Kinship & Family StructuresModels in Anthropology

Section systems, and how the Kariera and Aranda rules work

How four-section (Kariera) and eight-subsection (Aranda) systems work: marriage and descent rules worked by hand, abstract labels, and what the model leaves out.

Portrait of Ines ValderaInes Valdera · · 9 min read
Section systems, and how the Kariera and Aranda rules work

Across much of Central and northern Australia a person has a skin name as well as their other names. The Central Land Council describes skin as Aboriginal English for the categories anthropologists call sections and subsections: four or eight named divisions of a community, each person born into one, with the names fixed in relation to one another so that knowing someone's skin tells you a good deal about how you stand to them. These systems were documented for the Kariera of the Pilbara region of Western Australia by A. R. Brown (later Radcliffe-Brown) in 1913, and for the Arunta, today usually written Arrernte, by Baldwin Spencer and Francis Gillen in 1899. They are still in use. Their rules are also some of the cleanest small-scale mathematics in all of kinship, and you can run them with a pencil.

Kin types below use the usual letters, read outward from the person speaking (Ego): F father, M mother, B brother, Z sister, S son, D daughter, H husband, W wife. So MMBDD is "mother's mother's brother's daughter's daughter".

Four boxes from two halves

Start with two ways of splitting a community in half. A patrimoiety is inherited from your father: call the two halves P and Q. A matrimoiety is inherited from your mother: call them X and Y. Everyone belongs to one of each, so there are four combinations, and those four are the sections. A rule that you must marry outside both of your moieties then does almost all the work.

Matrimoiety X Matrimoiety Y
Patrimoiety P A C
Patrimoiety Q D B

The letters are the abstract labels used in our section system simulator. Brown called the Kariera divisions classes and recorded their names, and they fit the grid exactly:

Section Kariera name (Brown 1913) Marries A man's children A woman's children
A Banaka B C D
B Burung A D C
C Palyeri D A B
D Karimera C B A

Brown's own statement of the rule was that a Banaka man marries a Burung woman and their child is Palyeri, while a Burung man and a Banaka woman have Karimera children. He called the father and child pairs (Banaka with Palyeri, Burung with Karimera) couples, and the mother and child pairs (Banaka with Karimera, Burung with Palyeri) cycles.

Rules you can run by hand

Two rules generate the whole table.

  1. Marriage: change both halves. Your spouse's section differs from yours in patrimoiety and in matrimoiety.
  2. Descent: a child takes the father's row and the mother's column.

Worked example 1. A man of section C is in row P, column Y. Changing both halves puts his wife in row Q, column X, which is D. Their children take his row (P) and her column (X): section A.

Worked example 2. A woman of section B is in row Q, column Y. Her husband is in row P, column X, section A. Her children take his row and her column: P and Y, section C. Check it against the table: a B woman's children are C.

Worked example 3. Now put Ego, a man, in section A (row P, column X) and find his cousins.

  1. His father shares his row, P, and must be in the other column, because he married a woman of column X. Father: row P, column Y, section C.
  2. His mother shares his column, X, and is in the other row. Mother: row Q, column X, section D.
  3. His mother's brother is also in D. A D man marries a C woman, and the children take row Q and column Y: section B.
  4. His father's sister is in C. She marries a D man, and her children are again row Q, column Y: section B.
  5. His father's brother is in C and marries a D woman; their children are section A. His mother's sister is in D and marries a C man; their children are section A too.

So both cross cousins, MBD and FZD, sit in B, the very section Ego marries into, and both parallel cousins sit in his own section with his brothers and sisters. A four-section system is a sociocentric map of a terminology that equates cross cousins with potential spouses, the pattern our explainer on cross and parallel cousins traces in Dravidian terms.

Loops of two generations

Follow a man's descendants in the male line from A: his son is C, his son's son is A again. Follow a woman's descendants in the female line from A: her daughter is D, her daughter's daughter is A. Every line returns after two generations, which is why a section holds people of alternate generations: Ego's section includes his father's father, and the section he marries into includes his mother's father.

For readers who like algebra, write w for the move to the spouse's section, f for the move to a man's children and m for the move to a woman's children. Each one swaps the sections in pairs:

  • w swaps A with B and C with D
  • f swaps A with C and B with D
  • m swaps A with D and B with C

Do any two and you get the third. From A, w takes you to B and then f takes you to D, which is where m takes you in one step. Together with "stay put", these moves form the four-element group mathematicians call the Klein four-group, and the order in which you apply them never matters. André Weil worked out this kind of algebra for Lévi-Strauss in 1949, a story told in our piece on the first kinship algebra.

Eight subsections: the Aranda pattern

In an eight-subsection system, often called the Aranda type, each section splits in two, and the simulator's labels keep the section letter: A1 and A2 are the two halves of section A, B1 and B2 the halves of B, and so on. Spouses always share a digit: A1 marries B1, A2 marries B2, C1 marries D1 and C2 marries D2. A man's children land in the section the four-section table predicts. Between A and C the digit stays the same (A1 with C1, A2 with C2), while between B and D it swaps (B1 with D2, B2 with D1).

Subsection Marries A man's children A woman's children
A1 B1 C1 D2
A2 B2 C2 D1
B1 A1 D2 C1
B2 A2 D1 C2
C1 D1 A1 B2
C2 D2 A2 B1
D1 C1 B2 A1
D2 C2 B1 A2

Worked example 4, with Ego a man in A1:

  1. Father: a man whose children are A1, so C1.
  2. Mother: C1's wife, so D1.
  3. Mother's brother: also D1, and a D1 man's children are B2. So MBD is in B2. His father's sister is in C1, and a C1 woman's children are also B2. Ego marries into B1, so both first cross cousins are in the right section, B, but the wrong subsection.
  4. Mother's mother: look down the last column for a woman whose children are D1. That is A2.
  5. Mother's mother's brother: A2, whose children are C2. So MMBD is in C2.
  6. A C2 woman's children are B1. MMBDD is in B1, Ego's spouse's subsection.

The second cross cousin through the mother's mother's brother, rather than the first cross cousin, is the one the subsection grid lines up with marriage. Laurent Dousset's handbook describes exactly this: subsections separate first from second cross cousins, and the formal rule points to the second.

Two other things change. Follow a woman's line from A1: her children are D2, a D2 woman's are A2, an A2 woman's are D1, and a D1 woman's are A1 again. The female line now takes four generations to come home, while the male line still takes two. And the order of steps starts to matter. From A1, the spouse step followed by the man's-children step lands in D2, but the same two steps in the other order land in D1. The eight subsections behave like the eight symmetries of a square, a group in which order matters, the territory of our note on nonabelian kinship systems. Drop the digits and you are back at the four sections A, B, C and D: every row of the table above turns into a row of the four-section table.

This is a documented structure, not a construction. Spencer and Gillen's 1899 table for the northern Arunta used eight names, and it matches the grid above once the names are swapped for letters. They also reported that the four extra names had been adopted from the Ilpirra, the Arunta's northern neighbors, and were spreading south, while southern Arunta people used four names and drew the finer distinction through relationship terms.

What the boxes leave out

A section is a coarse filter. Brown was emphatic that among the Kariera, marriage was "regulated by relationship, and by relationship alone": a man married a woman who stood in the right kin relation to him, and the section followed from that, not the other way round. Several other cautions come from the people who know these systems best.

  • Practice is looser than the formal rule. Dousset notes that while second cross cousins are the preferred choice in subsection systems, first cross cousins are an acceptable alternative.
  • The systems travel. Dousset traces sections spreading into the eastern Western Desert, a process completed by the 1930s or 1940s, with names that shift from group to group, so a section name in one language cannot be assumed to match the same name next door.
  • They change. The Central Land Council notes increasing numbers of wrong skin marriages and families working to accommodate them, while other rules, such as avoidance between a man and his mother-in-law, hold more strongly. Its chart lists skin names for nine language groups, among them Eastern and Central Arrernte, Alyawarr and Warlpiri.
  • Subsection names often come in male and female forms, so an eight-subsection system can have sixteen names.

Then there is a mathematical caution. Imagine a community of 400 people spread evenly over four sections: 100 people per section, about 50 of them women. The spouse section a man is born facing holds roughly 50 women, spread over his own generation, his grandparents' and his grandchildren's. With eight subsections the figure halves to about 25 before age and kinship narrow it further. Woodrow Denham (2013) argued that diagrams drawn for one small, closed society, with closed generations, are fictions: taken literally they would drive inbreeding far too high, while real communities married out, as most observers had reported. He cites a figure of about 15 percent of marriages outside the group reported by Tindale (1953) and Birdsell (1993), and puts the rate for the Alyawarra, from his 1971 to 1972 fieldwork and other records, at 22.3 percent. Laurent Dousset's rejoinder and comments by Patrick McConvell, Valerie Munt, Peter Sutton and Dwight Read were published alongside it, and our note on closure in Aboriginal kinship follows the exchange.

To test yourself, open the simulator, choose eight subsections and pick a man in C1. Before clicking, predict his wife's subsection, his children's and his cross cousins'. Then trace his MMBDD by hand with the table above. The answers are D1, A1, D2 and D1: his second cross cousin lands where his wife does.

Sources and further reading

More in Kinship & Family Structures