Group Bias in Mate Selection and Outmarriage

The outmarriage rate is defined as the fraction of the members of a group that marry outside their group over the fraction of those who marry. For example, if a group has 1000 members, 800 of which marry, and 200 of which have spouses outside the group, then the outmarriage rate is defined as 200/800=0.25.

Now, on first view, groups that have higher outmarriage rates (that marry outside their group more) seem to be less biased in favor of their own group than those that have lower outmarriage rates. For example, if one has a rate of 0.5 versus another's of 0.05 then one would be tempted to conclude that the second group is more biased in favor of its own. This is however false.

The reason for this is simple: large groups tend to marry their own, because many candidates for marriage belong to their group. Small groups tend to outmarry, because most candidates for marriage don't belong to the group.

Let's be more systematic. Suppose that we have two groups A and B with marrying sizes [i.e., those who end up marrying] equal to |A| and |B|. If neither group had any bias to favor people from either A or B, we expect that the probability that a person of group A marries one from B is approximately |B|/(|A|+|B|). The figure is approximate, because a person can't marry themselves. Also, we made the assumption that the groups have equal numbers of males and females; if for example A consists only of males, then the outmarriage rate will have to be 1.

Now, suppose that we measure the outmarriage rate O(A) for group A and find it to be approximately equal to f(A)=|B|/(|A|+|B|). This means that members of group A are not biased with respect to members of group B. If O(A)<f(A) then they are biased against B. If O(A)>f(A), then they are biased in favor of B.

Let's have a concrete example. Suppose that |A|=800, |B|=200. If A is totally biased against B then we will have 400 A+A marriages and 100 B+B ones. If A is totally biased in favor of B then we will have 200 A+B marriages, and 300 A+A. In the first case, the outmarriage rate for A will be 0; in the second case, it will be 0.25. For B, these will be respectively 0 and 1.

If there was no bias, we can see that the outmarriage rate for A is expected to be f(A) = 200/(200+800) = 0.2. For B it is f(B)=800/(200+800) = 0.8. Thus, we expect 160 A+B unions, 320 A+A unions and 20 B+B unions.

Conclusions:

There are a few important conclusions to be made:

1. If a population's bias is fixed, then its outmarriage rate increases as its contribution to the total population decreases. Small groups tend to outmarry more than big groups.
2. If we are given the outmarriage rates, we can determine whether a group is biased or not, and in what direction. We calculate the expected f(A),f(B) and compare them with the empirical O(A), O(B).
3. By comparing the outmarriage rates of different groups, we cannot derive conclusions as to their level of bias in mate selection. A certain group may have a higher outmarriage rate than another and yet be more biased in favor of its own kind.

Final Note:

The quantity O(A)/f(A), that is, the observed outmarriage rate divided by the expected outmarriage rate of a population is a useful measure of its bias. If it is 1, then there is no bias. If it is > 1 then there is bias against one's own group, if it < 1 then there is bias in favor of one's own group. It will be interesting to gather up statistics for bias for various racial and ethnic groups.

Posted by Dienekes at June 16, 2003 05:24 PM | PermaLink