Theo Smith writes:
I am often frustrated by what I call a “double possessive.” We seem to say and write “friends of Jim’s” not “friends of Jim” when the item possessed is stated before that which possesses it. But when the possessor is identified first, we say, for example, “Jim’s friends.” What’s up with this? The double possessive appears in that “of” indicates possession and so does the apostrophe s (‘s) appended to the possessor. What can you tell me about this?
This “double genitive” construction includes both a friend of Jim’s and a friend of his. It’s one of those English idioms that tries the souls of logic lovers, but it has been in the language for a very long time because it works.
The double genitive makes it possible to distinguish between definiteness and indefiniteness. It also eliminates ambiguity. For example, there’s a distinct difference of meaning between the following phrases:
a photo of Daniel
a photo of Daniel’s
Although in use since Chaucer’s time or before, the double genitive attracted the attention of 18th century grammarians; their disapproval did nothing to stamp it out.
Modern style manuals offer guidelines.
According to the Chicago Manual of Style,
The possessive form may be preceded by of where one of several is implied. “A friend of Dick’s” and “a friend of his” are equally acceptable. 7.29
The AP Style Book goes into more detail:
DOUBLE POSSESSIVE: Two conditions must apply for a double possessive–a phrase such as a friend of John’s–to occur:
The word after of must refer to an animate object, and
The word before of must involve only a portion of the animate object’s possessions.
Otherwise, do not use the possessive form of the word after of: The friends of John Adams mourned his death. (All the friends were involved.) He is a friend of the college. (Not college’s because college is inanimate).
For a linguist’s take on the double genitive, read Mark Liberman’s “Genitive Anxiety.”