A grammar exercise says that this is correct: "The final choice made Heather and I change our decision." Why is the pronoun "I" correct when, if you dropped "Heather and" and changed "our" to "my" you would use the objective pronoun me (The final choice made me change my decision.)
There are several similar questions on this site, and most of the answers I've looked at point to the obvious ungrammaticality of sentences that result from removing the first member of the coordinated phrase:
*The final choice made I change my decision.
No-one disputes that this is wrong, but there are linguists who do dispute the rationale for claiming:
The final choice made Heather and I change my decision.
is wrong for the same reason, or even wrong at all.
One of these linguists is Geoffrey Pullum, co-author of the Cambridge Grammar of the English Language. I have included part of his CGEL discussion of the issue here in an answer to a similar question.
Pullum returns to the issue in one of his posts on Language Log, where he defends Australian politician Julia Gillard from accusations of grammar ignorance:
Now, I think there may be many people who imagine that in a sentence like The Australian community knows Kevin and I we have an occurrence of the pronoun I showing up as an object. We certainly do not. We have the pronoun I showing up as the word following a coordinator in a phrase and I which is the second of two phrases making up the coordination Kevin and I. It is the coordination that is an object. Being a part of a phrase that serves as an object is not at all the same as being an object. Consider I resent the fact that he lied. The object of resent is a noun phrase, the fact that he lied. Inside it is a pronoun. But that pronoun (he) is a subject. It just happens to be inside an object.
Later in the blog Pullum says:
Whether we want to regard it as correct or acceptable in Standard English to use the nominative after and is another matter, and much more difficult to adjudicate. We can say that it's very common; huge numbers of Standard English speakers do appear to follow that rule (see pages 9-10 of The Cambridge Grammar of the English Language for a discussion of this highly controversial point). Shakespeare apparently did (at least, he has one of his characters say between you and I in The Merchant of Venice). But whether people should be following this rule is off the agenda here — like whether Pearson is a stuck-up right-wing snob or whether Gillard is a jumped-up illiterate Welsh immigrant or whether Language Log writers are chain-swinging anti-correctness thugs. Here I'm just making a single point about the use of evidence.
I rather suspect that Pullum himself would not write or say sentences such as the ones he analyses in the blog and the CGEL; and neither would I or most of the knowledgeable contributors to this site.
If the sentence is phrased " Kevin and I are known by the Australian community.," using 'to know' in a passive mode, then 'I' would be correct i.e. 'I am known.'