Wither the octoroon re affirmative action remedies?

The essay below by Nat Hentoff addresses the question how the government will decide who is a minority and who is not regarding the application of affirmative action remedies.

How do you decide this issue? What would be a fair way to make this determination in an increasingly racially blended society?
Who Decides Who’s Black or Hispanic?
Should Individuals of More Than One Race Be Preferred?