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/Nthe 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



shared 2-3-4. place



5. place



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.



N = 10

N = 1000

1. place



shared 1-2. place



2. place



shared 2-4. place



5. place



second last place



last place



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:



N = 10

N = 1000

1. place



shared 1-2. place



2. place



shared 2-4. place



5. place



second last place



last place



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.









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[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.