Large numbers, meta-cognition and predictable mistakes

People don’t think accurately about problems. We take shortcuts across the logical landscape. We use rules of thumb, culture, tradition and old wives tales. We guess and intuit and estimate.

Most of the time, these shortctus get us to where we’re going. Sometimes we miss a bit to the left, sometimes we miss a bit to the right. But it works out.

However, there are some patterns of thought that we keep getting wrong. Some logical shortcuts lead us off in the same wrong direction every time. Like a forward who always kicks the ball off to the left.

This is where meta-cognition comes in. It’s like a coach. It says, Buddy, you always miss to the left. Why not just aim a bit more right? Buddy starts aiming right, and he kicks a lot more goals.

Meta-cognition is thinking about thinking. It asks us to put the goggles on, and examine all the rules, biases and heuristics we use in decision-making. If we find our decision making failing in a random way, oh well. But if we find our decision-making failing in a systematic, predictable way, EUREKA! We have something we can do something about.

One predictable mistake humans make is to misunderstand large numbers.

In a recent speech to the Environment Business Australia Forum, Ken Henry, Treasury Secretary, spoke about methods of valuing the environment. The problem, he said, with surveys asking people how they would value saving penguins from oil slick death, is that the people tend to value saving 2,000 birds exactly the same as they would value saving 20,000 birds.

This failure to deal with orders of magnitude might be wired in. According to research by Pierre Pica our brains may not naturally grasp the spacing of large numbers. He worked with the Munduruku, an Amazonian tribe that can only count to five.

…Each volunteer was then shown random sets of between one and 10 dots. For each set, the subject had to point at where on an unmarked line they thought the number of dots should be located. Pica moved the cursor to this point and clicked. Through repeated clicks, he could see exactly how the Munduruku spaced numbers between one and 10…

They left plenty of space between 1, 2 and 3. But 5 was over half-way and 7, 8, and 9 were bunched up on the right.  Read more here.

This matches research on how children regard numbers. Prior to getting schooling in the number system, they space numbers out on what looks like a log scale.

The Munduruku – and the children – seem to be making their decisions about where numbers lie based on estimating the ratios between amounts. When considering ratios, it is logical that the distance between five and one is much greater than the distance between 10 and five.

Once number education kicks in, this method is supplanted. But when making snap judgments about issues that are not crucial to us (like theoretical questions about payments to save penguins), it’s possible that we go back to our intuition. Which can make us wrong.

So what? Well, there are probably many applications for this knowledge. If you were going to hold a raffle I’d suggest you price the tickets nice and low so people didn’t have to think much about it, and offer a $2,000 prize. It might net you almost as many entries as a $20,000 prize, and a lot more profit!

Other predictable mistakes – The Availability Heuristic

This one has to do with predictions of probability. People can’t clearly consider all the possibilities of the future, and so they tend to view as more likely anything they can vividly imagine.

Pollsters divided US voters into two groups. Group one was asked the odds of Ford becoming President. (This was prior to 1976, when the probability rapidly converged on unity.)  Group two was asked to imagine Ford as President, and then asked the odds of him becoming President. You won’t be surprised to hear that group two thought it was more likely Mr Ford would win.

This logical slip-up may help explain why people are willing to spend up on home security (everyone can vividly imagine being stabbed in a break-in), and not as much guarding against less vivid threats, by quitting smoking, getting a prostate check, etc.

There’s tons more predictable mistakes psychologists have found: check ’em out here.

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Thomas the Think Engine is the blog of a trained economist. It comes to you from Melbourne Australia.

9 thoughts on “Large numbers, meta-cognition and predictable mistakes”

  1. Stumbling on Happiness (Dan Gilbert) included discussion about whether our psychological limitations made it more worthwhile to ask a stranger what would make us happy and follow that rather than our own intuition. Fun stuff :)


  2. Well that explains why I keep buying lotto tickets. I know the probability of winning is effectively nil, but I can also vividly imagine that private island…


  3. Sir

    I don’t see why reverting to a log-scale in evaluating the utility of large numbers is an inherent error in logic. Surely winning $2,000,000 is almost as good as winning $20,000,000 – they are both a lot of money! (or put another way, diminishing utility from marginal $ won). Ditto with tragedy / 2,000 vs 20,000 birds dying.

    May be it is formal scholastic training that leads to assume that if something is 10 times as big it must be 10 times better!


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