As someone who voted in NYC for about 27 years, I can tell you they dont need to throw out any ballots. When you vote at your local high school, the floor is littered with discarded ballots - lost by the old biddies who have no control or interest in voting rights. When they lost my registration form one year, I had to fill out an absentee form. I can still remember the bored woman tossing it to the side (to join all the other litter).
I vote in a small NJ town now and the orderly and concerned women and men who volunteer make an astounding change of pace!