In one such experiment the participants were asked to draw a marble from one of two urns. If they drew a red one, they would win a prize:
Urn A contained 10 marbles, of which 1 is red.
Urn B contained 100 marbles, of which 8 are red.
Which urn would you have chosen? About 30% to 40% of the participants went with the urn that had the larger number of winning marbles (Urn B), instead of picking the one that gave them a better chance of winning (10% in Urn A, 8% in Urn B). Psychologist Paul Slovic calls this the denominator neglect. In his book Thinking, Fast and Slow, Daniel Kahneman explains why some people are susceptible to choosing Urn B:"When I think of the small urn, I see a single red marble on a vaguely defined background of white marbles. When I think of the larger urn, I see eight winning red marbles on an indistinct background of white marbles, which creates a more hopeful feeling." (p. 329)Going for the larger urn just seems like the right thing to do. But you've basically been fooled by how the decision was presented to you. This is usually called the framing effect. How someone frames a risk, an argument, a fact, etc. influences your initial reaction to it (System 1 at work):
"The idea of denominator neglect helps explain why different ways of communicating risks vary so much in their effects. You read that 'a vaccine that protects children from a fatal disease carries a 0.001% risk of permanent disability.' The risk appears small. Now consider another description of the same risk: 'One of 100,000 vaccinated children will be permanently disabled.' The second statement does something to your mind that the first does not: it calls up the image of an individual child who is permanently disabled by a vaccine; the 999,999 safely vaccinated children have faded into the background." (p. 329)
Kahneman acknowledges that some people are capable of using framing in order to manipulate. Looking for more healthcare funding for the mentally ill? No problem. Just make sure to let people know how scary these individuals actually are and that you could be their next victim:
"The power of format creates opportunities for manipulation, which people with an axe to grind know how to exploit. Slovic and his colleagues cite an article that states that 'approximately 1,000 homicides a year are committed nationwide by seriously mentally ill individuals who are not taking their medication." Another way of expressing the same fact is that '1,000 out of 273,000,000 Americans will die in this manner each year.' Another is that 'the annual likelihood of being killed by such an individual is approximately 0.00036%.' Still another: '1,000 Americans will die in this manner each year, or less than one-thirtieth the number who will die of suicide and about one-fourth the number who will die of laryngeal cancer.'" (p. 330)As you can see, it all depends on how the risk is presented. A decimal number like the one above is obviously not as scary as the number 1,000 per year. And you can be sure that healthcare providers are not the only ones capable of using the power of framing to their advantage. Lawyers know a good deal about it as well:
"A good attorney who wishes to cast doubt on DNA evidence will not tell the jury that 'the chance of a false match is 0.1%.' The statement that 'a false match occurs in 1 of 1,000 capital cases' is far more likely to pass the threshold of reasonable doubt. The jurors hearing those words are invited to generate the image of the man who sits before them in the courtroom being wrongly convicted because of flawed DNA evidence. The prosecutor, of course, will favour the more abstract frame - hoping to fill the jurors' minds with decimal points." (p. 330f)So next time you look at that beautiful picture hanging on your bedroom wall, ask yourself this: if it weren't for that pretty frame, how beautiful would it really be?
Die Lösung: Kopfrechnen lernen!
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