http://edge.org/conversation/the-marvels-and-flaws-of-intuitive-thinking

Now have a look at a very small variation that changes everything. There are two companies in the city; they're equally large. Eighty-five percent of cab accidents involve blue cabs. Now this is not ignored. Not at all ignored. It's combined almost accurately with a base rate. You have the witness who says the opposite. What's the difference between those two cases? The difference is that when you read this one, you immediately reach the conclusion that the drivers of the blue cabs are insane, they're reckless drivers. That is true for every driver. It's a stereotype that you have formed instantly, but it's a stereotype about individuals, it is no longer a statement about the ensemble. It is a statement about individual blue drivers. We operate on that completely differently from the way that we operate on merely statistical information that that cab is drawn from that ensemble.

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A health survey was conducted in a sample of adult males in British Columbia of all ages and occupations. "Please give your best estimate of the following values: What percentage of the men surveyed have had one or more heart attacks? The average is 18 percent. What percentage of men surveyed both are over 55 years old, and have had one or more heart attacks? And the average is 30 percent." A large majority says that the second is more probable than the first.

Here is an alternative version of that which we proposed, a health survey, same story. It was conducted in a sample of 100 adult males, so you have a number. "How many of the 100 participants have had one or more heart attacks, and how many of the 100 participants both are over 55 years old and have had one or more heart attacks?" This is radically easier. From a large majority of people making mistakes, you get to a minority of people making mistakes. Percentages are terrible; the number of people out of 100 is easy.

Regarding framing effects, one could write a computer program into which one could plug in numbers and have a decision converted into an Allais paradox.

One could commit to donating an amount of money to charity any time a free thing is acquired. (Arieli Lindt/Hershey's experiment)