On another thread, in a discussion of pronoun usage, a passage from the Cambridge Grammar of the English Language was referred to.
Here it is in full:
Another kind of illegitimate argument is based on analogy between one area of grammar and another. Consider yet another construction where there is variation between nominative and accusative forms of pronouns:
 a. They invited me to lunch.
 b. %They invited my partner and I to lunch.
The ‘%’ symbol is again used to mark the B example as typically used by some
speakers of Standard English but not others, though this time it is not a matter of regional variation. The status of the construction in B differs from that of It’s me, which is undisputedly normal in informal use, and from that of !Me and Kim saw her leave, which is unquestionably non-standard.
What is different is that examples like B are regularly used by a significant
proportion of speakers of Standard English, and not generally thought by
ordinary speakers to be non-standard; they pass unnoticed in broadcast
speech all the time.
Prescriptivists, however, condemn the use illustrated by 3b, insisting
that the ‘correct’ form is They invited my partner and me to lunch.
And here again they seek to justify their claim that 3b is ungrammatical
by an implicit analogy, this time with other situations found in English, such
as the example seen in A. In A the pronoun functions by itself as direct
object of the verb and invariably appears in accusative case. What is
different in B is that the direct object of the verb has the form of a
coordination, not a single pronoun. Prescriptivists commonly take it for
granted that this difference is irrelevant to case assignment. They argue
that because we have an accusative in A we should also have an
accusative in B, so the nominative I is ungrammatical.
But why should we simply assume that the grammatical rules for case
assignment cannot differentiate between a coordinated and a non-coordinated pronoun? As it happens, there is another place in English grammar where the rules are sensitive to this distinction – for virtually all speakers, not just some of them:
4 a. I don’t know if you’re eligible.
4 b. I don’t know if she and you’re eligible.
The sequence you are can be reduced to you’re in A, where
you is subject, but not in B, where the subject has the form of a
coordination of pronouns.
This shows us not only that a rule of English could apply differently to
pronouns and coordinated pronouns, but that one rule actually does. If that
is so, then a rule could likewise distinguish between 3a and 3b. The
argument from analogy is illegitimate. Whether 3b is treated as correct
Standard English or not (a matter that we take up in Ch. 5, §16.2.2), it
cannot be successfully argued to be incorrect simply by virtue of the
analogy with 3a.
This passage is curious for three reasons:
1. It implies that the rule in operation in 4b is similar to the rule in operation in 3b; whereas in fact the "rule" in 4b relates to contraction in coordinated pronouns, not case in coordinated pronouns.
(In passing, I would say that the CGEL's assertions about contraction in 4b are untrue: a speaker of Standard English would also say I don't know if she and you'r' eligible, where 'r' is a schwa.)
2. It argues that since we don't apply the rule in 4a to 4b, we don't need to apply the rule in 3a to 3b.
This is an "argument based on analogy between one area of grammar and another" (case in coordinated object pronouns vs contraction in coordinated pronouns).
However, the CGEL has already described argument by analogy as "illegitimate", and indeed repeats the assertion – "The argument from analogy is illegitimate" – immediately after arguing from analogy.
3. It describes "They invited my partner and I to lunch" as "used by some speakers of Standard English, yet "Me and Kim saw her leave" as "unquestionably non-standard".
This is not true: in BrE, at least, people who say e.g. "she wanted to speak to John and I" will also say "Me and John did such and such". (Though they will probably write neither.)
Moreover, the use of the structure "to X and I" is used only by a certain kind of speaker; whereas the "me and X did Y" structure is used by all kinds of speaker.
There is therefore no reason, in the CGEL's own terms, to say that one is "standard" and one "non-standard".
(My intention here is to comment on the validity of the CGEL's logic, by the way, not to deal with the respective merits of "between you and I"/"between you and me", etc.)