I think the idea of requiring persons to supply a Social Security number for all dependents 5 years or older is excellent. It will definitely stop divorced parents from both getting away with claiming children as dependents, as well as similarly claiming the family pet.
Besides, this sets the table for the inevitable National Identification Card. Of course, we will discover people are inclined to lose or misplace their cards. So why not just tattoo all babies immediately after birth? And while we're at it, we can include important information that isn't readily visible like color or race is--such as religious belief and their parents' political affiliations, too!