What could it be…..? Riddle?

Arnold Schwarzenegger has a big one,
Michael J. Fox has a small one,
Madonna doesn’t have one,
The Pope has one, but doesn’t use it,
Clinton uses his all the time,
Bush is one,
Mickey Mouse has an unusual one,
Liberace never used his on women,
Jerry Seinfeld is very, very proud of his,
Cher claims that she took on three,
We never saw Lucy use Desi’s

What is it?

NOTE: this is a previous question asked by dobiegang, i will be posting the real link (including answer) soon after all of you people answer this.