Many use "I hope you don't mind me asking you a question" but, according to your explanation, it is also possible (it sounds natural) "I hope you don't mind my asking you a
a question".
***** NOT A TEACHER *****Hello,
I apologize for not explaining more clearly those ideas in my first post.
1. I think that the appropriate question in most circumstances is, indeed, "I hope (that) you don't mind
my asking you a question."
2. Using "me" would be correct (according to the ideas in my first post) if you were emphasizing that it was
you who were doing the asking. Remember reporter No. 2 in my first post, whom the president apparently
dislikes? Well, let's say that reporter No. 2 meets the president later in the day. The reporter knows that the
president dislikes him, but he has a job to do, so he respectfully asks, "Sir, I hope you don't mind
me asking
you a question again -- even though I know that you dislike
me."
3. I agree with you that choosing the right pronoun at "the time of speaking" can be confusing. So may I
leave you with two points:
a. Go ahead and use the possessive in
every case. (I don't think that anyone dislikes you!)
b. I am 99.99% sure that most Americans are not aware of this "rule." In fact, I am sure that many
(most?) Americans may actually use "me." In other words, they see no difference between "me" or "my"
in that kind of sentence. (They should -- in almost all circumstances -- use "my" for "good" English, of course.)
James
P.S. Here is an example from one of my favorite grammar books:
a. I do not approve that
man coming with Mary.
b. I do not approve that
man's coming with Mary.
According to the scholars who wrote the book:
a. = disapproval of the
man is indicated.
b. = the
coming of the man is not approved.
* Homer C. House and Susan Emolyn Harman,
Descriptive English Grammar (1950, second edition), page 319.