Will you fund multiple startups working on the same idea?
Yes. If you fund as many companies as we do it's unavoidable you'll end up with some overlap. Even if you tried not to accept competing companies, you'd still get overlap because startups' ideas morph so much. The way we deal with it is that when two startups are working on related stuff, we don't talk to one about what the other's doing.
In practice it has not turned out to be a problem, because most big markets have room for several slightly different solutions, and it's unlikely that two startups would do precisely the same thing.
This seems easier to do with two startups in the same batch than with a new startup and an existing YC partner, although I suppose they could use the same approach.
For example if you already have an investment in email application, you will opt-out from similar investments in the future.