According to the mob's rules for membership, you must be at least half Italian (on your father's side). However, they really seem to stretch the definition of being half Italian. To most people being half Italian means one of your parents was born in Italy, but this does not seem to be the case. Look at this example:

Example 1) My father was born in the United States. My grandfather was born in the United States. My great-grandfather was also born in the United States. My great-great-grandfather was born in Italy. (this is just a hypothetical example, but according to the rules a man with this lineage could be made)

To most people the above example does not make you truly Italian or even half Italian. But according to the rules, a guy with lineage as in example 1 could be made, correct? (Take Junior Gotti - he was "more" Italian than the guy in example 1 but neither of his parents was born in Italy)