease given no symptoms, which is low.

the headline Private Homes Are Dangerous Spots. The problem is that the home is where we spend most of our time, so even if homes are not particularly dangerous, a lot of accidents happen to us there because a lot of everything happens to us there.

In the case of probability, it makes a big difference whether the denominator of the fraction—the number of opportunities for an event to occur—is counted independently of the numerator, the events of interest.

If you take note of the predictions by a psychic that are borne out by events, but don’t divide by the total number of predictions, correct and incorrect, you can get any probability you want. As Francis Bacon noted in 1620, such is the way of all superstitions, whether in astrology, dreams, omens, or divine judgments.

the country has more than six thousand fund managers, and modern mutual funds have been around for about forty years. The chance that some manager had a fifteen-year winning streak sometime over those forty years is not at all unlikely; it’s 3 in 4. The CNN Money headline could have read Expected 15-Year Run Finally Occurs: Bill Miller Is the Lucky One. Sure enough, Miller’s luck ran out, and in the following two years the market “handily pulverized him.”

When we are allowed to identify them post hoc, coincidences are not unlikely at all; they’re pretty much guaranteed to happen.

coincidences happen more often than our statistically untutored minds appreciate.

p-hacking (referring to the probability threshold, p, that counts as “statistically significant”).60 Imagine a scientist who runs a laborious experiment and obtains data that are the opposite of “Eureka!” Before cutting his losses, he may be tempted to wonder whether the effect really is there, but only with the men, or only with the women, or if you throw out the freak data from the participants who zoned out,

None of these practices is inherently unreasonable if it can be justified before the data are collected. But if they are tried after the fact, some combination is likely to capitalize on chance and cough up a spurious result.

until recently few scientists intuitively grasped how a smidgen of data snooping could lead to a boatload of error.

The cluster illusion makes us think that random processes are nonrandom and vice versa. When Tversky and Kahneman showed people (including statisticians) the results of real strings of coin flips, like TTHHTHTTTT, which inevitably have runs of consecutive heads or tails, they thought the coin was rigged. They would say a coin looked fair only if it was rigged to prevent the runs,

constellations are not neighbors in any galaxy but are randomly sprinkled across the night sky from our terrestrial vantage point and only grouped into shapes by our pattern-seeking brains.

When a series of plagues is visited upon us, it does not mean there is a God who is punishing us for our sins or testing our faith. It means there is not a God who is spacing them apart.

Extraordinary claims require extraordinary evidence. —Carl Sagan

Bayes’ rule or Bayes’ theorem is the law of probability governing the strength of evidence—the rule saying how much to revise our probabilities (change our minds) when we learn a new fact or observe new evidence.

In recent decades Bayesian thinking has skyrocketed in prominence in every scientific field. Though few laypeople can name or explain it,

Suppose that the sensitivity of a breast cancer test (its true-positive rate) is 90 percent. Suppose that its false-positive rate is 9 percent. A woman tests positive. What is the chance that she has the disease? The most popular answer from a sample of doctors given these numbers ranged from 80 to 90 percent.3 Bayes’s rule allows you to calculate the correct answer: 9 percent.

The great insight of the Reverend Thomas Bayes (1701–1761) was that the degree of belief in a hypothesis may be quantified as a probability.

What we are after is the probability of a hypothesis given the data, or prob(Hypothesis | Data). That’s called the posterior probability, our credence in an idea after we’ve examined the evidence.

Remember that the probability of A given B is the probability of A and B divided by the probability of B.

Stated as an equation: prob(Hypothesis | Data) = prob(Hypothesis and Data) / prob(Data). One more reminder from chapter 4: the probability of A and B is the probability of A times the probability of B given A. Make that simple substitution and you get Bayes’s rule:

Recall that prob(Hypothesis | Data), the expression on the left-hand side, is the posterior probability: our updated credence in the hypothesis after we’ve looked at the evidence.

Prob(Data | Hypothesis) is called the likelihood. In the world of Bayes, “likelihood” is not a synonym for “probability,” but refers to how likely it is that the data would turn up if the hypothesis is true.4 If someone does have the disease, how likely is it that they would show a given symptom or get a positive test result?

And prob(Data) is the probability of the data turning up across the board, whether the hypothesis is true or false.

In the case of medical diagnosis, it refers to the proportion of all the patients who have a symptom or get a positive result, healthy and sick.

Translated into English, it becomes “Our credence in a hypothesis after looking at the evidence should be our prior credence in the hypothesis, multiplied by how likely the evidence would be if the hypothesis is true, scaled by how common that evidence is across the board.”

As they say to medical students, if you hear hoofbeats outside the window, it’s probably a horse, not a zebra. If you see a patient with muscle aches, he’s more likely to have the flu than kuru (a rare disease seen among the Fore tribe in New Guinea), even if the symptoms are consistent with both diseases. Second, believe the idea more if the evidence is especially likely to occur when the idea is true—namely

And third, believe it less if the evidence is commonplace—if it has a high marginal probability, the denominator of the fraction.