The same figures reversed, and they pick a different treatment

In 1982 some participants were given a real choice from medicine: surgery or radiotherapy for an operable lung cancer. Some were told the prognosis in terms of the people who would still be alive. Others were told exactly the same numbers in terms of the people who would die.

In the first group, 18 % chose radiotherapy. In the second, 44 %. The same operation, with the same probabilities, lost more than half its supporters simply because the paper talked about the dead instead of the living.

Nobody changed their mind, because nobody saw both versions: these were different groups given the same data written the other way round. What moved was the proportion. The study was authored by Barbara McNeil and her team in the New England Journal of Medicine, and they ran it on patients, on students and on practising doctors. The difference showed up in all three groups, doctors included.

Amos Tversky and Daniel Kahneman had published the experiment all of this comes from a year earlier in Science.

They described an outbreak that was going to kill 600 people and two programmes to fight it. Told in terms of who is saved: the safe one saves 200; the risky one has a one-in-three chance of saving all 600 and a two-in-three chance of saving nobody. 72 % chose the safe one.

Another group got the same two programmes told in terms of who dies: with the safe one, 400 die; with the risky one there is a one-in-three chance that nobody dies and a two-in-three chance that all 600 do. There, 78 % chose the risky one.

It's worth doing the arithmetic slowly, because that is where the trick is. The safe programme in the first group saves 200 out of 600: that leaves 400 dead. The safe programme in the second group kills 400 out of 600: that leaves 200 alive. They are the same programme. And the two risky ones are the same as well: a one-in-three chance that nobody dies, a two-in-three chance that everybody does. There isn't a single different figure between the two versions.

One group stuck with the sure thing; the other, in almost the same proportion, would rather gamble.

What changes is where they put the zero. If the sentence talks about lives saved, the zero sits at nobody being saved, and 200 alive read as a gain: you protect what you've got. If it talks about deaths, the zero sits at nobody dying, and 400 dead read as a loss, and faced with a certain loss a lot of people would rather take their chances. The numbers haven't moved; the zero has.

This lives outside the laboratories, and it was there before anyone studied it. In 1988, Irwin Levin and Gary Gaeth gave a group of people minced beef to taste. Some had been shown a label saying "75 % lean" and others one saying "25 % fat". It was the same meat. The ones who had read "75 % lean" rated it better on flavour, on quality and on how greasy it seemed to them, and they went on rating it better even after eating it.

The tutoring centre down your street advertises an 85 % pass rate, not a 15 % failure rate. And when you sign up to a fee that is "only" 1.5 %, on 1,000 euros that is 15 euros that don't come back.

The bank boasting that 97 % of its customers are satisfied is telling you that 3 in every 100 are not. That sounds like very little until you give it a size: if the bank has two million customers, that is sixty thousand unhappy people. The figure hasn't changed; you have looked at it from the other side and now it fills a whole town.

None of this requires bad faith. Somebody has to decide where the sentence starts, and that decision already pushes, even when the person writing it is being honest and has put every figure in front of you.

Tomorrow, before deciding anything with a percentage in front of you, say it out loud from the other side —if they give you the 90 who survive, say the 10 who don't— and decide with both figures in view.