Is it: She thinks he and I are tight. She thinks him and me are tight. Which, if any, is correct -- and why? Thank you very much.
The bolded is correct. Why? Because thinks is not a transitive verb in this usage, thus does not modify the subsequent pronouns as direct or indirect objects.
To add to @Wreybies' comment: The way I test such dilemmas is to leave out the distractions. He is tight. I am tight. If you try that with him and me you can see it is wrong.
He and Mike hate each other. (I think this is correct, but how do you break it down, leaving out the distractions, as you did above?)
This is a different setup and the break-it-down method may be a little less intuitive, but I'll give it a try. Your question seems to be stemming from the plurality of pronouns or proper nouns (He and Mike) and this often stumps folks. In this new example [He and Mike] are functioning as a single unit, the subject, and the fact that there is more than one in play doesn't matter. All that matters is who is the actor and who is the acted upon (if anyone). In He and Mike hate each other, [He and Mike] is the actor, the subject of the sentence, hence you use the subject pronouns just as you have here. The acted upon of this sentence - since hate here is a transitive verb - is [each other]. You can replace [He and Mike] with they and it becomes clear. He and Mike hate each other. They hate each other. <-- WIN Them hate each other. <--FAIL Since you would not turn they into them, you will not turn he into him.
One more, please. Joe announced, "The winners of the tournament were Mike and me." This one can go both ways: The winner was Mike; the winner was me. But! Mike and I were the winners of the tournament. ( = Mike was the winner; I was the winner.) So, is it: (1) The winners of the tournament were Mike and me. Or, (2) The winners of the tournament were Mike and I. How do I parse this one to get the correct answer? It seems as if both are possible—but only one can be truly correct here, right? Thanks again. Victo
The bolded is correct, even though the not bolded is very, very common. So common, that you will read in many sources that it's also acceptable. *shrug* The not bolded is flat-out wrong to me. It is not acceptable, to me. Were is a copula verb and copula verbs do not create a direct object, so no object pronoun. But... Sometimes popular opinion has a withering eye and will not stand the protestations of pedantic thought. I lived in the American South-East for many years (Florida) and heard any number of extremely common, painfully wrong constructions on an everyday basis. If I opened a mouth to correct, I was met with indignation.
Were refers to past tense. Is it past tense? If not then change were to are. And as Wraybies said, the bold one is correct, but it can also be reversed to, Mike and I were the winners of the tournament. If you want to use 'Mike and me,' you need to switch the names around to 'me and Mike.' You could also say, Mike and myself (but that depends more on context). Sentence structure is frustrating, but they're all correct if your reader understands the general concept.