An overconfidence.

The truth is always somewhere near the middle.

An appraisal by count-of point.

An appraisal by a representative ness.

An appraisal by encountering.

The Small Numbers law.

The values of errors are mutually cancelled in a mass of data.

The expert appraisal is a realization of an accidental value.

This delusion is discussed in particular by V.N. Toutoubalin [90].

In the extreme cases there is added a belief in a normal distribution law or a more witty delusion that provided the accidental values are abnormal then their logarithms are certainly normal[90].

This is a trap for the experts (even with a certain formal experience) in the sphere of making statistical conclusions in accordance with which a selection is obligatorily a representative one in relation to the general totality as a whole.

The experts often define a probability of events by the fact on how often they come across these events and how important those events are for them [187].

When appraising a subjective probability the experts almost do not take into account a priori probabilities which exert an influence upon belonging to a certain class.

Let's explain this fact with the following example. Let's consider a problem. In a group of 100 people it is necessary to define a profession of one of them taken at random. At the same time it is known that there are 70 engineers and 30 lawyers in the group. Unfortunately, during an interrogation of a great number of respondents, a distribution of answers is approximately 5O by 50. This example is described in the works of P. Slovak, P. Kaneman and A. Tverskoy [181,182,187].

While defining a subjective probability of a supposed future, an initial information is used as a count-of point then it exerts a sufficient influence upon the result.

So, when appraising the probabilities of events the groups of the people were given higher and lower initial values and they were asked to correct those values. The average results by the groups were sufficiently different [187].

This is correct for the case when, during the appraisal the expert is informed beforehand about the limitations of the probable extreme meanings of a prospective index.

The experiences showed [183] that the people do excessively trust their opinions especially when they concern the past events about probability of natural phenomena.

When carrying out test research works with the students in the Harvard School of Business M. Alpert and Ch. Raifa found out that 426 out of 1000 trustworthy intervals defined them, 98 per cent did not contain the true value of an appraised parameter [120].

Such results are not rare although at the first glance they seem to be unexpected. While making an empirical investigation of properties of histogram expert appraisals during test investigations jointly with S.A. Petrovsky, we obtained that out of 1413 appraisals 782 ones did not contain a veritable value [69].

In addition, when making the histogram appraisals, the examinees were asked to indicate the limits of the value being appraised between which of its true value is included according to their opinion practically with a hundred per cent certitude.

The work [183] is devoted to the study of overconfidence as a delusion. A lot of references to corresponding research works are mentioned in the work [154].