Cross and parallel cousins, and why the difference matters

Maine's marriage statute names a man's first cousins one at a time: the daughter of his father's brother, of his father's sister, of his mother's brother, of his mother's sister. Then it treats all four alike. Each is forbidden to him unless one of the couple provides a physician's certificate of genetic counseling. Many of the world's kinship systems would never list those four women together. To them two of the four are close to sisters, and the other two are a different kind of relative altogether, in some places the very kind a person is expected to marry.

The difference is between parallel and cross cousins. In kin-type shorthand, read outward from the person speaking (Ego): F father, M mother, B brother, Z sister, S son, D daughter, H husband, W wife. MBD is "mother's brother's daughter".

The test: look at the pair in the middle

Every first cousin is joined to Ego through two siblings: one of Ego's parents and one of the cousin's parents. If those two siblings are the same sex, the cousin is parallel. If they are a brother and a sister, the cousin is cross.

The sex of Ego and of the cousin plays no part. FBS is exactly as parallel as FBD.

One consequence is pure logic, so you can check it yourself. Under patrilineal descent FBD belongs to Ego's own line, because her father and Ego's father share a father. Under matrilineal descent MZD does, for the mirror reason. Under either rule, both cross cousins belong to other lines: FZD takes her line from a father outside Ego's patriline, or from a mother who is in Ego's father's matriline rather than Ego's. Wherever descent runs in one line, cross cousins are the cousins who are never "us".

Why a vocabulary would care

Kinship terminologies of the type anthropologists call Iroquois put parallel cousins with brothers and sisters and give cross cousins a word of their own. Our walk through the six classic systems shows that pattern next to the others on one family tree.

Dravidian terminologies of South India draw the same line but give it a sharper meaning. Louis Dumont (1953) read them as an expression of marriage: the parallel side is kin, the cross side is the side you marry into, so cross-cousin terms run together with the terms for in-laws. Thomas Trautmann's Dravidian Kinship (1981) built that reading into a full model of how such terms are computed. For first cousins, Iroquois and Dravidian give the same answers. The difference shows up one generation further out.

Second cousins: where two rules part company

Second cousins share a pair of great-grandparents, so the chain from Ego to the cousin has two generations on each side of a sibling pair. Both rules start from that sibling pair and work downward, but they look at different things.

• Iroquois rule: look only at the bottom pair, Ego's parent and the cousin's parent. Same sex, parallel; opposite sex, cross. Everything higher up is ignored.
• Dravidian rule: start at the top sibling pair and call it parallel. Step down one generation at a time. If the pair you are leaving is the same sex, the relation carries over unchanged; if they are a brother and a sister, it flips. A cross relative of a cross relative is therefore parallel.

Worked example 1, MMBDD (mother's mother's brother's daughter's daughter), for a male Ego:

1. Top pair: MM and MMB, a sister and a brother.
2. Bottom pair: M and MMBD, two women.
3. Iroquois: the bottom pair is the same sex, so MMBDD is parallel.
4. Dravidian: start parallel; the top pair is opposite sex, so flip to cross (M and MMBD are each other's cross cousins); the bottom pair is the same sex, so keep it. MMBDD is cross.

Worked example 2, FFZDD:

1. Top pair: FF and FFZ, a brother and a sister.
2. Bottom pair: F and FFZD, a man and a woman.
3. Iroquois: opposite sex at the bottom, so cross.
4. Dravidian: flip at the top to cross, flip again at the bottom to parallel. FFZDD is parallel.

Here are all eight second cousins on the mother's side under both rules:

Run the same check over all sixteen kinds of second cousin and the two rules agree on exactly eight. The Dravidian rule is arithmetic modulo 2: write 1 for an opposite-sex pair and 0 for a same-sex pair, add down the chain, and an odd total means cross. The Iroquois rule reads only the last digit.

Mauro Barbosa de Almeida (2010) made this precise. He wrote kin types as words built from steps (up a generation, down a generation, a change of sex) and showed that the Dravidian verdict, kin or affine, is the parity of the reshuffling needed to put such a word into a standard order; he also sketched how the Iroquois case fits a more general version of the same calculus. Our note on the structure of Dravidian terminology takes that approach further.

Marrying a cross cousin: three directions

Where cross cousins are marriageable, the rule can point both ways or only one, and each choice builds a different pattern of alliance between groups. Claude Lévi-Strauss organized his Elementary Structures of Kinship (1949) around exactly this.

Bilateral

A man may marry either MBD or FZD. When two families keep exchanging sisters, the two are often the same woman. Two groups that swap spouses in every generation are enough to sustain it, which Lévi-Strauss called restricted exchange. The genealogy has a side effect worth knowing: if Ego's father married Ego's mother while Ego's mother's brother married Ego's father's sister, then MBD and FZD are one person, a double first cousin.

Matrilateral (MBD only)

Now the direction of giving is fixed. If my group takes wives from yours, your group never takes wives from mine. Closing the circle therefore needs at least three groups: with two, the givers would also be takers. Lévi-Strauss called this generalized exchange. The textbook case is the Kachin of highland Burma, where Edmund Leach (1954) described the line between mayu, the bride-givers, and dama, the bride-receivers, and its ties to rank.

Patrilateral (FZD only)

Here the direction flips every generation. Take three groups, A, B and C, with men staying put and women marrying out. The table follows who gives wives to whom.

Check generation 2 of the patrilateral column by hand. A man of group A marries his FZD. His FZ is an A woman of generation 1, and in generation 1 A women went to B, so his FZD is a B woman. Group A now takes from the group it gave to. Rodney Needham (1958) argued that no society could hold to that rule strictly for long. Lévi-Strauss, in the preface to his second edition, replied that he had already shown it could never form a closed overall structure, but that nothing stops it from surviving under precarious conditions.

How many societies allow it?

Murdock's Ethnographic Atlas, as coded in the D-PLACE database (variable EA023), records which first and second cousins a man may marry in 1,042 societies. The counts are D-PLACE's; the percentages are ours.

• Either cross cousin, but not a parallel cousin: 206 societies (19.8%)
• Only the matrilateral cross cousin, MBD: 44 (4.2%)
• Only the patrilateral cross cousin, FZD: 5 (0.5%)
• Any first cousin: 117 (11.2%)
• No first cousin at all (four codes added together): 636 (61.0%)

"Permitted" is the Atlas's word, and permission is weaker than preference, which is weaker still than prescription. Even so, the gap between 44 and 5 is the asymmetry the theorists argued over. George Homans and David Schneider (1955) offered an explanation of why the matrilateral form is the commoner one, and Needham's Structure and Sentiment (1962) was a book-length reply.

Genes and law, kept short

Genetically, cross and parallel cousins are the same. Each first cousin shares one pair of grandparents with Ego, and the coefficient of relationship counts two paths of four links: r = 2 × (1/2)^4 = 1/8. The child of first cousins has an inbreeding coefficient F = 1/16 whichever kind of cousin the parents are. Our worked examples of the coefficient of relationship go through the path counting. Repeated sister exchange is the case to watch: double first cousins share both pairs of grandparents, so r doubles to 1/4.

For couples who are second cousins or closer, a working group convened by the National Society of Genetic Counselors (Bennett and colleagues, 2002) recommended a thorough medical family history and otherwise the same screening offered to any couple of the same ancestry, with no extra preconception screening.

The law follows the English vocabulary rather than the genealogy of descent lines. American states set their own rules, and Maine's statute, the one quoted at the top, names all four first cousins in one breath. If you set both sides to two generations below the shared couple in the cousin calculator, it returns 1/8 whichever of the four you had in mind. The cross and parallel split lives in language and in marriage rules, not in the arithmetic of shared descent.

Sources and further reading

• Dumont, Louis. 1953. "The Dravidian Kinship Terminology as an Expression of Marriage." Man 53: 34 to 39. https://doi.org/10.2307/2794868
• Trautmann, Thomas R. 1981. Dravidian Kinship. Cambridge: Cambridge University Press.
• Barbosa de Almeida, Mauro William. 2010. "On the Structure of Dravidian Relationship Systems." Mathematical Anthropology and Cultural Theory 3 (1). https://escholarship.org/uc/item/9t64g4cm
• Lévi-Strauss, Claude. 1969 [1949]. The Elementary Structures of Kinship. Translated by James Harle Bell and John Richard von Sturmer, edited by Rodney Needham. Boston: Beacon Press.
• Needham, Rodney. 1958. "The Formal Analysis of Prescriptive Patrilateral Cross-Cousin Marriage." Southwestern Journal of Anthropology 14 (2): 199 to 219. https://doi.org/10.1086/soutjanth.14.2.3628958
• Bennett, Robin L., Arno G. Motulsky, Alan Bittles and others. 2002. "Genetic Counseling and Screening of Consanguineous Couples and Their Offspring: Recommendations of the National Society of Genetic Counselors." Journal of Genetic Counseling 11 (2): 97 to 119. https://doi.org/10.1023/A:1014593404915
• D-PLACE. "Cousin marriages permitted [EA023]." https://d-place.org/parameters/EA023
• Maine Revised Statutes, Title 19-A, section 701, "Prohibited marriages; exceptions." https://legislature.maine.gov/statutes/19-A/title19-Asec701.html