When and why we use double-genitive with respect to the word 'of'?

Question

I wanted to know why and when to use double-genitive. So for example why can't we use 'I am a fan of YOU' instead of 'I am fan of YOURS'. This is so as using the word 'of' itself meant that the noun mentioned first (before 'of') already belongs to the second noun (after 'of'). For example, in 'I am a fan of YOU' , the word 'of', to me, already suggests that 'I am your fan' without using 'YOURS'. It is like if we use 'fan of YOURS', it meant like 'I am your fan that belongs to you'.

So why is it necessary to use the double-genitive here?

A similar question has been asked: Why use apostrophe-s to denote possession when using 'of'

But one of the answers said that it is optional to put apostrophe for the example given in the question except to clarify the meaning of the sentence. (This is a picture of Bill/Bill's) So, what are some examples that are compulsory to use the double-genitive?

For examples, is it:

1) 'fan of YOURS' or 'fan of YOU'?

2) 'The death of HIS is...' or 'The death of HIM is...'

3) 'friend of HER' or 'friend of HERS'

4) 'queen of England' or 'queen of England's'

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On a side note, we say:

5) 'meaning of the WORD' instead of 'meaning of the WORD'S'

6) 'son of my FRIEND' instead of 'son of my FRIEND'S'

7) 'plays of Shakespeare' instead of 'plays of Shakespeare's'

8) 'city of Rome' instead of 'city of Rome's'

Overall, my question is why is it that we sometimes uses double-genitive and sometimes don't? Is it because of whether the noun before 'of' is an object or a person except in the case of 6)? If not, when do we use double-genitive and why? (in the event that the meaning of the sentence doesn't change regardless of it being double-genitive or not)

Answer 1

Regarding the 'double genitive', here is what the 'Practical English Usage' by Michael Swan says:

Answer 2

There was one of your examples that made the difference clear to me (split by me to better facilitate my explanations below):

1. This is a picture of Bill
2. This is a picture of Bill’s

In the first case, ‘This is a picture of Bill’, using the single genitive, it is a genitive of quality, ɔ: that which describes what the picture is; in other words, it is a picture showing Bill. This becomes clear when replacing ‘Bill’ with some other noun, such as ‘[a] tree’, ‘[the] colour blue’:

1a. This is a picture of [a] tree. ɔ: There is a tree in the picture.

1b. This is a picuture of [the] colour blue. ɔ: The picture is blue.

In the second case, ‘This is a picture of Bill’s’, the final genitive-’s indicates possession; in other words it is a genitive of belonging. That means the sentence says something about who has ownership of the noun. Using examples 1a and b above, this becomes clear by the absurdity of the new sentences:

2a. This is a picture of [a] tree’s.

2b. This is a picture of [the] colour blue’s.

Either there is something missing in those sentences—one could ask ‘Of a tree’s what?’ or ‘Of the colour blue’s what?’—and get an answer such as ‘This is a picture of a tree’s trunk’, or ‘This is a picture of the colour blue’s paint box’, though the latter still is a bit weird.

Therefore, one can conclude that when using a double genitive, it indicates posession, genitivus subiectivus; and when using a single genitive (just ‘of’), it usually indicates

• quality (genitivus qualitatis: a woman of great knowledge—ɔ: a very knowledgable woman),
• specification (genitivus explicativus: penalty of death—ɔ: death penalty),
• the object of an action (genitivus obiectivus: fear of death—ɔ: to fear death),
• kind, as in what type of thing something counted is (genitivus generis: a large number of soldiers)
• part, as in a whole that something is part of (genitivus partitivus: she alone of them all)

Source: Lots and lots of Latin, referencing the standard Latin grammar in Norway, Samson Eitrem’s Latinsk grammatikk, 3rd edition, Aschehoug 1996, §§ 78–83.