I only concede that a person is real if they have a corporeal form, a sentient mind, and free will.
However, as a caveat - I'm not so inflexible in my standards as that makes me sound! If anyone ever tries to claim that they do not possess one of these things, I don't automatically assume they're a figment of my subconscious (or worse, my imagination!). I treat their claim with extreme prejudice, extreme skepticism. I put the burden on them to prove their incorporeality, or their nonsentience, or their status as a deterministic automaton. I don't credit every whinge and wheedle of the disaffected existentialist fringe!
There. A straightforward answer to the problem! Assuming there ever was one.