To make it clear right away: There is no "complete matriarchal people" known today. Every so called matriarchal society lost more or less of their typical life style under patriarchal influence; so this description will be “fictional" and somewhat theoretical. Even though it matches reality, the characteristics listed below cannot be experienced by travelling to one ethnical community or tribe.
If we presume - according to many discoveries in different fields of
knowledge - that in pre-patriarchal times all humans were organized in
matriarchal structures, the following description will give you the
basics of these structures and an understanding of how a peaceful
society can attain balance in their community. And those of you, who
are unsure if historical matriarchies existed – don’t worry – all the
elements can be found on the planet today, just not in one place any
longer, but with different tribes and peoples.
A Matriarchy is a type of society, which is distinguished from all other types of societies by the absence of power structures and institutionalised hierarchies. This is why rural sociologist Christian Sigrist  refers to it as an ‘adjusted anarchy’, and culture sociologist Thomas Wagner  calls it an ‘egalitarian consensus democracy’.
The means of production are commonly owned and set of rules prevent the accumulation of possessions or power. Compared to socialist or communist systems they are characterized by the absence of a centralised administration and ruling authority. Decisions concerning every area of life are made by consensus including all genders and generations.
The Term The term Matriarchy is a reproduction from the 19. Century and corresponds etymologically to designations such as monarchy, hierarchy, patriarchy, etc. (From Greek mêtêr "mother" and archê "beginning, origin", later sometimes also "rule").
Although most anthropologists associate the term Matriarchy with the work of J.J. Bachofen or L.H. Morgan, it was used for the first time by E.B. Taylor (1896) in an article with the title "The Matriarchal Family system".
Bachofen used the term "Gynaikokratie" (from Greek. gyne "woman" and kratos "to rule, prevail") in the sub-title of its German issue of "Mother Right" (Das Mutterrecht - eine Untersuchung über die Gynaikokratie der alten Welt nach ihrer religiösen und rechtlichen Natur, 1861).  In the English edition this was translated however falsely with "matriarchy".
When internationally the first ethnologists and scholars of matriarchal studies began to learn about peoples who showed matrilocality and matrilineage they drew falsely the conclusion that mothers are rulers, on the one hand because of the translation error, and in addition, in similarity to their own patriarchal culture. The modern studies of matriarchy corrected this misunderstanding in the German-speaking countries in the second half of the 20. Century and investigates this field since then. In the international science discourse the term matriarchy is maintained, although sometimes it is misconstrued as "mother's rule" or "woman's rule"; both never existed in accordance to today's state of research. Today Matriarchy is used in the sense of "motherly beginning" as a beginning of a cycle, because these societies are coined by cyclic thinking unlike linear.
Replacements as gylanic, matrilinear, matrilocal, matrifocal, egalitarian etc. instead of matriarchal are problematic, because
- first of all thereby only several characteristics of matriarchal societies are taken into account and not this social order as whole.
- Secondly these reducing terms are used to deny the existence of matriarchal societies and are unfit therefore.
It is important to fill and correctly use the term Matriarchy with error free and unmistakable contents.
In a further contribution I will write in more detail about the development of patriarchy, but to start with here are the first details of the theory. The Saharasia-Theses  is valid in the discourse of Matriarchal studies because no signs of violence and warlike activities are evident during pre-patriarchal times (see also discussion of DeMeo/Keeler ) and matriarchal lifestyles can be taken as given. University faculties such as archaeology, ethnology and anthropology have so far not been able to refute this.
Displacement of matriarchal societies
Approx. 5000 B.C.E. the displacement of matriarchal societies began (see Marija Gimbutas’ Kurganculture ) starting in the Middle East. In connection with this the monotheistic world religions developed (i.e. Sumer, Old-Egypt, Judaism, Christianity, Islam, Buddhism) which are spreading slowly. The original ethnic and kinship group religions were either retained by groups who lived matriarchally, as for example the Northamerican Iroquois or the new religions were integrated into the present traditions.(i.e. the Korean Shamanism integrated Confucianism).
Egalitarian consensus society
Compared to nation states with their bureaucratic centralized structures egalitarian or societies free of domination possess a number of very intelligent conventions which both serve to deal with conflict and deal with political and economic inequalities should they arise. They were called ‚adjusted anarchy’, or stabilized domination-free systems by Max Weber.
Organizing festivals and games, especially gambling, have a great importance in the process of balancing out any inequalities . In ethnographic literature this point of minimizing differences in possessions is often stressed. It has a similar distribution effects as organizing festivals have. (The contribution of differnet types of games to maintaining the equilibrium within a group has hardly been analysed in a systematic way. For example the conflict reducing potential of the different ritualised Indian ball games, i.e. hockey played by the South-American Mapuche-Huilliche or the North-American Lacrosse .)
Especially the example of Juchtán, Mexiko portrays the “economy of festivals” as scientifically documented by ethnologist and sociologist Bennholdt-Thomson . These festivals enable the constant distribution of possessions and monetary wealth. Rich traders are expected to participate actively by taking responsibility of Velas (festivals) and by visiting those others have directed. In this way their wealth is circulated back into the local economy and in turn the community honours them for what they do. The festivals also have a great influence on the social relationships. It creates a constant net of reciprocal support which generates a social community which in turn ensures the economic existence of that community.
Another method which appeared in the meantime to level off economic inequality and to prevent the authority of leaders from decaying into dominance is the principle of the “seperation of halves” (i.e. with the Iroquois and Horons). Female chiefs or clan-leaders would serve together with their male counterparts in the same position, which constituted the common principle of doubling up of offices. As Henry Lewis Morgan stated for the Iroquois  what resulted from this principle is a kind “enforced” communication and frequent change of office of leadership.
And finally there is the type of decision making, house free of domination, called egalitarian consensus democracy. The equilibrium of matriarchal societies is constantly renewed by consensues decision making, which aim is to come to unanimity.
A counsel made up of men and women excluding nobody make up the smallest unit of the society, the clan house. Each decision is made after thorough discussion by consensus. Now the delegates of each house meet on the level of the village to discuss the issues which arose in the houses, with the aim of finding consensus again. Likewise it goes on to the level of the tribe, till the whole nation is in agreement.
It is important to note, delegates do not represent their personal opinion, but only represent the interests of the community which sent them, and in any unclear situation they have to go back to their group to receive new instructions. This prevents political power from mounting up. This system is thanks to its stability and strengths able to create functioning large assemblies with several hundred thousands of individuals without centralized institutions.
It is easier to achieve majority rule than create consensus. The parties hereto are aware of this, but they refuse the line of least resistance for the following reasons: The opinion of the majority is not sufficient basis for making a decision, because the minority is in this process excluded from expressing their will in the decision.
To express it in a different way, the principle of majority representation denies the minority representation in any given decision, but representation is a basic human right in matriarchal societies. It is believed that continuous non-representation is creating a feeling of dissatisfaction which in turn threatens the balance of the whole community .
Spiritual life and accompanying rituals of matriarchal societies are incomparable to patriarchal religions such as Christianity, Judaism, Islam or Buddhism. Everybody, women, men, children of all ages, as well as the older generation, even the ancestors all take part in the rituals, they are carried out by regular members of the community, and there are no clerics, no laity. Besides such rituals where everyone is involved in, like mourning rituals, there are also special rituals such as adolescent initiation which are carried out by the elders, or the healing ceremonies carried out by male or female shamans or medicine men, or – women. They also perform special rituals for house building, and Wise Women are performing special birthing and naming rituals .
In matriarchal societies rituals are a community activity, a creative process, not to be compared with the ceremonies carried out in Western Churches. Everybody involved is occupied in preparing the details and in the carrying out of the actual ritual to meet the specific need which the ritual is to serve. It is to create a special kind of energy, in which all participants partake and enables the raising of consciousness to experience the transformation which brings healing. 
The aim of all ritual is the encounter between humans and the other-world, non-ancestor spirits and ancestors and to find a connection for the individual’s life purpose. In the constant repetition of the rituals the powers which have brought humans to this world are continuously intensified.
Such rituals mirror the agility of human imagination (not the opposing power of stagnation and solidification) and therefore are never exactly the same. What is important to note at this point is the fact that shamans and medicine men and women of matriarchal societies are not only learning to use established traditions (such as trance- and healing rituals) during their decade-long training but they also have the task to integrate new and unknown phenomena, for the use and positive influence of the community. This explains why indigenous people often belong “officially” to Islam (i.e. the Minangkabau of Sumatra) or Christianity (many African tribes or the South-American descendants of the Mayans). Nevertheless they did not give up their traditional cultures, unless they were actually forced by patriarchal colonists, missionaries or invaders.
These shamanistic abilities enable matriarchal societies to keep abreast with current developments, react flexible in respect to political issues and maintain equilibrium for their community. In the spiritual world view of these indigenous groups ritual, community and the healing arts are closely connected, which in turn are indivisible from the natural world. Each member of the community has a great interest to live in such a way as to come into harmony with the powers of nature on a continuous basis.
Ancient matriarchal societies such as the Minoan Culture of Crete or the indigenous groups of the Old Europeans cultures portrayed by archeologist Marija Gimbutas are best known. Ethnologists and cultural sociologists know of current matriarchal cultures all over the world, even though these cultures have lost some of their traditions through colonial domination, missionary influences and interaction with bordering nations and are not necessarily designated with the term “matriarchal”.
Here are three examples:
The Minangkabau of Sumatra is the largest matriarchal nation, and they have maintained their “Adat”, a matriarchal set of rules for selfgovernment. There are three Million people who belong to the Minangkabau who live according to the ancient “Adat” in all the major cities of Sumatra and Indonesia. They are active in trade, administration, economy, politics and culture and are regarded in Indonesia as a people of a high level of education, culture, cosmopoliticalism and great economic power. The American anthropologist Peggy Reeves Sanday has lived many years among the Minangkabau and documented their way of live outstandingly .
The linguist Carlos Lenkersdorf researched the Tojolabalians in great depth, a Mayan group which lives in Ciapas . Their language has no objects, there are only subjects . When everything, humans, animals, plants and objects of nature and culture are seen as subjects, this is a mirror of the common egalitarian way of life. It portraits clearly the egalitarian lifestyle of these people and their rejection of domination.
The Goajiro-Arawak of Columbia and Venezuela are with 60.000 people the largest surviving tribe of South America. The economic basis of each kinship group is cattle, it is commonly owned and cared for. The men tend to the animals the women milk them and produce cheese and prepare the meat. Theaft of animals and the rape of a woman are comparable in severity and punished severely, because the whole group feels offended by it, as a result these offences are not committed within the kinship group. The fathers line is known, but does not have any importance. The children live with the mother to begin with, later a sister of the mother cares for the girls and a brother for the sons . They are thus raised in the maternal clan. Even though the Arawak-culture of the Goajiro has been confronted by several threats which has brought about different changes to their culture, the matriarchal ancestry is still clearly visible.
Translated by Jutta Ried