Priceless: The Myth of Fair Value (and How to Take Advantage of It) (6 page)

3–good

4–very good

5–excellent

A category scale has a fixed number of possible responses, labeled with words. There is a lowest or worst score and a highest or best score.

A different approach is a
magnitude scale
. In this, you’re asked to rate something on an unbounded numerical scale. The lowest rating is zero, and the highest rating is—well, there
isn’t
a highest rating. Why should there be? There is no upper limit to physical quantities such as loudness or heaviness, and no obvious limit to subjective perceptions of them.

Sometimes magnitude scales supply a standard of comparison, called a
modulus
. You might be shown a projected disk of light and be told that it’s a 100 on a scale of brightness. You would then be asked to estimate the brightness of other disks. One that’s half as bright would be a 50, one twice as bright would be a 200, and of course total invisibility would be a zero.

A modulus is supposed to be helpful, like a scale of miles on a map. But Stevens’s wife, the former Geraldine Stone, suggested that he try dispensing
with the modulus. Stevens found that his subjects gave more self-consistent judgments
without
it. Thereafter his preferred technique was to instruct subjects to give a number, any number, corresponding to
how bright
or
how sweet
or
how unpleasant
.

This sounds like a prescription for chaos. In a way, it was. Different people assigned wildly different numbers to the same thing. This wasn’t necessarily a problem. In medieval times, tradesmen’s weights and measures varied from town to town. But an ox that weighed twice as much as another ox on one town’s scales would weigh twice as much elsewhere, even though the actual number of pounds might be different. In Stevens’s experiments, the subjects’ absolute judgments were inconsistent, but the ratios were meaningful. It made more sense to let subjects invent their own mental yardstick and scale their answers to that.

Why isn’t a modulus helpful? With the modulus, subjects were afraid of making a “mistake.” Without it, they went with their first impulse, and this was usually more accurate. “I liked the idea that I could just relax and contemplate the tones,” one of Stevens’s subjects told him. “When there was a fixed standard I felt more constrained to try to multiply and divide loudnesses, which is hard to do; but with no standard I could just place the tone were it seemed to belong.”

In the psychophysics literature, going back to the 1930s, the word “anchor” was sometimes applied to a modulus or to the two endpoints of a category scale. Judgments were said to be “anchored” by these standards of comparison. It appeared, however, that the anchor could distort judgments, like a bubble in a glass window.

Stevens is not remembered as a compelling teacher. He nonetheless had several impressive classroom demonstrations. In one, he showed his students a gray paper disk surrounded by white. In a darkened room, with a spotlight on the gray disk, the gray looked white. Then Stevens illuminated the white around the disk. The “white” central disk turned black—by contrast with the now dazzling white surround.

Similar principles underlie many perceptual illusions. The one on page 37 (by MIT cognitive scientist Edward H. Adelson) is close in spirit to Stevens’s demonstration. The gray color of square A is identical to the color of square B. The illusion is so compelling that it makes a great bar bet. To collect, make sure you have some Post-it Notes.

Carefully block off the surrounding checkerboard squares with Post-it Notes, leaving just the squares containing A and B visible. (You’ll need about six small notes.) Not until you place the last note does it seem even
conceivable
that the two colors could be the same. Then suddenly, they “snap” to the same medium gray.

It’s not hard to understand how the illusion works. The cylinder casts a shadow, darkening “white” square B (which is really gray). In terms of ink dots on paper, B is the same gray value as “black” square A. But the eye and brain have more important things to do than gauging absolute grayscale values. They are trying to make sense of the world, or in this case, a picture. That means attending to contrasts. We see a checkerboard on which all the “white” squares are the same color, and a uniform shadow with blurred edges. The contrast between light and shadow doesn’t interfere with the contrast of the checkerboard squares, or vice versa.

One of Stevens’s epigrams ran, “Black is white with a bright ring around it.” The Orwellian tone of that statement is justified. Stevens knew only too well that you can get people to believe almost anything about their own perceptions with a little sleight of hand. Subjectively, there are no absolutes, only contrasts.

The childhood of Harry Helson (1898–1977) was straight out of Dickens, or Lemony Snicket. He was born to impoverished Ukrainian immigrants who separated when he was four or five. Harry’s mother fell on such hard times that she had to pack her son off to live with the father that both despised. Harry hated the new arrangement and ran away from home. He was taken in by a pair of spiritualists.

They were the Dyers of Bangor, Maine, and this was the golden age of séances and bell-ringing spirits. The Dyers opened their home to visiting mediums and lecturers. It is hard to say what young Harry believed or disbelieved about these houseguests, corporeal and otherwise. One friend said that Harry did a few “amateurish experiments” in the occult. Another recalled that “he did have several experiences that he was wholly unable to account for and that, I think, resulted in later years in an openness about all aspects of human experience.”

With this grounding in body and spirit, Helson grew up to be a psychophysicist. A manifestation in a darkened room was a turning point in his career. Helson was working under ruby-red light in a photographic darkroom when he noted something odd. The tip of his cigarette glowed green.

The light emitted by the smoldering tobacco would have looked ember-red under ordinary light, of course. This experience helped Helson crystalize an important idea: that of an
adaptation level
. Evidently, Helson’s eyes had adapted to the unusual red light of the darkroom. The glowing cigarette was a cooler, yellower red than the red of the safelight.
That made it look green
in comparison
. Helson’s eyes and brain were not registering an absolute color (the way a digital camera might), but a difference between the color of the cigarette and the baseline color of the room.

Helson eventually concluded that all the senses adapt to a given level of stimulation and then register changes from that baseline. He demonstrated this in a famous set of experiments with weights. Helson had volunteers lift pairs of small weights, one after the other, and describe how heavy the second weight felt. He found that subjects were biased by the first weight, which served as an anchor, or baseline for comparison. (He was using the word “anchor” in a somewhat different sense from those I’ve already described.) When the anchor weight was lighter than the second weight, it made the second weight feel heavier. When the anchor was heavier, it made the second weight feel lighter. This relativity of perception could lead to outright contradiction. Helson could arrange things so that a weight that felt heavy after a light anchor could feel light after a heavy one.

Conceptually, this was no big surprise. If you want to look thin, make friends with fat people! We’ve all noticed contrast effects. Have you ever taken a sip of tea, expecting it to be coffee? For a fleeting moment, the taste is indescribably alien. It doesn’t taste like tea, or like coffee. You’re tasting the gap between what you expected and what you got.

Almost from the field’s inception, psychophysicists cast their nets widely. Gustav Fechner attempted to scientifically gauge aesthetic preferences for two versions of a Hans Holbein Madonna that were baffling connoisseurs of the time. In the 1920s, at the University of Chicago, Louis Leon Thurstone contrived an alarming classroom project. “Instead of asking students to decide which of two weights seemed to be the heavier,” he wrote, “it was more interesting to ask, for example, which of two nationalities they would generally prefer to associate with, or which they would prefer to have their sister marry.” Elsewhere psychophysicists were putting their measuring rods to everything from the fineness of ivory carvings to the prestige of occupations to the historical importance of Swedish monarchs.

“The fact is that common principles exist in all fields of judgment,”
confidently asserted American psychophysicist William Hunt. In some of his experiments, Hunt had volunteers rate crimes “for the enormity of the breach of ethics involved.” He came up with this puzzler.
Part 1
: Consider the crime of murdering your own mother, “wilfully and without provocation or justification.” Now think of a crime exactly one half as bad. Write it down: __________________________________________

Part 2
: Once again, think of murdering your mother, “wilfully,” etc., etc. . . . Now think of “cheating at solitaire while playing by yourself.” Finally, devise a crime that’s exactly halfway between those two in seriousness. Write it here: ________________________________________

On a scale of evil, cheating at solitaire is about as close to a zero as you can get. You might expect that the answers to
Part 1
would have been similar to the answers to
Part 2
—for much the same reason that Ferdinand Plateau’s artists painted the same medium gray. They weren’t. In 12 cases out of 14, the
Part 1
answer was a more serious crime than the
Part 2
answer.

Hunt concluded that the examples supplied in his questions influenced the answers. In
Part 1
, there was only mother-murder to serve as a frame of reference. This inspired thoughts of other atrocities. In
Part 2
, there were two examples, one serious and one not. Not many would think of cheating at solitaire as a “crime.” The mere fact that the question called it that encouraged subjects to contemplate picayune offenses as crimes. This pulled down the average seriousness of the answers.