First of all, slavery was NOT the purpose of the electoral college. One way to buttress that without citing a particular verse - Hamilton, who authored 29 of them and was the driving force behind the process, was virulently anti-slavery. While it is not impossible, it's unlikely that someone who was so strongly anti-slavery would write in defense or approve of writing in defense of that institution.

Secondly, while I've read the Federalist Papers a couple of times, the last time was several years ago. So I'm not 100% sure of which paper to direct you to... but you're not being an ass to ask for clarification.

I THINK (but I'm not sure) that either Federalist 38 or 68 is the one you should read.

If I remember correctly, Hamilton makes the case that the president should be chosen by capable (in other words, not common) men.

I do think it behooves you to read more than just the pertinent sections, though, as it provides context. For example, in an earlier section, either Hamilton or Madison talks about the necessity of avoiding an unstable government (I'm paraphrasing from memory) and that ties into the defense of an electoral college, I think.

At any rate, though, if you look up Papers 38 and 68, I believe one of those is the correct one.

Also, since you may prefer articles, here is a piece from Slate which defends the electoral college, which I found interesting: https://slate.com/news-and-politics/2012/11/defending-the-electoral-college.html