Vladimir A. Lefebvre (1997) On the Nature of the Constant 0.62. Psycoloquy: 8(10) Human Choice (10)

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PSYCOLOQUY (ISSN 1055-0143) is sponsored by the American Psychological Association (APA).
Psycoloquy 8(10): On the Nature of the Constant 0.62

# ON THE NATURE OF THE CONSTANT 0.62 Reply to Lebedev on Human-Choice

School of Social Sciences
University of California, Irvine
Irvine, California

VALEFEBV@UCI.EDU

# Abstract

It is shown that the hypothesis that the constant 0.62 appears as result of combining two different probability distributions is falsified by experimental data.

# Keywords

choice; computation; decision theory; ethical cognition; mathematical psychology; model building; parameter estimation; probability; rationality.
1. Lebedev (1996) suggests an alternative explanation for the phenomenon of the golden section. In his opinion, the golden section appears as a result of adding two probability distributions: the first with a maximum at point 0.5, and the second at 0.75. The mean probability of choice is (1/2)(0.5+0.75)=0.625 which explains the phenomenon.

2. This hypothesis is attractive because of its simplicity and because it can be falsified experimentally.

3. Let us imagine the following experiment. Each subject must indicate to what extent an object possesses a certain quality (which does not have an operational meaning) by marking a linear scale, one end of which corresponds to a complete absence of the given quality and the other to its maximum degree.

4. Let us now determine what distribution would correspond to Lebedev's hypothesis. The experimental conditions do not set a positive-negative orientation of the scale, so for some subjects the left end will be the positive pole, and for the others the right end will be the positive pole. As a result we can expect a distribution with three peaks. The first one will be at the middle of the scale, the second one will be at (3/4) of the length of the scale from the left end, and the third one at (3/4) of the length from the right end.

5. The model described in the target article (Lefebvre, 1995) will make a different prediction. The distribution will have not three but two peaks, at a distance of 0.62 of the length of the scale from each end.

6. Such an experiment has already been conducted without any relation to the golden section (Poulton, 1989). Each subject was presented with three samples of paper, one black, one white, and one grey, whose degree of "lightness," on the psychological scale, was approximately halfway between the first two. The subjects had to indicate the "lightness" of a grey sample by marking a linear scale, one end of which corresponded to "black" and the other to "white."

7. It is important to note that every subject made only one evaluation, that is, within the framework of this experiment no "scale of lightness" could be constructed (see Lefebvre, 1992; 1997).

8. The distribution of marks in Poulton's experiment has two peaks located at approximately 0.6 of the scale length from each end. There is a clear gap between the peaks. Poulton notes in particularly that the subjects avoided marking the middle of the scale.

9. This experiment falsifies the hypothesis about a mixture of distributions. The hypothesis formulated in the target article passes this test. Moreover, it explains paradoxical results of Poulton's experiments, that the subjects do not mark the middle of the scale.

## REFERENCES

Lebedev, A.N. (1996) About Human Choice and Lefebvre's Model. PSYCOLOQUY 7(28) human-choics.9.lebedev.

Lefebvre, V.A. (1992) A Psychological Theory of Bipolarity and Reflexivity. Lewiston: The Edwin Mellen Press.

Lefebvre, V.A. (1995) The Anthropic Principle in Psychology and Human Choice. PSYCOLOQUY 6(29) human-choice.1.lefebvre.

Lefebvre, V.A. (1997) The Cosmic Subject. Moscow: The Russian Academy of Sciences Institute of Psychology Press.

Poulton, E.C. (1989) Bias in Quantifying Judgments. Hove & London: Lawrence Erlbaum.

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