What is the term for the arbitrary rule that automatically places the children of a union between members of different socioeconomic groups in the less-privileged group?

The correct term is hypodescent.

Explanation:

The anthropological term hypodescent describes a system where the people of mixed races are automatically put into the category that is considered to be socially inferior.  This is not a system that acknowledges mixed race categories or degrees of racial mixing. In this notion, any racial mixing dilutes the purity of the racial categories. It is a system that tends to discourage racial mixing and intermarriage. We have the example of this kind of system in American history, which is the notion of the one-drop rule. In this framework, one drop of black ancestry made you black by the dominant social standards. This over simplifies the notions of race and it is a very discriminatory part of our history that has perpetrated systemic racism.  

the earthquake in haiti was a magnitude of 7.0 according to the u.s geological survey yet the smaller earthquake in haiti killed more than 200,000 and left more than 1.2 million people homeless. the chile earthquake was a magnitude of 8.8 and 500 times more stronger but chile's earthquake only injured 712 people.

answer; i believe its (transgender);