Economic-political sociology and industrial organization research

Rank-Difference-Index - RDI

Horizontal industrial organization


English Summary:

Here we shall discuss social classes, and the relations between classes, with respect to management broadly defined. First we shall look upon the social classes, then discuss the relations between the classes. In a footnote *) we shall go deeper into these questions and discuss the optimal way of management and organization in general. The concept of industrial organization related to management and economic-political sociology is here broadly defined. Mathematical precisations of the theory, with examples, are found below this English summary and the footnote, related to Table 1. The text in this table is in Norwegian, but the variable names are also translated to English, see above the table.

A new Rank-Difference-Index, RDI, that measures how top heavy the rank hierarchy/rank pyramid is, and the Gini-index, that measures how top heavy the income hierarchy/income pyramid is, are explained. They are both 100% (=1) with 100% vertical organization, political/administrative and economical respectively, and zero with 100% flat organization, no rank differences and no income differences respectively.

At least seven significant social classes of rank and income, may be accounted for in anarchist sociology, political economy and social plus industrial organization research, not just two, i.e. the division in A, "people", and B, "authorities", is a simplification. The people, A, seen as a class, is defined in contrast to the superiors in rank and/or income, B, i.e. the authorities/bureaucracy political/administrative and/or economical broadly defined. A and B are aggregated classes, and we have here in this document defined A and B precisely, based on the seven more basic social classes. First we have the following classes, two of income and two of rank:

1. low and

2. middle income classes, as well as the

I. autonomous class of rank, i.e. selfemployed on individual and co-operative basis or approximately similar positions, [i.e. persons working in firms with small rank differences that are relatively independent and educated consultants and similar functionaries/specialists in the hierarchic enterprises without subordinates, and a relatively free position vis-à-vis the superiors, in public and private sector (not accounting for contractors with no real autonomy and with more or less slave-contracts)], and the

II. "bottom line" skilled and non-skilled workers, houseworkers, and lower functionaries in the hierarchic enterprises in private and public sector, including contractors of the above mentioned type.

Furthermore a) the unemployed, persons with disability and partial incapacity, old, sick, students and political prisoners, are among the people. The persons with relatively lowest rank and income b) are usually only a small part of the population, sometimes called the marginalized. As a small group of the people broadly defined, this group must appeal to the solidarity of the rest of the people, to get better off. They usually do not have the resources to free themselves alone. Hard and violent actions will usually only increase the coercion and marginalization. Group a) and b) may be seen as a part of II, "the bottom line", but may have separate interests and problems, and sometimes should perhaps be accounted for as separate classes.

The B, authorities, are the

3. relatively rich (economical plutarchs or plutarchists) and the

political/administrative rulers, III the top and IV, the lower commanding officers within the hierarchical enterprises in public and private sector, being criminal [typical ochlarchs/ochlarchists, i.e. mafia, terrorists etc., - any villain is an arch, small villains, middle villains and arch villains as well] - or not, i.e. to put it simple, the bureaucracy economical and/or political/administrative broadly defined in private and public sector.

The authorities - bureaucracy, B, are the logical union of the three upper classes, 3, III and IV, i.e. B = 3 U III U IV, meaning the upper class persons may either be plutarch/plutarchist and/or top or lower commanding officers, - if you have any of these economical or political/administrative characteristics you are among the upper classes, the bureaucracy* broadly defined economical and/or political/administrative in private and/or public sector, and not a member of the people, A.

If you have neither of these characteristics, i.e. are neither plutarch/plutarchist, nor top, nor lower commanding officer, you are among the people, A. Thus A is the negation of B, when A + B = P, is the whole relevant population, i.e. usually the grown up persons in a society. NB! A is thus usually not the sum of 1., 2., I. and II. Say, if you are among I. or II. but also 3, you are not a member of the people. And even if you are a member of 1., the low income class, but also of IV, the lower commanding officers, you are not a member of the people, but of the authorities, the bureaucracy.

Some of these non criminal of the upper classes, may be idealists and be solidaric with the people, and thus in a way, at least ideologically, also be a part of the people, not the upper classes. The anarchist prince, Pjotr Kropotkin, is a well known example of such an idealist. Instead of put in class III or IV, the upper classes of rank, such idealists may sometimes be put in the most relevant of the other classes of political/administrative rank, say, among the autonomous, class I.

Some of the formally seen people may be solidaric with the upper classes, say, perhaps in the purpose of climbing in the hierarchies, and thus in reality more or less be among the ramifications of the bureaucracy. Sometimes they may be accounted for as member of class 3, if aspirating to be rich, or III or IV if aspirating to be political/administrative "crown princes", or be seen as "yellow" followers of the upper classes, and accounted for as a kind of "sergeants", respectively. But usually a class analysis will follow the occupation and position structure, the political/administrative rank and remuneration systems/maps of the industrial organizations broadly defined. And thus, there is rarely a unity between the people. The classes of the people have different interests, both seen as classes and as individual members of the classes. Many people love their leaders, or look at them as a necessary more or less evil.

The relations between the classes, and the people broadly defined vis-à-vis the upper classes, may have a structural form of hard repression, less repression, and elements of co-operation with more or less coercion. Thus, the hierarchy ( if any) may be organized more or less from the bottom upwards, or from the top to the bottom. All of the population, or at least the grown up persons, have both a political/administrative and an economical coordinate. Some may have a high score both political/administrative and economical, some may have a low score on both dimensions, and some may have mixed scores. A class-analysis must also take into account these relations between the classes, not only the class structure in a narrow sence, as investigated above.

Thus a given hierarchy may also be more or less authoritarian, dependent on how authoritarian the relations between the classes and the persons are. And thus, performance must be included in the concept of structure. These relations of performance may be from ultra to less authoritarian to more or less co-operative, with small rank and/or income differences, i.e. the system may work more or less from the bottom and upwards, including horizontal industrial organization broadly defined, or the opposite, from the top, downwards towards the bottom. Thus, there are two ways of making the system less authoritarian,

1. To change the hierarchy economical and/or political/administrative, in horizontal direction.

2. To change the relations between the persons within a given hierarchy, in horizontal direction, i.e. less authoritarian.

The struggle to achieve 1. and 2. is anarchist class struggle. Real class struggle is non-ochlarchical (ochlarchy = mob rule broadly defined). It may take the form of direct actions: strikes, also general strike and workplace occupation strike, direct dialog, negotiations and arbitration, sit-ins, demonstrations, press releases, referendum and direct democracy in general, etc. and indirect actions (e.g. voting in elections of mandated persons, general and local, etc.). The anarchist ideal has 100% horizontal organization, i.e. 100% socialism and autonomy, no hierarchy, and no authoritarian relations between people/persons, and no authorities political/administrative and economically, and no disorganization, chaotical tendencies. Thus, there is 100% anarchy, order included.

The "turning point", when both the political/administrative and economical influence on the societal management are going more from the people, from the bottom upwards, than from the top, the bureaucracy, downwards towards the bottom, is the middle point of the economical-political map. Here is where the anarchist quadrant on the E.P. map begins, and with even more influence from the bottom upwards relatively to the opposite, from the top downwards towards the bottom, the system becomes increasingly more and more anarchistic, i.e. going inwards and/or upwards in the anarchist quadrant of the map, see Economic-political map and The formula of anarchism. Anarchy and anarchism are thus real democracy and real democracy is anarchy and anarchism.

The "turning point" is connected to all of the anarchist principles, but particulary one is important in industrial organization research, i.e. the concept of "autogestion", say, briefly defined in Donals Rutherford's Dictionary of Economics, Routledge 1992, as "A French approach to workers' participation in the running of enterprises... This philosophy of management holds that enterprises should be less hierarchical, with all employees participating directly in decision-making, especially about work organization, employment procedures (e.g. promotion), technology and methods of production. This democratization would include a new framework for discussions between enterprises."*)

Furthermore a revolutionary change in anarchist direction is about changing the social structures of positions and organization, human relations included, towards more socialism and autonomy, less rank and income differences, more efficiency and fairness, and taking into account the other IFA-principles, the Oslo-Convention and anarchist human rights, i.e. significant. Anarchists are mainly fighting (class struggle) for changing the economical and political/adminstrative organization, the structure of positions and relations, not against persons and other resources. However if an especially "bad boss" is in position, it may be useful to put some effort in getting a new and less authoritarian, and more competent type.

This economic-political sociological theory of social and industrial organization should also be seen in context with a) the general theory of anarchist economics, also discussing other aspects of industrial organization, such as market power, e.g. to avoid concentration of market power; profit and bureaucracy (system) costs, etc. summarized at General theory, and b) the praxeological works referred in International Journal of Organization Research, see IJOR. Also relevant in this context is the article Horizontal organization, about more decentralized, downsized -- especially the bureaucracy, team-oriented organizations with empowered workers. Empowerment is a keyword in this connection. For horizontal organization of police and defense corps, see Antimilitarism - an anarchist approach.

Horizontal organization, a bottom up approach as opposed to a top down approach, economically and political/administrative, means organization without ruler(s) - arch(s), i. e. not without management, but 1. organization with significant small income and rank differences, 2. empowered workers with significant influence and freedom within a framework, and 3. real democratic control one way or the other. It is not a system where the management takes orders from the workers, unless the case with 100% flat organization. A horizontal organization has a degree of flatness, an anarchy degree, between 50 % and 100 %, the anarchist ideal. Workers mean the frontline in an organization.

Experience shows that external consultants who are specialists in horizontal organization often are necessary for optimal development.

*) Notes on horizontal industrial organization and more. The term bureaucracy broadly defined as the upper classes in the above mentioned way means only the characteristics or functions as archs economically and/or political/administrative in contrast to planning and pure administrative, coordinating work done in a rational, optimal, way. It is the "ranks above grassroots functions" economically and/or political/administrative, not the persons as such, that are interesting in this context. Thus, without these characteristics or functions, a person is no longer among the upper classes. And thus, doing away with the bureaucracy, the upper classes, it means of course not to do away with these persons, but their functions as archs, plutarchy included, i.e. a change in social organization towards more and more real democracy economically and political/administrative. Furthermore, as any "dead meat" none or little working persons in the industrial organizations de facto make other people slave for them, one way or another, they are all among the archs, and thus a part of the bureaucracy.

The word "bureaucracy" origins from French, a) "bureau" meaning writing table or desk, an office and or people engaged in an office; in old French a coarse brown cloth with which writing tables were covered, from "burel" a coarse cloth, and b) "cracy", that origins from Greek "kratia, from "kratein", to be strong, usually connected to management, a) ruling/archy or b) horizontal management/anarchy = real demo-cracy. Bureaucracy is usually, and here, used for ruling by upper classes, or the ruleres/superiors in itself seen as professionals, at job, not the persons seen privately. In an anarchy of low degree there may be an insignificant tendency of bureaucracy, but if the bureaucracy is significant, it is ruling and archy. As upper classes usually rules from tables and offices and/or using "brown tie" in the meaning authoritarian, this may be a relevant word to use for upper classes, the archs, broadly defined.

It also traditionally means governmental officialism or inflexible routine and the concentration of authority in adminstrative bureaus, as well as inefficient "paper mills". In this context "governmental" should not be mixed up with public sector or administrative and coordination work in itself, just the authoritarian tendencies in private and public sector, tendencies of plutarchy/capitalism and/or political/administrative hierarchy. Planning work must not be mixed up with ruling, to plan vs to rule, and it is an input, i.e. cost, not output, i.e. a final good in itself creating human welfare or utility. Bureaucracy is also the opposite of autogestion and the other anarchist principles, implemented in an optimal way. Efficiency, a.o.t. to avoid concentration of market power; and fairness, decentralization, also geographically, and autogestion, are among the key-factors or basic principles, see System theory and General theory. Management by objectives (MBO) instead of by bureaucratic ruling, is another key-factor.

Thus, it shall be optimal but as little as possible of planning, not to mention ruling, in an efficient and fair society and economy. Planning and co-ordination, management work, must never be a) allowed to grow bureaucratic, as an approximation to Parkinson's law, nor in a way of nothing is done as in Holberg's "Den stundesløse", and not quasidemocracy as in "council communism" and similar, where b) de facto large transaction and planning costs and majority or minority (if manipulative) dictatorship, ochlarchy (mob rule) and quasiscience, everything medium or bad, and no best or optimal quality, will rule, and c) no efficiency and fairness, as well as the other anarchist principles, will be achieved.

Councils and general dialog, both confederal, federal or local, have a place in an efficient and fair system, but decentralization, delegation and mandating from the bottom to the top, if any, (or from the top, if any, to the bottom) using different skills and competence, differentiation, large scale facilities and (new) technology in an optimal way is a must. The situation where everybody tells everybody what to do in a common micro-management, everybody shall know everything about everybody and everything, is archy, not anarchy. Mandated persons must have freedom within a framework decided by councils or congresses or similar. The framework must be optimal, regarding a.o.t. efficiency and fairness, not too wide or too narrow. If the framework is too wide it is lack of management, if the framework is too narrow it is micro-management, i.e. inefficient.

General assemblies and councils, "stortings" and "lilletings", are just for certain general decisions of more principal character and general controlling, and shall not be archies, doing micro-management and ochlarchy included, with cantankerous persons setting "standards", but anarchies, i.e efficient and fair, etc. And, say, new technology as internet and e-mail, cheap and efficient and fair in use, and with written matter of fact material with summaries and links to more material, and based on real science and quality level, etc., should be used as much as possible in stead of time-consuming, travel-cost ricing, and manipulative personal meetings. Pamps on holiday type conferences with champagne, caviar and limmos are not cost efficient.

The purpose of the system is simply that competence, scientifical reasoning, etc. have influence and get through in an efficient and fair way in the system, also based on the other anarchist principles, and ignorance, populism, quasi-science and ochlarchy, the oppostie of the anarchist principles, - not. A system where greedy incompetent persons rule by ochlarchy and competence and genius have no influence, is not anarchist. A system that asks the incompetent persons all of the time what to do, and not competence, is not anarchy or anarchist. If so, democracy is not real but turns into ochlarchy on way or the other. Anarchism is quite the opposite of this. In an anarchist system everybody should be educated to, or by other means, understand their own limitations with respect to competence, and shut up when things pass this border, not act according to "§ 1. The boss is always right, and if this is not true, then § 2. § 1 always rules", implementing it as "I", with big I, is the boss, always.

The system should, seen all in all, always be directed to create the right amount of outputs with at less costs as possible, never mixing up the final utility and output of real law and order, security and defense, with its's costs, and of course not planning and co-ordination work, not to mention ruling, i.e. pure input and costs, with output and utility. The "good feeling" of having power to rule others, is a false feeling, both in itself, say, because it corrupts, and because the ruled have the opposite feeling, even if they may be fooled to think it should be so, told that, say, slave-contracts are freedom and the boss is always right. Thus, the ruling feeling is an evil, and certainly not the good. The good feeling, the feel good factor, of having influence because of skills and competence and new thinking, creating more output directly or indirectly via more efficiency and fairness etc. in society, is however a positive feeling of being a civilized human being, connected to politics/administration and economics, and is no danger, but a social "fringe benefit".

The theory of social organization and systems presented at Economic-political map and mathematically at Formula of Anarchism should as indicated above in general be seen in the context of the economic-political sociology and industrial organization research at this page, i.e. Class analysis etc. and the general theory of anarchist economics at General theory , as well as the praxeological research referred in International Journal of Organization Research, see IJOR , Folkebladet - Anarkistorganet and the most of the rest of the AIIS files. And this is just a summary of the research of the International Institute for Organization Research at Web IIFOR .

These pages have several words that are well known to highly educated people. However many people are well educated, but perhaps not highly enough. If you want to see the definition of a word or phrase used in this context, try first to search in the mentioned html-files. Secondly, if you want more information, try the anarchist search engine powered by Google at AIIS. Third, if you have problems with understanding words that are not defined at the AIIS web-pages, try , say, Cambridge dictionary .

If you, after doing the best to understand, still have problems learning the material, click on the Anarchist International University Federation and its Basic course for help. If you have questions about the research and/or want more results, click on IIFOR.

Anarchism, i.e. horizontal organization, is a.o.t. based on dialog, and free - matter of fact - criticism. To achieve this, it is necessary to understand what it is all about. A minimum basic knowledge to be taken seriously in a debate on anarchy, anarchist(s) and anarchism is probably the material at the Basic course, i.e. a brief summary of the updated research front on anarchism.

The main variables used in Table 1. translated to English. Rank and income difference indicators.

Ad the political/administrative classes: rang = rank; overordnede OE = superiors; underordnede UE = subordinates; toppsjefene B = top bosses; undersjefene b = sub bosses; den autonome klassen A = the autonomous class (self employed and similar); underklassen U = the sub class, rank and file in hierarchies. NB! A is here the autonomous class, = I in the summary above. A and B must not be mixed up with A and B in the summary above. B + b is a part of the bureaucracy. The sign for logical union, U, in the summary above, must not be mixed up with the variable U here, meaning the sub class of rank. In general rank = (UE+1)/(OE+1). In the special case Rank(U) = (1/(B+b+1)), because UE = 0 and OE = B+b. In the special case Rank(B) = (b+U+1), because OE = 0 and EU = b+U. In connection to the Rank-Difference-Index, the classes of rank, B, b, U and A are shares (relative frequences) of the population, say, B = 0,1, b = 0,2, U = 0,4 and A = 0,3.

An indicator of political/administrative rank differences, is the Rank-Difference-Index, RDI = ([rank(B)/rank(U)] - 1)/3 for B > 0 and U > 0. RDI = ([rank(B)/rank(U)]-1)/3 = ([(b+U+1)/(1/(B+b+1))]-1)/3 = ([(b+U+1)(B+b+1)]-1)/3. If B and U is zero, all belong to the autonomous class, RDI = 0, no rank hierarchy. In the case with 100% vertical organization, rank(B) is about 2 and rank(U) is about 0.5, thus rank(B)/rank(U) is about (2/0.5) = 4; ([rank(B)/rank(U)] - 1) = 3 , and ([rank(B)/rank(U)] - 1)/3 = 3/3 = about 1, i.e. about 100%. Thus the RDI is about 1, 100%, with 100% vertical organization political/administrative, maximum rank differences, and RDI is zero with 100% flat organization. If b is exact 100% (= 1), i.e. one on the top and one on the bottom, A = 0, and b includes an infinite number of sub bosses, the RDI is exact = 1 (100%). If B = 0,1, b = 0,2 and U = 0,4 and A = 0,3; RDI = ([rank(B)/rank(U)] - 1)/3 = ([(b+U+1)(B+b+1)]-1)/3 = ([(0,2+0,4+1)(0,1+0,2 +1)]-1)/3 = 0,36 = 36%. (Rank (A) = 1).

Ad economic classes: overklassen = upper class; middelklassen = middle class; underklassen = the sub class; the upper class is part of the bureaucracy. An indicator of income-differences is the Gini-index. It is 100% (1) if one has all income (in an infinetely large population), and 0 if all have the same income. For more information about the Gini-index, click on: Gini-coefficient.

The logical union of the economic upper class and (B + b) is the bureaucracy, authorities = B. The relevant population (usually the adults) - B, is the people, grassroots = A.

For the rest of the words you may use the translation tool from Norwegian to English (or other languages) at "Links" at the bottom of this document. The Gini-index is one of the factors in the measurment of the degree of socialism, and the Rank-Difference-Index, RDI, is one of the factors in the measurment of the degree of autonomy, related to the anarchist economical political map.



Kvalitativt ulike styringsmessige reelle menneskelige relasjoner (stillingstyper)

To samleklasser: (Se nedenfor) Gjelder hovedstillinger/ekvivalenter når ikke annet er spesifisert. Kvantitav rang = (underordnede+1)/(overordnede+1) Alle med ingen over seg, dvs som ikke er underordnet (Overordnede = nei, dvs OE = 0) Alle som har noen over seg, dvs som er underordnet (Overordnede = ja, dvs OE = 1)
Alle som har noen under seg, dvs styrer andre, har noen underlagt seg politisk/administrativt. (Underordnede = ja, dvs UE = 1) F. eks. i middelalderen var adelen og under industrialismen fabrikkeierne, en viktig del av borgerskapet (bursjoasiet) i anarkistisk mening. Dette må ikke forveksles med borgerstanden. Samleklassen "øvrigheten" politisk/administrativt består av to klasser:


Alle med ingen over seg,og noen under seg. Eks. generaldirektør/eneeier i et firma med underordnede. For hele klassen sett under ett gjelder følgende: Rang(B) = (småborgerne+underklassen+1) > 1. Når storborgerskapet (B) utgjør 10%, småborgerskapet (b) 20%, den autonome klassen (A) 30% og underklassen (U) 40% av populasjonen, får en: Rang(B ) = (0,2+0,4+1) = 1,6. NB! Rang kan også måles individuelt, og +/- ulike korreksjoner, bl.a for gradering. Målestokken kan også endres.
[OE,UE] = [1,1]
Alle med noen over seg, og noen under seg f. eks. underdirektør i et firma eller etat, med underordnede og overordnede. For hele klassen sett under ett gjelder følgende: Rang(b) = (underklassen+1)/(storborgerne+1). Rang (b) er typisk > 1. F.eks. Rang(b)=(0,4+1)/(0,1+1)= ca 1,27 . (Atypisk <1 for B>U og = 1 for B=U).
Alle med ingen under seg, dvs de som ikke styrer over andre, alle som ikke har noen underlagt seg politisk/administrativt. (Underordnede = nei, dvs UE = 0) Samleklassen "folket" består av personer fra de to klassene til høyre, men folk som er med i disse og likevel tilhører overklassen økonomisk er en del av øvrigheten, byråkratiet, og ikke med i folket og grassrota.


Alle med ingen over seg og ingen under seg, eksakt eller tilnærmet. Eks. frisør, bonde, fisker, lege, butikkinnehaver etc. som driver selvstendig på individuell basis eller sidestilt, solidarisk, i et kooperativ, nettverk, el.l. Også relativt fritt stilte fagstillinger i stabsfunksjoner uten underordnede, innen hierarkier, kan regnes som autonome. Rene kontraktører, som ikke har noen egentlig autonomi, og med mer eller mindre slavekontrakter, regnes ikke med her. Autonomi = selvforvaltning, -styre, -bestemmelse, være sin egen sjef. Rang(A) er 1.
Alle med noen over seg og ingen under seg. Eks. ekspeditrise eller arbeider ("på golvet" - uten noen under seg), og underlagt butikksjef/avdelingsleder/formann. U er "ikkesjefer". Rang(U) = 1/(Små & storborgerne+1) <1, f.eks. 1/(0,2+0,1+1)= "ca" 0,77. Rang(U) er udefinert for B+b="0," da en hierarkisk situasjon forutsetter både over og underordnede. Menige blir ikke automatisk selvstendig næringsdrivende, kooperatør el.l. om sjefene blir borte.


Alle som har en lønn/ekvivalent som ligger over det midlere inntektsintervallet, (dvs fra og med ca 2x aritmetisk gjennomsnitt. Med "ca" menes "+/- et lite [kalibrerende] tall", NB! hvor "-"et her er det utslagsgivende.) I den typiske kapitalistiske avlønningspyramiden utgjør dette vanligvis et lite mindretall. F.eks 0,15; 15% av populasjonen. I et idealtypisk anarki vil dette tallet være null.

Den økonomiske øvrigheten eller overklassen er en del av byråkratiet, inntektsmessig.

Alle som har middels inntekt,(dvs lønn/ekvivalenter i intervallet fra og med ca det aritmetiske gjennomsnitt, via øvre middel, opp mot overklassen). I den typiske kapitalistiske avlønningspyramiden utgjør dette noen flere enn overklassen, men i sum utgjør middel- og overklassen ofte et mindretall. F.eks 0,25; 25% av populasjonen. I et idealtypisk anarki vil dette tallet være 100%. Hvor strengt en her regner på avviket fra gjennomsnittet, avhenger av det kalibrerende tallet som definerer "ca". Dette vil bl.a. avhenge av hvilke forskjeller som anses som rettferdige. Her kan ombyttekriteret i kombinasjon med Pareto-optimalitet prinsipielt bestemme "ca" avviket som anses akseptabelt.

Personer som er med i denne økonomiske klassen, og ikke tilhører rangsklassene B og b, er med i folket, grassrota.

© IIFOR, A.U., ANORG FORLAG 1993 (All rights reserved) ISSN 0800-0220, ISBN 82-90468-23-7 - Updated 2010.

Alle som tjener under middels inntekt (dvs resten av populasjonen). I den typiske kapitalistiske avlønningspyramide, hvor midtinntekten (medianen) ligger under ca gjennomsnittsinntekten, vil flertallet høre hjemme i denne klassen. F.eks 0,6; 60% av populasjonen. I et idealtypisk anarkistisk samfunn vil dette tallet være null.

Er den kapitalistiske tendensen i inntektsfordelingen betydelig (signifikant, over 50% kapitalistisk), regnes det som (økonomisk) plutarki. Bl.a kjøpekraften vil da være så skjevt fordelt at markedet i vid forstand ikke kan betraktes som demokratisk, men være utilbørlig preget av rikmanns/pengevelde. En krone tilsvarer en stemme i markedet. Demokrati/anarki betyr dermed ca like mange stemmer på hver. Er pengene betydelig/signifikant skjevt fordelt, er "stemmene i markedet" tilsvarende skjevt fordelt og markedet blir udemokratisk/plutarkisk.

Personer som er med i denne økonomiske klassen, og ikke tilhører rangsklassene B og b, er med i folket, grassrota.

Tabellen over belyser klassestrukturen økonomisk og politisk/adminstrativt på en prinsipiell måte. Når en skal avgjøre hvor demokratisk et system er, i hvilken grad det fungerer mer nedenfra - fra folket - og opp, enn ovenfra, fra øvrigheten og ned, må en imidlertid ikke bare se på klassestrukturen, men også relasjonene mellom klassene og personer. Det er jo ikke det samme om sjefene er kav psykopater og autoritære maktmennesker eller relativt frihetlige og demokratisk anlagt. Men klassestrukturen er åpenbart et relevant studieobjekt i en anarkistisk systemanalyse. Den er også knyttet til koordinatene på det økonomisk politiske kartet, det økonomiske og det politisk/administrative, graden av sosialisme og autonomi, selv om man altså ikke må se seg blind på klassestrukturene alene, men ta hensyn til relasjonenes karakter når koordinatene for et system/objekt skal fastlegges.

En indikator for rangsforskjeller basert på de strukturelle klasse-forholdene er Rank-Difference-Index, RDI = ([rang(B)/rang(U)] - 1)/3 for B > 0 and U > 0. Rangsklassene B, b, U og A måles som andeler av populasjonen, f.eks. B = 0,1, b = 0,2, U = 0,4 og A = 0,3. Summen av alle klassene = 1,0. Hvis B og U begge er null, er alle med i den autonome klassen og RDI = 0, dvs. det er ikke noe rangshierarki.**) Rang(B) kan maksimalt bli 2, dvs. med én på toppen og ca 100% (= 1) underordnede. Rang(U) kan minimalt bli 0,5, dvs. med én på bunnen og ca 100% (= 1) overordnede. I tilfellet med 100% vertikal organisasjon, én på toppen, ca 100% undersjefer og én på bunnen, blir rang(B) maksimal = ca 2 og rang(U) minimal = ca 0,5 og dermed ([rang(B)/rang(U)] = 2/0,5 = ca 4. Dermed blir ([rang(B)/rang(U)] - 1) = 4-1 = 3 og RDI = ([rang(B)/rang(U)] - 1)/3 blir 3/3 = ca 1 (100%). Ved 100% vertikal organisasjon er altså RDI = 1, 100%. Ved 100% flat organisasjon er RDI = 0. I eksemplet i tabellen blir RDI ca 0,36, dvs. 36%, som er en ganske "normal" verdi. Dersom det er uendelig mange personer i b, dvs. b = eksakt 100% (=1), og null A, og vi har en på toppen og en på bunnen, blir RDI eksakt lik 1, dvs 100%. Man kan også si at viss antall personer i b vokser over alle grenser, og A = 0, så vil RDI gå mot 100%, (=1) som en grense.

Et annet spesialtilfelle, en toppsjef og en underordnet og A = 0 og b = 0, gir underordnede, dvs. underklassen lik 50% (= 0,5) og overordnede, dvs. toppsjefene også lik 50% (=0,5) og dermed rang(B) = 1,5 og rang(U) = 1/(0,5 +1) = 1/1,5 = 2/3 = ca 0,67. Dermed blir RDI = ([1,5/0,67]-1}/3 = (2,24-1)/3 = (1,24)/3 = 0,41 eller 41%. Dersom alle bedriftene eller mer generelt organisasjonene i samfunnet er av denne typen, f.eks. småbedrifter med en sjef og en underordnet, får vi samme resultat, dvs. RDI = 0,41 = 41%, ikke særlig topptungt. Samfunner er da ikke spesielt hierarkisk sett under ett, men heller ikke veldig flatt politisk/administrativt organisert. Består samfunnet av nesten bare småbedrifter som er kompaniskaper, uten over og underordning, blir A = bortimot 100% (= nær 1) og B og U blir små tall, f.eks. B = 0,01 (1%) og U = 0, 01 (1%) og så blir rang(B) = 1,01 og rang(U) = 1/(0,01+1) = 0,99, og RDI = ([1,01/0,99] -1)/3 = 0,02/3 = 0,0067 eller 0,67%, dvs. tilnærmet flatt organisert. Er alle bedriftene kompaniskaper uten over- og underordnede er A = 1 (100%) og B=U=b=0, og da er som nevnt RDI = 0, samfunnet er 100% flatt organisert politisk/administrativt.

Rank-Difference-Index, rangsdifferanse-indeksen kan altså variere mellom 0 og 1, (100%), og er større jo mer topptungt og vertikalt systemet er politisk/administrativt, og er null ved helt flat organisasjon.

Som nevnt er Kvantitav rang = (underordnede+1)/(overordnede+1). For underklassen U blir kvantitativ rang, rang(U) = (0 + 1)/(B + b + 1) = 1/(B + b + 1), hvor B og b er målt som andel av populasjonen i samfunnet, f.eks. dersom toppsjefene B = 0,1 og undersjefene b = 0,2 er rang(U) = 1/(0,1 + 0,2 + 1) = 1/1,3 = 0,77. For toppsjef-klassen B blir kvantitativ rang, Rang(B) = (underordnet+1)/(overordnet+1) = (b + U + 1)/(0+1) = b + U + 1. F.eks. når U = 0,4 og b = 0,2 blir rang(B) = 0,2 + 0,4 + 1 = 1,6. Rangsdifferanse indeksen RDI =  ([rang(B)/rang(U)] - 1)/3 = ([(b+U+1)/(1/(B+b+1))]-1)/3 = ([(b+U+1)(B+b+1)]-1)/3 = ([1,6/0,77] – 1)/3 = ([1,6x1,3]-1)/3 = (2,08-1)/3 = 1,08/3 = 0,36, eller 36%. I dette eksemplet er den autonome klassen = 1 - (0,1+0,2+04) = 0,3, eller 30%.

En tilsvarende indikator for inntektsforskjeller er Gini-indeksen. Den er 100% (1) når én har all inntekt, og 0 når alle har lik inntekt. Gini-indeksen måler hvor topptung den økonomiske pyramiden er. Har én all inntekt, er indeksen 1 (100%), og har alle lik inntekt er indeksen 0. I de skandinaviske landene ligger Gini-indeksene på rundt 0,25, dvs. 25%. For mer informasjon om Gini-indeksen, klikk på: Gini-coefficient .

Det statistiske grunnlaget for rangs- og lønns-analysene er ulike former for sosio-økonomiske data i vid forstand, bl.a. bedrifters organisasjonskart med stillings- og avlønnings data, og som også belyser over- og underordningsforhold o.l.

Forøvrig, dersom offentlige myndigheter hele tiden griper direkte inn i privatliv og privat næringsliv i en form som de facto betyr at private er satt "under offentlig administrasjon", eller det offentlige på en utilbørlig måte blir styrt/influert av (det økonomiske) plutarkiet, så det også blir politisk/adminstrativt plutarki - eller mafiaen overtar det meste og det blir generelt oklarki (pøbelvelde, mob rule), må slikt medregnes i kommandostrukturene og klassesystemet. Den autonome klassen kan da de facto opphøre å eksistere, og hierarkiet blir mer topptungt enn de vanlige nærings-strukturene i privat og offentlig sektor skulle tilsi. I siste instans kan det bli et totalitært enevelde/monarki eller fåmannsvelde/oligarki, kun med kommandolinjer nedover, som styrer praktisk talt alt via et enormt byråkrati i et fullstendig korrupt kaos og med tilnærmet 100% vilkårlighet, hvor a) folket en masse er redusert til sulteforede slaver i fangeleire uten innflytelse på noen ting, fullstendig prisgitt øvrigheten, dens luner, sadisme, tortur og mordlyst - inkludert folkemord, og b) denne overklassen plutarkisk røver tilnærmet alt, - hvor skillet mellom offentlig og privat sektor/sfære er tilnærmet helt utvisket, rettferdigheten er ca null og effektiviteten tilnærmet den samme. Dette er nær det absolutte nullpunkt på kartet hva det frihetlige angår, dvs ca 100% autoritært, "den fullkomne totalitære faenskap".

Jens Bjørneboe skjønte glimtvis litt av dette, i "Bestialitetens historie", men han overdrev. Likevel var de nok så skremmende disse studiene at de kanskje bidro til at han gjorde ende på seg p.g.a. alvorlig depresjon. De skrekkvisjonene enhver med noenlunde fantasi kan tenke seg av autoritær bestialitet via bruk av moderne genteknologi, kloning, bioteknologi, datateknologi, robotteknikk, implantasjoner, psykofarmaka, tortur i alle former, i autoritære systemer, er så jævlige at det kan få enhver til å sette mye inn på å få til en frihetlig humanistisk utvikling og hindre fremveksten av autoritære systemer i liten og stor skala. Bare sett i gang å tenke på dette selv, - la skrekkfantasiene løpe litt, og du vil nok innse at Orwell's "1984" er barnemat av mulig jævelskap, i forhold til hva den moderne teknologiske utvikling kombinert med autoritære systemer kan medføre, - så forstår du nok hva som menes. Slike autoritære systemer må aldri få anledning til å utvikle seg! Det er mulig det må settes stopp for en del tendenser i forskningen, ut fra en realistisk forståelse for hvordan dette en gang i fremtiden kanskje kan misbrukes til jævelskap av et oppdatert mektig "Talibanistisk" regime, el.l.. Hva som allerede i dag måtte foregå av tvilsom forskning i denne forbindelse kan også tas i betraktning... Å definere systemer 100% på bunnen av det økonomisk-politiske kartet, se Economic-political map , er altså ganske umulig, det blir kun snakk om en tilnærming. I tilknytning til det økonomisk-politiske kartet er tilsvarende diskusjon for toppen av kartet gjort, og eller ikke her er det mulig å definere det annet enn tilnærmet. Det absolutte, 100% frihetlige samfunn, kan bare tilnærmes. Friheten kan som kjent ikke fanges absolutt - straks man tror man ha funnet hele oppskriften, så finner man snart likevel noe som kan forbedres.

Klasseanalysene er først og fremst myntet på land og internasjonale sammenligninger mellom land, men kan også brukes på mindre områder, som kommuner/kollektiver, bedrifter/næringer, eller motsatt, større regioner eller verden sett under ett. En fornuftig kalibrering for landsanalyser kan ta hensyn til den internasjonale situasjon og det politisk mulige. Hvis man er fullstendig "allergisk" overfor enhver skjevhet i inntektsfordelingen, eller i det politisk/adminstrative rangs-system, vil hele verden framstå som ultrafascistisk og de ulike land kun ha ubetydelige gradsforskjeller av dette. En slik kalibrering er vel ufruktbar med hensyn på praktisk frihetlig politikk. Det kan medføre urealistisk håpløshet og desperasjon. En motsatt type kalibrering, hvor nær sagt alt som kaller seg demokrati regnes som signifikant anarkistisk, er vel omtrent like ufruktbart. Det kan medføre likegladhet og mangel på engasjement - "det er bra som det er". Det må værer en viss realisme i midtpunktet på det økonomisk-politiske kartet ved kalibreringen, nemlig der systemet prinsipielt "vipper over" - slik at det alt i alt med en viss rett kan sies å fungere mer via innflytelse fra folket - nedenfra og opp, enn fra øvrigheten - ovenfra og ned, økonomisk og politisk/administrativt i privat og offentlig sektor. Her ligger det en klar prinsipiell føring på en vitenskapelig fruktbar kalibrering, selv om en slik betraktning/kalibrering i praksis sannsynligvis må bygge på en del konvensjonelt fastlagte størrelser, delvis basert på skjønn.

Det er altså relativt uvitenskapelig å kalibrere det økonomisk politiske kartet i hytt å pine, subjektivt. Da mister man det reelle poenget angående midtpunktet. Dette kravet til kalibrering av midtpunktet gjør at kartet intensjonelt ikke skal brukes som et mikroskop til å forstørre autoritærer tendenser og dermed kjøre alle mulig systemer mot bunnen på kartet, eller det motsatte, forskjønne virkeligheten på en urealistisk måte i frihetlig retning, så all autoritær humbug kommer høyt opp på kartet. Dersom man har moro av det kan man naturligvis ta seg den kunstneriske, subjektive frihet, å forstørre alle autoritære tendenser og, som enkelte pønkere [ikke anarkopønkere] skjelle ut relativt libertære land som gjennomført ultrafascistiske høl, eller det motsatte, hausse opp verden som et tilnærmet paradis - "den beste av alle mulige verdener", begge deler kan kanskje av og til være bra mental-terapi, men anarkistisk - og dermed realistisk vitenskapelig og politisk, er ikke noe av dette.

IIFOR har beregnet libertær-graden, = (100% - autoritærgraden), for alle land som er nevnt i HDI-statistikken fra FN, også de som FN ikke har beregnet HDI-rang for. Her er følgende praksis blitt fulgt i estimeringen av libertærgraden:

The formula of anarchism is just a mathematical precisation of the economical-political map at Systems theory. The estimimates of the degree of anarchism, or more general the libertarian degree, are calculated by the formula of anarchism at Anarchist formula on basis of estimates of the degree of socialism and the degree of autonomy. The degree of socialism and the degree of autonomy may be measured in several practical ways. One is just to ask people what they think about the matter for a given country. Another more objective way of practical measuring is the following: The degree of socialism is dependent on income-differences, (say, measured by the gini-index), and efficiency, (say, measured by GDP per capita). The degree of autonomy is dependent on the rank-differences, see Economic sociology, life expectancy at birth (years) and adult literacy rate, see Ranking of countries according to libertarian degree. The estimates of the libertarian degree at this file are done via the more ojective way/method.

The estimates are accounting for economic and political/administrative freedom, solidarity, and equality etc. also democracy vs. totalitarian systems, i.e. mostly dictatorship, heavy ochlarchy or extreme capitalist liberalism, in a practical way. The gini -index measures how top heavy the income hierarchy is. If one has all of the income the index is 100. This is the most top heavy income hierarchy. If everybody has the same income, no hierarchy - the distribution is flat - the index is zero. As a rule of the thumb a gini -index less than 35 indicates socialism (possession), and an index more than 35 indicates capitalism - economical plutarchy (property). This is only a rule of the thumb, the concept of socialism also includes efficiency. Thus a system with high efficiency, a large GDP per capita, and a gini -index at 30 may be more socialist than a system with low GDP per capita and a gini -index at 25. Socialism means a lot of wealth plus a reasonable flat distribution of income. The libertarian degree is as mentioned dependent on the degree of socialism and the degree of autonomy, see Formula of anarchism. The ranking and point estimates at Ranking of countries according to libertarian degree are made by IIFOR . IIFOR has published point estimates of the libertarian degree for all of the countries mentioned in the HDI -statistics of the UN, also the countries without HDI rank. The estimates of the libertarian degree for countries ranked from 101-186 are between ca 29%-20%. The ranking of countries from 101-186 is very uncertain. Also the estimates for the 100 most libertarian countries are a bit uncertain.

Countries with less than 33 ,33 % libertarian degree, i.e. more than 666 per thousand authoritarian degree are totalitarian, i.e. either dictatorships, heavy ochlarchies ( ochlarchy = mob rule broadly defined), say, with rivalling polyarchy , or have a very low degree of autonomy and/or socialism in general. The countries ranked from no 65-186 according to libertarian degree, have less than 33 ,33 % libertarian degree, and are thus very authoritarian, i.e. totalitarian. On the other end of the ranking we have three anarchies of low degree, no 1 Norway with ca 54% anarchy degree, no 2 Switzerland with ca 53% degree of anarchy and no 3, Iceland with ca 52% degree of anarchy. These societies are real democratic, the systems work significantly more from the bottom, grassroots, and upwards, than from the top downwards to the bottom. Thus it is anarchism. Anarchies have more than 50% anarchy degree, i.e. significant. The countries in the middle, ranked from 4-64 according to libertarian degree, are semi-democratic, the systems work more from the top downwards to the bottom, than from the bottom, grassroots, and upwards, but they are not totalitarian. They have a libertarian degree between ca 49,99% - 33,32%. These countries mostly are parliamentarian democracies. The investigation is based on UN-statistics, OECD statistics, EUROSTAT, statistics from the Statistisk Sentralbyrå in Norway , and several other sources. In the column for the libertarian degree we have used “,”, the European standard instead of American/UK standard, i.e. “.” as decimal separator. The term “ca” is an abbreviation for the latin circa, which means about or approximately. More information about methodology for estimation of the libertarian degree, see Economic-political map.

**) Vi har her implisitt forutsatt at den autonome klassen A øker og erstatter hierarkiet på ordnet vis. Dette er ikke den samme situasjonen som kan oppstå om de overordnede b + B bare "går hjem" el.l., dvs. et hierarki med ubesatte overordnede stillinger. Det kan da oppstå en kaotisk situasjon. Denne er nærmere diskutert i Anarkidebatten, i artikkelen "Anarki kontra kaos, regjering og kaos-herskere", søk på anarchy vs chaos i debatt . En slik kaotisk situasjon er ikke videre stabil, det kan utvikle seg andre former for kaos, et nytt hierarki eller de menige uten ledere svinger seg opp til rang 1 og går inn i den autonome klassen. Det er også en generell diskusjon om anarki kontra kaos i den aktuelle artikkelen i Anarkidebatt. Ellers er det flere relevante artikler på Anarkidebatten. Spesielt kan nevnes "Anarki kontra stat - en kortfattet utredning om stats- og anarki-begrepene", "Sammenbrudd i sentraladministrasjonen skaper oklarki - ikke anarki" og "Styring og styrere kontra hersking og herskere". Også Et kortfattet notat om anarkibegrepene og Konsistent anarkistisk politikk på dagsaktuell, mellomlang og lang sikt er relevante i denne konteksten.

Resolution, decided with general consent, by:
The International Anarchist Congress
The 11th Anarchist Biennial 27-28.11.2010
International Congress-Seminar on Anarchism
The AI/IFA network represents more than 50 000 anarchist world wide
To see the Website of the Congress - Click here!

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