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Another area of weakness in human reasoning can be found in the psychology and economics literature on preference reversals. The principle of procedure invariance tells us that, given two options, if one prefers A to B, then this preference should not change when the method for eliciting the preference changes. Yet participants often state a preference for A over B when they are asked to make a direct choice, but are prepared to pay more to obtain B than they are to obtain A.

Take two lotteries: a relatively safe lottery, where one has a 10% chance of winning nothing and a 90% chance of winning £10; and a relatively risky lottery, where one has a 10% chance of winning £90 and a 90% chance of winning nothing. If asked to choose, people usually prefer to buy a ticket for the safer lottery. In contrast, if asked at what price they would sell their ticket, they set a higher selling price for the ticket of the risky lottery. This phenomenon is observed in different contexts of choice and matching too (Stalmeier, Wakker, & Bezembinder 1997).

The classic example of the violation of procedure invariance in the literature is the Traffic Problem (Tversky & Thaler 1990, 201–202):

(1) The Minister of Transportation is considering which of the following two programs would make the electorate happier:

Program A is expected to reduce the yearly number of casualties in traffic accidents to 570 and its annual cost is estimated at $12 million.

Program B is expected to reduce the yearly number of casualties in traffic accidents to 500 and its annual cost is estimated at $55 million.

Which program would you like better?

(2) The Minister of Transportation is considering which of the following two programs would make the electorate happier:

Program A is expected to reduce the yearly number of casualties in traffic accidents to 570 and its annual cost is estimated at $12 million.

Program B is expected to reduce the yearly number of casualties in traffic accidents to 500.

At what cost would program B be as attractive as program A?

Options 1 and 2 represent two different ways of eliciting people’s preferences for one of the two life-saving programmes. In option 1, participants are given all necessary information about the two programmes: how many lives they would save and at what cost. When preferences are elicited in this way (direct choice), two-thirds of participants express a preference for programme B (which allows more lives to be saved at a higher cost). In option 2, participants are told how many lives would be saved and the cost of programme A, but they are not told the cost of programme B. Rather, they are asked at what cost programme B would become as attractive as programme A. When the preference is elicited this way (price matching), 90% of participants provide values smaller than $55 million for programme B, thereby indicating a preference for programme A.

If we take the evidence concerning people’s responses to the Traffic Problem as ecologically valid and reliable, it tells us something interesting: people have inconsistent attitudes about what the Minister of Transportation should do concerning the Traffic Problem. They believe that the Minister should implement programme B to save the lives of 70 more people a year, even if the programme costs $43 million more than programme A. They also believe that the Minister should implement programme A, which would save fewer lives, unless programme B cost considerably less than $55 million. Depending on the method by which the preference is elicited, participants seem to attribute different monetary value to human lives.