That might be kind of convenient actually - racist assholes of all colours will label themselves and probably kill eachother while (hopefully) most of the population's foreheads will read "None".
I don't think this is likely unless if none is the most voted option none gets killed. But if one always gets killed then there will be lots of campaigning and manipulating for certain votes. And the past years have shown people will fall for it.
If voting is mandatory, the most ethical thing to do would be to figure out which race has the least amount of people. Instead of killing millions of people, you could probably get it down to a few dozen or hundred. Of course, nobody dies either way and the mark would show that you tried to do the right thing.