Foolish wisdom about the wisdom of the crowd.

Hello. As I promised, I post the results of Experiment No. 2 , the task of which was a more detailed study of the phenomenon of giving out by a large number of people while averaging the correct answer (or non-giving).

Thanks to everyone who participated in the survey.

Before turning to the results, we briefly consider methods for analyzing the results of experiments and measurements widely used in science and technology. Those who are familiar with this, can immediately proceed to point 2. And he, like all other points - under the cut.
')

1. Measurement Theory

Measurement is the process of comparing a measurable quantity with a standard. The result of the measurement is a value equal to the number, indicating how many times the measured value exceeds the standard, and having the dimension of the standard.
Measurements are direct and indirect.
Direct measurement - a process in which the result of the measurement itself is the desired value
Indirect measurement is a process in which one or several values ​​are obtained, on which mathematical transformations are subsequently performed, the result of which is already the desired quantity.
But the most important thing in measurements is errors . In the physical world you can never measure anything accurately, but in the physical world, however, absolutely exact values ​​are never required. Values ​​are required in each case with a certain accuracy, and the measurement result itself has no value if we cannot indicate its error.

Errors are classified according to several criteria:

By frequency of occurrence:

1. Systematic. Errors of this class occur with each measurement, and have a predictable value.
2. Random. These errors occur unpredictably and can have different magnitudes and signs from measurement to measurement.
3. Gross mistakes. Sometimes they are classified as random. Their essence is in a repeated strong violation of the experimental or measurement technique (for example, something was measured with a faulty device, or the wrong number was recorded in the measurement log). Since these errors can have an unpredictable value, they are detected and discarded.

By nature of error:

1. Instrumental. It exists in two forms: the limited accuracy of the measuring device itself (for example, a school ruler is more accurate than you cannot measure with an accuracy of 0.5 mm). And the recalibration of the device (rarely, what two school lines converge on 20cm).
2. Mathematical. Everything is simple - somewhere rounded, somewhere an integral numerical method was taken
3. Methodical. Not fully understood the essence of the physical phenomenon. (they used the physically incorrect formula for calculations, or they didn’t set up the experiment completely, they didn’t take it into account)
4. Operator errors. He did something wrong, wrote something else, etc.

By the mathematical nature of the error

1. Additive. The measured value is different from the measured by a constant. This occurs when the instrument scale is shifted. (or light squint operator)
2. Multiplicative. The measured value differs from the measured one by a certain number of times, i.e. the error is a constant percentage of the value.
3. Other Due to the complexity and inconvenience of processing results that contain different from the first two errors, they try to minimize them, make them small enough and forget about them.

2. Comparison of errors in measurements and in the mass survey.

It is important to note the following:

1. All errors in traditional measurements that are deterministic in nature can be detected and mathematically compensated.
2. All errors in traditional measurements that are of a random nature, due to the isotropy of space, accumulate (as a rule) evenly on both sides of the measured value, therefore, they can be compensated for by a large number of measurements with subsequent averaging.
3. The value for which the measurement error is not specified is not necessary for anyone , because we do not have the slightest idea how it relates to the real one. Here you ask me: "What is the weight of a goose?" I will tell you that 10kg, and if you are an intelligent person, you will not give a damn about these my words, because you do not know the error of this meaning. (maybe I allow an error of 200%). And this applies to all dimensions in life. (and we do not voice the error always, since it is implied that it is smaller than substantial, although there are incidents here as well).

What is the situation with the errors of the crowd assessment method?

1. The human psyche is a descriptive thing with great difficulty. In psychology, and so everything is "up to the elephant."
2. The processes in the human psyche are not isotropic once. Therefore, errors can accumulate unidirectionally.
3. When people assess, there may be strange cases when it is not clear whether this is a normal opinion, a blunder or a deliberately introduced trash result. I still think seriously whether some of the answers were called.
4. Errors of the human psyche have a huge variation depending on the quantitative, qualitative and emotional factors. And if in simple cases it is possible to use the CPPO (Adjustment Factor for the answer), then in difficult cases this will not help. In the case of nuts, we received a small relative error, and by the way, which one? (rummages in archives) 3%. Why? Because up to 200, everyone is able to count (and the human brain is able to count quite well “on the machine”, in the case of the human body, the situation will be slightly worse, and if you ask for the number of pebbles on the beach, or the number of water molecules flowing from Baikal to Angara, in an hour, then it is good if the result will differ in the number of times not exceeding 10.

3. Closer to the body

Indeed, the density of the human body in water is about one. And here "about" is ± 1/60. The person depicted in the photograph, having breathed the full lungs of air, easily floats on the water, without making any movements, and, after a deep breath, begins slowly but surely to go under water with his head. Its weight is 66.5 kilograms (ok, mass). Therefore, its volume is 66.5 liters.

What gave us an analysis of the results:
The average volume according to the public (if we discard the options that are supposed to be discarded) is 56.5 liters. Why is that? It turns out, as psychologists report, in everyday life it is common for a person to exaggerate the volume of bodies of the correct form, and to downplay the volume of bodies of irregular shape.
Several people, in the comments, voiced the thought about the density of a person approximately equal to 1, and I even began to fear that many would begin to estimate the mass (and the mass of a person in the range of 55-75 people evaluate very well, according to the same psychologists), but did not save the public (because many did not read the comments, and did the right thing, it was unnecessary to do this in that topic): the relative error is 13.5%.
It would seem nice. But.

1. If the task were to estimate the mass, the error would be much less, since there would be no options for 35kg and 80 (corresponding to 35 and 80 liters)
2. The calculated measurement error based on the variation of the user options themselves is 17% (assuming we do not know the real answer). At the same time 40% of users called the number by 17% or less different from the true

Long-awaited outcome

We interviewed 93 people, I sat and took into account the results, watched so that there were no “cheating”, sifted out unusable values, and all in order to get the result with such accuracy as a poll of 2-3 experts can provide. In this case, the expert in this case will be just a person who remembers the average density of a person, or can quickly figure it out.
At the same time, we were in danger of running into a flash mob, or in a region where the human psyche is typically mistaken several times.
We did completely unnecessary direct measurement, although it was possible to make a much more accurate indirect.

My personal conclusion. This average public opinion is an unreliable and even dangerous thing.
And who needs to publish books about his infallibility and omnipotence, as well as related social phenomena, I will tell in my next podcast.

Thank you for attention.
Good night ))