The price of excellence
Abstract. Twentieth-century man has an important interest
in bearing a favourably selected social identity. The more excellent one's
social identity, the greater his/her chance to obtain, at a definite cost, an
economic benefit (access to a scarce resource or to an advantageous
transaction). Both payment and an excellent social status are required for an
economic chance. This paper deals with a calculation device for converting the
values of these mediating factors into each other: the excellence measure.
This device for calculating
excellence values is presented in the paper, among other use, when applied
to optimize human resources management. Instead of the accepted procedure of
according index-numbers to various individuals' traits, the one presented by
the paper ranks candidates for an office according to various criteria which
are themselves ranked, too. Excellence values calculated from the ranking of
the candidates are established for each of the criteria and these values are
weighted and finally averaged.
The price of excellence
Prof. László GARAI, Dr. Hung. Acad. Sc.
Head of Dept of Economic Psychology of Attila Jozsef University*
The economic psychology of excellence
In the 1950s and 1960s
economists, sociologists, psychologists and philosophers described, independently
of each other and using different terms, the phenomenon of the craving for
status; they claimed that it might become
just as much a passion for man in the modern age as the craving for money was
for those living in the period of classical capitalist formation the 18th
and 19th centuries.
The change is also
manifest in the fact that while the former passion prompted the gaining
money, the latter one may well encourages the spending money not even
earned, but borrowed. The latter, however, does not bring pleasure through the
consumption of the goods in line with their utility value, but through the fact
that the goods acquired, or the money spent on them, symbolize status.
For a time it was customary to describe the period following the Second World
War as the period of a consumer society, and to speak (with a degree of
social criticism and ideological disapproval) of the craving for status
symbols and conspicuous consumption. In connection with this it was
emphasized that in his consumption man was being guided less and less by the
rational goal of achieving the greatest possible joy for the lowest possible
cost, or the highest possible profit by the smallest possible inconvenience.
His guiding criteria were instead what was required by his position in society.
It seems that 20th century man has an important interest in acquiring
favourably selected social identity.
When individuals,
groups, states, and groups of states spend money on keeping up their social
status and their identity within that status their motive for this is not by
any means an aristocratic or snobbish zeal. The motive may be rather rational:
the endeavour to be enabled to participate in some kind of advantageous
transaction. [1] The more advantageous the status in society of a candidate among
those competing for a transaction, and the more excellent his social identity
in regard to the others, the lower the transaction costs for him/her. For this
reason it might make sense to spend money on increasing excellence. The only
question is, how much money is reasonable to be spent on how important an
excellence' increasing.
The present study
wishes to contribute to giving this question a possibly exact answer.
If money spent
symbolizes status, then it could be that the acquisition of money grips modern
man not because of his earlier passion for chasing it, but because acquired
money can also symbolize status. Activity is motivated primarily not by the
difference perceptible between the usefulness and unpleasantness of things or
even between their pleasantness and costliness, between income and expenditure
generally speaking, but increasingly by the difference between our
income and the income of others. [2].
When in the conditions
of so-called socialism those urging economic reforms argued that the money
incentive needed to be put in the service of social goals, they were actually
speaking about the motivating power of the craving for status when they
insisted that incomes of people (who were in theory equal) needed to reflect
unequal performance to a better extent. The matter is, that higher performance
does not invariably mean more performance of a quantitatively measurable kind.
The performance of an astronaut is perceived to be greater than that of an
abattoir worker, or that of a housewife, although the first produces nothing
measurable in the material sense, while the last-mentioned provides her
services over a seven-day working week, the merit of which can be recorded
materially. However, in the record of merit our intuition is guided, it seems,
not by this, but by unconscious consideration of which performance is the more
excellent. This is why one may find it in order for an astronaut to receive
remuneration higher than that of, say, a butcher decades after his performance,
while the housewife, who often continues her work until the end of her life,
receives neither a salary, nor a pension.
But remuneration can
be on a higher level without the payment of additional money: all organizations
establish a system of benefits whereby some employees are favoured against the
rest, the staff as a whole against those outside the organization, regular
customers against occasional ones, and even the totality of customers is
favoured against the whole population from which they emerge, etc. Among the
benefits are those whose utility can be measured in money: grantees among the
employees, and to a lesser degree all employees of the organization may, in
addition to their regular salary, be enabled to use items of the organization's
movable and immovable property free of charge or at a concessionary rate; they
may have access to services paid for by the organization wholly or in part;
regular customers might be given discounts when using services offered by the
organization, etc. However, the intuition we use when bearing in mind the value
of remuneration seems to be guided not primarily by considerations connected to
its size in terms of money, but by a weighing of how distinguishing the
benefit bestowed actually is.
Higher-level
performances, therefore, can be rewarded through higher-level pay not only in
that more is produced according to the paradigm of material
effectiveness, more is paid for it but also through remunerating a distinguished
performance in a distinguishing way. As a matter of fact, what is
measured is no longer the merit of the things produced, but that of the
person doing the producing. Behind a distinguished performance our
intuition suspects a combination of technical powers that is distinguished,
too, by virtue of its rarity, just as behind the distinguishing remuneration it
suspects a person's distinguished social power. In such a case, remuneration by
its distinguishing power symbolizes status and, thus, drives people through the
craving for status, even when these people seem obsessed by a craving for
money.
Around
the time of the political and social changeover in Hungary, family groups or
friends in voluntary enterprises within companies and in small private
businesses sometimes drove themselves at an inhuman pace not only to maintain
their standards of living or to be able to purchase goods quite beyond the
reach of the industrial proletariat and workers in the catering industry, but
at least as much as to show how well they were getting on. For them and for
others too, how well they were doing was expressed in money or in conspicuous
goods obtainable with it. But it was not the absolute amount that mattered, but
its distinguishing character. Just as refrigerators or cars were not (as they
had been earlier) suitable for demonstrating how far one had got, so in itself
an enormous income would not have been sufficient incentive to mobilize such
energy, if everyone had been able to work with colleagues selected by
themselves in voluntary enterprises within companies, or in a small-scale
independent enterprise.
The same passion was described by Kornai as the inner compulsion for expansion, when, at a time when the now-collapsed socialist system was still capable of operating, he sought an answer to the following question: "What prompts a manager of a company under socialism to make investments or to accumulate capital when he has no interest in any profit made?" The most important element was, in his view, that "the manager identifies with his own position. For such a manager there would always be a basis for comparison, in the light of which his unit would appear outdated or inferior. [...] Managers felt a professional rivalry in the best sense of the word. They wanted to augment their own professional prestige [...]. This could be accompanied by motives perhaps less noble, but nevertheless understandable from the human point of view. With the growth of a company or public institution came an increase in the power and social standing of its manager, and, together with this, consciousness of his own importance. Directing 10,000 people feels much better than directing 5000. Greater power can bring greater material recognition, more pay, bonuses and privileges, depending on the system of incentives in force." [3]
More exactly, what motivates managers in such cases is not so much the absolute size of the unit under one's direction or the absolute degree of that unit's expansion of the their, as the extent to which those index-numbers rank the person or his/her organization as compared with others. Kornai concedes: "If someone was appointed, let's say, rector of one of the biggest universities in the country, or was made responsible the protection of all the country's historic monuments, or was entrusted with care of the country's water supplies, then no increasing of either his salary, authority, or power would result from his being able to secure 20 per cent greater investment for his sphere of activity." However "the compulsion for expansion manifests itself at every level of the economic hierarchy: from the leader of a brigade consisting of a few workers to a minister directing hundreds of thousands or millions of people. When the distribution of investment resources is on the agenda, all fight so that our brigade, our company, our ministry gets the most investment possible." [4]
A smaller monetary
increase might be accompanied by a more powerful increase in status. On other
occasions a person might simply give up the idea of getting more money,
because, when the possibility arises, he favours an increase in status instead.
On the other hand, sometimes a person might give up a modestly paying but
excellence conferring office and be ready to accept the lower status of
competing with others on an equal basis, if so doing holds out the promise of
higher income.
*
Is it possible in such
a case to calculate the increase in a status someone must achieve to offset
loss of money, or how much of a decline in status he should accept for monetary
gain? Can an increase, or decrease, in status be measured at all? Can a
twofold, tenfold, or fiftyfold increase or decrease in status be compared with
a simultaneously occurring decrease or increase in money, in order to establish
whether someone has made a good or bad move when linking one to the other?
I am going to present
an excellence measure (E-measure) which makes it possible to calculate
the excellence value (E-value) of a well-defined social status and the
social identity one may get by it.
The excellence measure
applies the same logic by which the information theory calculates the value of the news about an occurrence that was expected with a p probability: as 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?' [...] contains one unit 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." [5]
As regards the
excellence value, the same relation is valid. Certainly, the value of attaining
a selected social position or avoiding a negatively chosen one is as much 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 "Hide and Seek", or a commanding
officer is decimating his unit. However, the excellence value depends not on
the substance of the stake, is based on nothing but the formal relations. The
excellence is a surplus value got 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
preliminary probability of belonging to a favourable social position within a
population, the greater the value attached to actually getting that identity.
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 mine [6]
pa = a/N — the previous probability for
anybody in the population to be among its favourably distinguished part; hence
qa = 1/pa = N/a.
Finally, the excellence
value of my position may be calculated as log10qa.
According to this
formula in the recent 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
E-value of my position is: 0,046.
My excellence value
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 difference can also be calculated in such a way that position is
evaluated not only in relation to those on top, but also in an 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:
It 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 mine [7]
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
log1010/9 = 0,000435
Finally, the totalled
up value of my position may be got 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.
It is worth to compare
values got by the application of the E-measure with those expected intuitively.
Let's calculate, e. g., the value of the shared 2-4. place in a group of N =
10, then the same value for a population of N = 1000, comparing those values
with those of both the preceding (1. place) and the following (5. place)
position:
|
N = 10 |
N = 1000 |
1. place |
1 |
3 |
shared 2-3-4. place |
0,35 |
2,40 |
5. place |
0,08 |
2,30 |
The difference 3 —
2,40 — 2,30 what we get for the values in N = 1000 is much
more moderate than the one 1 — 0,35 — 0,08 for the values in N = 10.
And this is what would be expected by our intuition, the 5th place in N = 1000 being almost as distinguished
a position as the shared 2-3-4th place while in N = 10 the
difference between the quite mediocre a 5th place and the shared 2-3-4th one that is close to the top
must be significant.
However, economic
psychologists have known for quite a time that there may be also a divergence
between what is implied by the economic rationality as calculated by a
mathematical formula and the psychological intuition.
Such
divergence has already been described by Bernoulli in the St. Petersburg
paradox. Allais took this a step further by describing the paradox named after
him. According to this, psychological intuition diverges not only from economic
rationality, but also from a psychological rationality, which would mean that
the divergence from a mathematically calculated result could itself be
calculated mathematically.
The
basis for the latter calculation would be the expectation that psychological
intuition is consistent. In contrast, Allais found that the consistency assumed
by Bernoulli and his followers does not exist; our intuition diverges from the
rational differently in the direct vicinity of full certainty (where it prefers
profit occurring at a greater level of probability even when the aggregate sum
of all the positive cases is smaller) than in the domain that is far from
certainty (where greater profits are preferred, despite the fact that the
aggregate is decreased by the small probability of occurrence).
The excellence measure
discussed in this paper aims to give an approximation of such a divergence of
second degree: from a degree rationally expected for a divergence from rational
calculations. For this reason we attempt to trace deviant intuition with
subsequent corrections.
A difficulty is, for
example, that the differences resulting from the comparisons of the positions
at the bottom end of a ranking within a group as calculated in the way given
above do not accord with the estimates stemming from our intuition. Namely, for
such a calculation a population would be symmetrical, where differences between
the rankings at the top of the scale should correspond to those at the bottom:
in a group of N = 10, for instance, where the values of the first and second
place equal, as we have seen it, 1 and 0,65, respectively, the
values for the last and the second last place would similarly be calculated as
-1 and -0,65 though for our intuition the difference between these
places is smaller. Still more is so in a population of N = 1000 where for our
intuition there is almost no difference between being placed as 999th or as 1000th.
Hence, a correction
has to be done to the calculated symmetry, and the larger the population in
question the most powerful must be that correction. For such a correction we
divide the stigmatizing value by logN+1 (that is, by 2 if N=10,
by 4 in the case N=1000 etc.). Thus, the corrected formula is:
logpa - logpb/(logN+1)
Unfortunately, this
formula is more complicated than the simplified one we have employed up till
now; on the other hand, it is worth looking at the following table and seeing
the values obtained so far for the two populations examined.
Position |
N = 10 |
N = 1000 |
1. place |
1 |
3 |
shared 1-2. place |
0,7 |
2,7 |
2. place |
0,68 |
2,68 |
shared 2-4. place |
0,375 |
2,4 |
5. place |
0,19 |
2,3 |
second last place |
-0,30 |
-0,67 |
last place |
-0,50 |
-0,75 |
In the figures
indicating values we may get rid of a good deal of unwieldy decimal fractions
by multiplying all of them (arbitrarily but consistently) by 100:
Position |
N = 10 |
N = 1000 |
1. place |
100 |
300 |
shared 1-2. place |
70 |
270 |
2. place |
68 |
268 |
shared 2-4. place |
37,5 |
240 |
5. place |
19 |
230 |
second last place |
-30 |
-67,5 |
last place |
-50 |
-75 |
The competitor's costs and profit
Can the excellence measure
be used, then, in a calculation by economic psychology to determine in dollars,
Euros or Hungarian forints the price of excellence if somebody comes first in a
group of ten or shares the second and third place with someone else in a
population of a thousand?
We must admit that our
method is not adapted for such calculations: it can reckon with social identity
only insofar as it is a relation, thus, also the value of an identity may
meaningfully be calculated only as related to the one of another identity.
Can then the
excellence measure be employed to calculate the sum of money worth paying for
promotion from 9th place to 7th place in a group of a hundred queuing up for
something?
It depends. The
excellence measure is adapted to reckon with those relations as related to
their historical antecedents.
E.g.,
if previously I have got to the 9th place from the 13th
one, then it may be calculated that thereby my E-value got increased from 87
to 103, that is, by 16 point. Suppose that the work, money etc. I
invested in this performance amounted to 400 $. These antecedents
altogether (and nothing but these) define for me (and for nobody but me) the
"dues" for 1 point of E-value increment as equalling to 25 $.
Thus, we can answer the above question: the E-value of the 7th place being 115, i. e., larger by 12
point than the 9th place, the monetary equivalent
of this promotion on such a background of its prehistory proves to be 300 $.
When using the
excellence measure, it should be taken into account that among competitors, a
missed effort results not only in the lack of a rise in status, but also in a
lowering of status compared to competitors who in the meantime have made their
own efforts.
If in the previously
evoked case I miss efforts to be done for acceding to the 7th place its alternative well be not the getting
bogged down at the 9th place but a slipping back in
relation with those others who do compete. If such an issue ranked me only at
the next place to the background, i.e., to the 98,6 points 10th place,
it would change the price of getting to the 7th place, and for two reasons.
First of all, because my past investment of 400 $ in the performance of
getting ahead from the 13th place turned out to improve my E-value not by 16,
only by 11,6 points (from 87 to 98,6), thus, the
equivalent of a one point improvement is proves to be 34,5 instead of
25 $. And, secondly, when my efforts
being done, as compared with their not being done, provides me the 7th place instead of 10th and not 9th place thereby provides me a 16,4 and not just 12 points growth
in E-value. The summed up issue of this double shift is that the rise in status
at stake equals to 566 and not just 300 $.It follows from the above
that in neglecting to make an effort we pay not only by failing to get on, but
also by losing the position we have already acquired. This raises the question
of how much it is worth when this does not occur and when we can maintain the
position we have.
The excellence measure
is suitable not only for rational calculation concerning status and money, but
also for predicting decisions regarding these as they occur in reality. This is
proved by everyday experience and experiments in economic psychology alike.
In
an (unfinished) experiment each participant got 1000 token dollars and had to
register out of a price list items s/he was intending spend that money on first
of all, secondly, thirdly etc. Some commodities were chosen only by three persons
(out of 100 participants of the experiment), others by 41 people. Each of the
subjects got a summarized feed back from this choice
of the experiment,population, but this feed back was forged at a precise point:
each subject got informed as if the item s/he put at the head of his/her list
would be chosen by the first choice of 49 people.
Following this
procedure the subjects were given the information that atoken warehouse, which
they can enter only one at a time, contains enough stock for a hundred people
to spend their money, but that there are only a very few couple of each type of
item [8].
Thus, the order of the customers’ entry to the warehouse was rendered crucial
from the point of view of purchasing: only the first three shoppers could be
sure that they could get the goods they wanted.
After being provided
with this information, the subjects were given the opportunity to buy their
place in the queue, too, from their 1000 $ spending money: a computer
ranked the shoppers according to the sum of money they offered for the places.
Shoppers could improve their positions by increasing their bid, while similar
offers by competitors diminished the effectiveness of these increased bids.
In the first round of
the sale 20 out of the 100 subjects put 100 $, almost as round a sum, 50 and
150 $ was put by 10 people each. In this
round the first place would be procured by 170 $, but those two persons who bade 160 $ would
get a shared 2-3rd place, while the above 10 people with their 150 $ shared but
the 4-13th place, thus, the prices being almost the same while the places were
quite different. Hence, a pressure was very strong for bettering the person’s offer in order to better his/her place or prevent
him/herself from being pushed more in the background by others’ overbidding. At
the same time, lowbids got still lower, since those getting for their 30-40
dollars last places realized that they may have it for (almost) nothing as
well.
In the meantime the
sale was restricted by the fact that the more a shopper spent on securing full
choice for his money, the less money he would have to buy the goods he had
freely chosen.
Instructions given to
the subjects indicated the rule whereby the final outcome of the game would be
fixed by the computer at the moment when no more shared places existed between
the players. When this finally occurred through the raising and lowering of
bids, it was very interesting to see that the ratios between the bids were well
in line with the ratios between the sums that the players were willing to pay
for individuals placing closely corresponded to those proportions calculable on
the basis of the excellence measure.
In this experiment,
according to the rules of the game the sum of money offered in a bid (would
have) needed to be paid only at the end of the game. The game would have taken
a different course had bids needed to be paid out immediately they were made.
This is the phenomenon mentioned above, whereby the competitor, threatened with
slipping down in the rankings, runs after his own money. The calculation made
for this case points out that the greater the slipping down, the more the
competitor would strive to hold the position he once held, and that if the
slipping down is of an order that despite the efforts he has made the
competitor still finds himself where he was, this will lead to yet further
efforts, the calculable magnitude of which is infinite.
This relationship is
demonstrated in the experiment in which participants can bid for a $1 banknote,
put up for auction at a starting price of one cent. The condition for
participation was that the bid had to be paid not only by the participant whose
bid took the dollar, but also by the one whose bid came second and who did not
win anything. In this experiment one person was willing to pay $20 in order not
to come second to a bid to pay $19.98, a state of affairs he could have secured
free from the beginning.
* Mail:
Budapest, PO Box 398. HUNGARY — 1394 Phone:
(361) 209-77-03 Fax: (361)
239-67-27 E-mail: garai@mtapi.hu
Internet: www.staff.u-szeged.hu/~garai/garai.html
[1] A
detailed exposition of the arguments can be found in the author's book The
human potential as capital: An approach by the economic psychology (Budapest: Aula Economic
University Press, 1998 — in Hungarian), in the chapter entitled "A model
of simple economic behaviour under organizational regulation".
[2] In his
classic experiment, Tajfel (Human Groups and Social Categories: Studies in
Social Psychology, Cambridge: CUP, 1981, pp. 268-71) also found that,
provided that the experimental subjects made a distinction (however small)
between their groups and those of others along some dimension, they will judge
the difference in income between the two groups to be larger than the absolute
value of the income of their own group.
[3] Kornai,
J.: The shortage, Budapest: Közgazdasági és Jogi Könyvkiadó, 1980 — in
Hungarian), pp. 204-205.
[4] Kornai,
J·.: Op. cit., p. 206.
[5] Renyi
A.: Diary on Information Theory (Budapest: Gondolat, 1976 — in
Hungarian), p. 20.
[6] I
myself am included in this number!
[7]
Warning! b ≠ a-, because I myself am
included in it, together with those whose position is neither superiour nor inferiour
to mine.
[8]
"Un ou deux de chacun" – the experiment was put on in France.