Imagine two societies, which I’ll call the Dairymen and the Beefeaters.
The Dairymen practice what I’ll call “Half-Sibling Bigynandry”. Each person marries, and has children with, two half-siblings of the opposite sex; one agnate (ie same father different mother) and one enate (ie uterine ie same mother different father).
The Beefeaters practice double-cousin marriage. Each person marries, and has children with, a cross-double-cousin of the opposite sex: for instance, a man marries the daughter of his father’s sister by his mother’s brother.
I will argue that, in the long view, the Beefeaters are much more inbred than the Dairymen.
In drawing representative family trees of individuals from these societies, one encounters different difficulties.
For a child from the Dairymen, one may, for the sake of specificity, assume without loss of generality, that every female in that particular tree has two grandmothers but only one grandfather, and every male in the tree has two grandfathers but only one grandmother.
For a child from the Beefeaters, one discovers that their grandparents’ relationships form a square; each of the grandfathers is husband to one of the grandmothers but brother to the other grandmother. Unless one puts the child and their parents in the center of this square, and draws the square of greatgrandparents around the square of grandparents, one must let lines cross, which will clutter up the diagram, rendering it difficult to interpret after a few generations and nigh incomprehensible after several.
So a Beefeater’s family tree will have the propositus or proband and their parents at the center, surrounded by a square of grandparents, surrounded by a square of great-grandparents, surrounded by a square of great^2-grandparents, surrounded by a square of great^3-grandparents, .... and so on. If one square’s sibling lines are horizontal and its marital lines vertical, then the next square’s marital lines will be horizontal and its sibling lines will be vertical; and vice-versa.
Compare a Dairymen child’s family tree to a Beefeater child’s family tree.
Going back one generation, the Dairyman has two parents, and the Beefeater also has two parents, just like every warm-blooded vertebrate on Earth.
Going back a second generation, the Dairyman has only three grandparents, while the Beefeater has four grandparents. Advantage Beefeaters.
Going back a third generation, the Dairyman has four greatgrandparents, and the Beefeater also has four greatgrandparents. Deuce.
Going back a fourth generation, the Dairyman has five greatgreatgrandparents, but the Beefeater has only four greatgreatgrandparents. Advantage Dairymen.
Going back a fifth generation, the Dairyman has six great^3-grandparents, but the Beefeater has only four great^3-grandparents. Game Dairymen.
In the sixth and seventh generations, the Dairyman probably has respectively seven and eight ancestors; but the Beefeater surely still has just four ancestors in every generation since the grandparents.
Eventually we ascend to a generation in which there were only n/2 sexually-mature-and-active Dairyman men and/or only n/2 reproductively-fit Dairymen women of childbearing age. If this is the (n-1)st generation before our Dairyman propositus, this is the highest generation at which they could have had one more ancestor than the generation count; any further back there’d have had to be some repetition.
But the Beefeater kid was descended through a bottleneck of four-ancestors-per-generation from time immemorial. (Unless they can remember when double-cousin-marriage was instituted!)