5 . On March 7, 1907, the English statistician Francis Galton published a paper which illustrated what has come to be known as the “wisdom of crowds” effect. The experiment of estimation he conducted showed that in some cases, the average of a large number of independent estimates could be quite accurate.

This effect capitalizes on the fact that when people make errors, those errors aren’t always the same. Some people will tend to overestimate, and some to underestimate. When enough of these errors are averaged together, they cancel each other out, resulting in a more accurate estimate. If people are similar and tend to make the same errors, then their errors won’t cancel each other out. In more technical terms, the wisdom of crowds requires that people’s estimates be independent. If for whatever reasons, people’s errors become correlated or dependent, the accuracy of the estimate will go down.

But a new study led by Joaquin Navajas offered an interesting twist (转折) on this classic phenomenon. The key finding of the study was that when crowds were further divided into smaller groups that were allowed to have a discussion, the averages from these groups were more accurate than those from an equal number of independent individuals. For instance, the average obtained from the estimates of four discussion groups of five was significantly more accurate than the average obtained from 20 independent individuals.

In a follow-up study with 100 university students, the researchers tried to get a better sense of what the group members actually did in their discussion. Did they tend to go with those most confident about their estimates? Did they follow those least willing to change their minds? This happened some of the time, but it wasn’t the dominant response. Most frequently, the groups reported that they “shared arguments and reasoned together”. Somehow, these arguments and reasoning resulted in a global reduction in error. Although the studies led by Navajas have limitations and many questions remain, the potential implications for group discussion and decision-making are enormous.

The Daffodils

by William Wordsworth

I wandered lonely as a cloud,

That floats on high o’er vales and hills,

When all at once I saw a crowd,

A host, of golden daffodils (水仙花);

Beside the lake, beneath the trees,

Fluttering and dancing in the breeze.

Continuous as the stars that shine,

And twinkle on the milky way,

They stretched in never-ending line,

Along the margin of a bay:

Ten thousand saw I at a glance,

Tossing their heads in sprightly dance.

The waves beside them danced; but they

Outdid the sparkling waves in glee:

A poet could not but be gay,

In such a jocund (欢乐的) company:

I gazed — and gazed — but little thought,

What wealth the show to me had brought:

For oft, when on my couch I lie,

In vacant or in pensive (忧愁的) mood,

They flash upon that inward eye,

Which is the bliss of solitude (孤寂):

And then my heart with pleasure fills,

And dances with the daffodils.

I was invited to a cookout on an old friend’s farm in western Washington. I parked my car outside the farm and walked past a milking house which had apparently not been used in many years. A noise at a window caught my attention, so I entered it. It was a hummingbird (蜂鸟), desperately trying to escape. She was covered in spider-webs (蛛网) and was barely able to move her wings. She ceased her struggle the instant I picked her up.

With the bird in my cupped hand, I looked around to see how she had gotten in. The broken window glass was the likely answer. I stuffed a piece of cloth into the hole and took her outside, closing the door securely behind me.

When I opened my hand, the bird did not fly away; she sat looking at me with her bright eyes. I removed the sticky spider-webs that covered her head and wings. Still, she made no attempt to fly. Perhaps she had been struggling against the window too long and was too tired? Or too thirsty?

As I carried her up the blackberry-lined path toward my car where I kept a water bottle, she began to move. I stopped, and she soon took wing but did not immediately fly away.

Hovering (悬停), she approached within six inches of my face. For a very long moment, this tiny creature looked into my eyes, turning her head from side to side. Then she flew quickly out of sight.

During the cookout, I told my hosts about the hummingbird incident. They promised to fix the window. As I was departing, my friends walked me to my car. I was standing by the car when a hummingbird flew to the center of our group and began hovering. She turned from person to person until she came to me. She again looked directly into my eyes, then let out a squeaking call and was gone. For a moment, all were speechless. Then someone said, “She must have come to say goodbye.”

A few weeks later, I went to the farm again.

I was just about to leave when the hummingbird appeared.

Mary Lee seemed to have everything. She was very beautiful with a wonderful figure and an attractive face. She was very rich. Her clothes were better than anyone else’s and she had more of them. Her books were always new and expensive as were her pens, school bags and bicycle. She was very clever too and without appearing to do very much work. She was always the first in all the examinations and always answered all the questions, while the rest of the class were still thinking.

With all this, or really because of all this, no one liked Mary Lee. She was too good, too clever and she was also very proud. No one was quite good enough to talk to her or to be seen with her or to be her friend. And so, with all her proud ways and riches and brains, she was lonely but she did not care because she was always the best in everything. She was like a princess in the class. She always thought that the other students kept their distance from her because she was too excellent. “Lions and tigers are always lonely, and only the weak get together,” she told herself.

As the end of term drew near, the pupils including Mary Lee began to think about the most important prize of all. This was the prize, offered by the principal, for the best essay to be written on one of two subjects: Happiness and Friendship. All the teachers and pupils paid close attention to the prize, for it was really a great honor. “I needn’t worry about that,” thought Mary Lee, as the others began to read and to think about the essay. “I shall easily win. After all, my compositions are always better than the other students’.”

“Pride goes before a fall,” they say and it certainly did in the case of poor Mary Lee.

Mary Lee suddenly realized that how silly she had been.

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