How do you feel about the arbitrary nature by which a person's race is defined?

My roommate and I began discussing this in relation to Halle Berry who is considered a black actress, despite the fact that her mother is white and, as far as I know, completely of European descent. The same issue has come up with our new President. Everyone is calling him the fist black President, but genetically speaking, he is only half black. His mother is white but no one is calling him our first mixed race President. Often racial labels are based on the shade of someone’s skin rather than genetic history or even such physical characteristics as facial features and body type. How does the collective feel about about these labels?