Always Carry a Bomb When You Fly! (Part 8 of Cognitive Biases)

Always carry a bomb when you fly. One bomb on a plane is very improbable, so according to the law of averages, the chance of a second bomb is almost impossible!

A cognitive bias is a pattern of deviation in judgment that occurs in particular situations, and boy howdy, are there a lot of them! This week we’re covering the gambler’s fallacy and the halo effect.

Click here and scroll to the bottom for a list of previous installments.

Gambler's fallacy

The gambler’s fallacy is a cognitive bias that promotes the belief that if a random sequence shows a deviation from expected behavior, then it should be evened out by an opposite deviation in the future. But as anyone who’s thought their number was “due” knows, it ain’t necessarily so.

If you’ve flipped 5 heads in a row, the gambler’s fallacy suggests that the next coin flip is more likely to be tails than heads. And indeed, the chance of flipping 5 heads in a row is only 1/32. But the chance of flipping 4 heads and 1 tail (or any other combination of 5 heads and tails) is the same 1/32. Once four heads have been flipped, the next toss of the coin is the same 50%/50% as the others.

So far, obvious enough, but there are two related fallacies and a couple of exceptions. The reverse gambler’s fallacy is the belief that if the universe is showing a predisposition toward heads, then heads are cosmologically more likely. Assuming the coin is fair (not one of those double-headed types), that’s equally false.

The inverse gambler’s fallacy (term coined by philosopher Ian Hacking), is the fallacy of seeing an unlikely outcome of a random process and concluding that the process must therefore have occurred many times before. If you roll a pair of fair six-sided dice and get 12, it’s wrong to suppose there’s any support for the hypothesis that these dice have been rolled before.

The gambler’s fallacy doesn’t apply when the probability of different events is not independent. If you draw a card from a deck (let’s make it a 4), then the chance of drawing another 4 is reduced, and the chance of drawing a card of another rank is increased. It also doesn’t apply if the outcomes aren’t equally probable. If those six-sided dice keep rolling boxcars, after a while it’s reasonable to suspect they may be loaded.

The gambler’s fallacy is related to two other cognitive biases, the clustering illusion (part 5) and the representativeness heuristic. The latter bias is the belief that a short run of random outcomes should share the properties of a longer run. Out of 500 tosses of a fair coin, the number of heads and tails are very likely to balance out, but that doesn’t mean the same thing will hold true in a sequence of 5 or 10 tosses.

Halo effect

Some years back, I was on a seminar trip in Texas and Louisiana. A huge storm shut down air traffic, and in the process I got separated from my luggage. The next day, I had to teach a seminar in blue jeans and a day-old dress shirt. The audience was very sympathetic — there was major flooding in Baton Rouge and several of them had disaster stories of their own to tell — and the seminar went well.

When I received my evaluation statistics a couple of weeks later, I was fascinated to find that my scores had dropped nearly 25% below my averages. It was certainly understandable that my scores for “Instructor’s appearance was professional” would drop, but there were drops in “Instructor had a good command of the material” and “The workbook contained information that will be of use to me after the seminar.”

That’s the halo effect, the tendency for people to extend their assessment of a single trait so that it influences assessment of all other traits.

There are other examples. In the 46 US presidential elections where the height of both candidates are known, the taller candidate won the popular vote 61% of the time and the shorter 33% of the time. (In three cases, the candidates were of the same height, and in three other cases, the taller candidate won the popular vote but lost to the shorter candidate in the Electoral College — most recently in 2000.)

In 1977, psychologist Richard Nisbett ran a series of experiments on how students made judgments about professors, demonstrating not only how strong the effect is, but also how much people are unaware when they’re affected by it. At least five people at that seminar in Baton Rouge assured me they didn’t mind my jeans at all. Two even said they preferred a more casual look for the instructor.

But the numbers told the truth.

Patterns, Probability, and Plagiarism (Part 5 of "Cognitive Biases")

This week's installment of Cognitive Biases, the ways in which our brains distort our thinking is brought to you by the letter “C.” The series begins here.

Clustering illusion

Is the sequence below random or non-random??

OXXXOXXXOXXOOOXOOXXOO

If you thing the sequence looks non-random, you’re with the majority…but you’re wrong. The sequence has several characteristics of a random stream, an equal number of each result and an equal number of adjacent results. But people seem to expect a “random” sequence to have a greater number of alternations (O to X or vice-versa) than statistics would predict. The chance of an alternation in a sequence of independent random binary events (flips of heads or tails) is 50%, but people seem to expect an alternation rate of about 70%.

The clustering illusion is a cognitive bias that creates atendency to see patterns where actually none exist. This is why most people believe in “streaks.” When you expect greater variation in a sequence, you tend to assume that there’s a trend. But that isn’t necessarily the truth.

Conjunction fallacy

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

Which statement is more probable?

1. Linda is a bank teller.

2. Linda is a bank teller and is active in the feminist movement.

In a 1982 study by Amos Tversky and Daniel Kahneman, 85% thought statement 2 was more probable than statement 1, but that’s wrong. The probability of two events occurring together is always less than or equal to the probability of either one occurring alone. Even if there’s a very low probability Linda is a bank teller (let’s make it 5%) and a very high probability that Linda is active in the feminist movement (95%), the chance that Linda is a bank teller AND active in the feminist movement is 5% x 95%, or 4.75%, lower than the first statement.

The conjunction fallacy happens when you assume that specific conditions are more probable than a single general one, which is a violation of basic logic. Now, one possibility is that because most people aren’t familiar with the rules of formal logic, they may assume that statement 1 (Linda is a bank teller) implies that she isn’t active in the feminist movement.

But the fallacy has been demonstrated with very educated audiences.

Another Tversky/Kahneman experiment in the early 1980s surveyed a group of foreign policy experts to determine the probability that the Soviet Union would invade Poland and the US would break off diplomatic relations in the following year. The consensus estimate was about a 4% chance. Next, another group of experts was asked the probability that the United States would break off relations with the Soviet Union the following year. They estimated only a 1% chance. This implies that the detailed, specific scenario of the first scenario all by itself made it more likely.

Cryptomnesia

Robert Louis Stevenson refers to an incident of cryptomnesia that took place during the writing of Treasure Island, and that he discovered to his embarrassment several years afterward:

I am now upon a painful chapter. No doubt the parrot once belonged to Robinson Crusoe. No doubt the skeleton is conveyed from Poe. I think little of these, they are trifles and details; and no man can hope to have a monopoly of skeletons or make a corner in talking birds. The stockade, I am told, is from Masterman Ready. It may be, I care not a jot. These useful writers had fulfilled the poet's saying: departing, they had left behind them Footprints on the sands of time, Footprints which perhaps another — and I was the other! It is my debt to Washington Irving that exercises my conscience, and justly so, for I believe plagiarism was rarely carried farther. I chanced to pick up the Tales of a Traveller some years ago with a view to an anthology of prose narrative, and the book flew up and struck me: Billy Bones, his chest, the company in the parlour, the whole inner spirit, and a good deal of the material detail of my first chapters — all were there, all were the property of Washington Irving. But I had no guess of it then as I sat writing by the fireside, in what seemed the spring-tides of a somewhat pedestrian inspiration; nor yet day by day, after lunch, as I read aloud my morning's work to the family. It seemed to me original as sin; it seemed to belong to me like my right eye.

Sometimes what seems like inspiration turns out to be memory, and you’ve committed inadvertent plagiarism, or cryptoamnesia. In a 1989 study, people generated examples (such as kinds of birds), and later were asked to create new examples and to recall which answers they had previously personally given. Between 3-9% of the time, people either listed examples previously given, or recalled as their own someone else’s thought.

Few writers would risk committing deliberate plagiarism, but the dangers of cryptoamnesia are real. It’s most likely to occur when you don’t have the ability to monitor your sources properly, when you’re away from the original source of the idea, or when the idea was originally suggested by a person of the same sex (!). It’s also likely to happen in a brainstorming session, in which you recall as yours an idea that came up immediately before your idea.

Of course, not all claims of cryptoamnesia are necessarily valid; sometimes the plagiarism was all too deliberate. But nothing else explains certain situations in which people with an awful lot to lose commit what appears to be blatant plagiarism with no upside whatsoever.

The courts have ruled that the unconsciousness of the plagiarism doesn’t excuse it; the classic (rock) case is Bright Tunes Music v. Harrisongs Music involving the similarities between “He’s So Fine” and “My Sweet Lord.”

That cost George Harrison $587,000.

Cognitive biases can be expensive.

More next week.