(MOSI) which makes it possible to calculate the value of outstanding social identity (VOSI) of a well-defined social status and the social identity one may get by it.
The measure of outstanding social identity applies the same logic by which the information theory calculates the value of the news about an occurrence that could be expected with a p probability: as it is well-known this value is equalled to the logarithm of the invert of p. Reference books on information theory point out that “when we want to express quantity of information [...] in numbers, we deliberately and consciously ignore the content and significance of that information”. Thus, “the answer to the question ‘Do you like cheese, young lady?’ [may] contain [the same quantity] of information as does the answer given to the question ‘Would you like to be my wife, young lady?’, although the content and significance of the two answers are obviously entirely different.”
As regards the VOSI, the same relation is valid. Certainly, the value of attaining a favourably selected social position or avoiding a negatively chosen one is as high as the stake it involves. Clearly, if a negatively chosen position is such that it affects one in ten people disadvantageously, then the value of “That’s not me, but someone else” will be different, depending on whether someone is about to hide in the next round of the “Hide and Seek” game, or a commanding officer is decimating his unit. However, the VOSI depends not on the substance of the stake, it is based on nothing but the formal relations. The excellence is a surplus value gotten by the comparison: when one gets off with a negative selection that would have affected not one in ten, but two, five, or nine; or when s/he is selected to the more favourable not out of two but of ten or a thousand candidates, or perhaps of total ten million population of Hungary. The rapport may be stated as follows:
the smaller the pre-estimated probability of belonging to a favourable social position within a population, the greater the value attached to actually getting that identity.
Formula1 Let it be
N – the population;
a- – the number of those in the population whose position is inferior to mine
a = N-a- – a value complementing the previous one, i. e., the number of those whose position is not inferior to mine61
Finally, the VOSI of my position may be calculated as log10qa.
According to this formula in the above decimation case: N = 10 and a- = 1; hence, the number of those whose position is not inferior to mine: a = 9; thus pa = 9/10; its inverse: qa = 10/9; finally, the VOSI of my position is: 0,046.
My VOSI may be defined by my position in various ranks. For instance, if in a population of N = 1000 I am the first then
a- = 999
a = 1
pa = 1/1000
qa = 1000
consequently, the E-value of my position equals log101000 = 3.
By force of the same first place in a group of N = 10:
a- = 9
a = 1
pa = 1/10
qa = 10
thus, my E-value is: log1010= 1.
If in the same population I take not the first, but the second place, then the corresponding calculation is:
N = 10
a = 2
pa = 2/10
qa = 5
hence, the excellence-value is: log105 = 0,7.
What happens, however, if I am neither first, nor second, but share with someone else first and second places? This position must be somehow more excellent than a second place occupied alone, but less excellent than a non-shared first place. How can these connections be reckoned with?
The index number expressing the difference can also be calculated in such a way that the position is evaluated not only in relation to those on top, but also in the opposite direction, to those at the bottom of the population. For this, the procedure to be employed is similar to that of Formula 1 above:
Formula 2It is to be settled by
N – the population
b- – the number of those in the population whose position is superior to mine;
b = N-b- – a value complementing the previous one, i. e., the number of those whose position is not superior to mine62
pb = b/N – the previous probability for anybody in the population to be among this unfavourably distinguished part; hence the inverse of pb:
qb = 1/pb = N/b.
Thus, a stigmatizing value of my position may be calculated as log10qb.
The stigmatizing value of being the first equals, of course, 0. For the 2nd place in a group of N = 10:
b- = 1
b = 9
pb = 9/10
qb = 1/pb = 10/9
log1010/9 = 0,046
By force of the same second place in a population of N = 1000:
b- = 1
b = 999
pb = 999/1000
qb = 1/pb = 1000/999
log1000/999 = 0,000435
Formula3 Finally, the summed up value of my position may be obtained by deducting the stigmatizing value from the distinguishing value: log10qa – log10qb.
This formula then may be applied to our above problem of distinguishing from the E-value of both a first and a second place that of the shared with someone else first and second places: the value log10b – log10a equals, respectively:
1. place: log1010 – log101 = 1 – 0 = 1
2. place: log109 – log102 = 0,95 – 0,30 = 0,65
shared: log1010 – log102 = 1 – 0,30 = 0,70
The medium value for the shared position is resulted from its a value being equal to that of the second place and the b value to that of the first one.