If a person lived alone in an apartment, would it be okay to make the brakhot when lighting Hanukkah candles, even though there are no other members of the household to see the lights, and therefore no implementation of pirsumei nisa / publicizing the miracle?
The Shulchan Aruch in O.C. 677:3 writes:
יש אומרים שאע"ג שמדליקין עליו בתוך ביתו, אם הוא במקום שאין בו ישראל מדליק בברכות
Some say that even though they are lighting for a person at his home, if he is in a place where there are no Jews he should light with the blessings.
The Rema adds
And this is our practice.
This is a person who is alone without any other Jews, family or non-family, and yet they light with the blessings. This seemingly demonstrates that the mitzvah can be performed with the blessings even without the pirsumei nisa to others.
(Although the Mishneh Berura #14 points out that this is a contradiction to what the Shulchan Aruch writes in 676:3, that is only regarding that which one makes a blessing even though his wife/family is lighting for him.)
However, the rationale for such a person lighting is, as the Rema writes at the beginning of his gloss,
כי חיב לראות הנרות
because he is obligated to see [Chanukah] candles.
That being the case, in the case that a person happens to not have anyone else who will witness his light, but he could walk out on the street and see the lights of other Jews, they would have no reason to specifically light. Nonetheless, the Rema continues that
אפילו אם הוא אצל יהודים ורואה הנרות, אם רוצה להחמיר על עצמו ולהדליק בפני עצמו, מדליק ומברך עליהם, וכן נוהגין
Even if one is in a place of Jews and wishes to be stringent upon himself and light for himself, he may do so with blessings, and that is our practice.
Putting these two points together seems to yield that the individual in the apartment by himself could light with blessings, regardless of if anyone else will see it.
It seems unreasonable that the Rema is basing his position on non-Jews seeing the lighting and fulfilling pirsumei nisa through them, firstly because I assume that pirsumei nisa is specifically to Jews, and more importantly, it does not seem reasonable that the Rema is depending on non-Jews wandering in to his private quarters, as he is lighting indoors at his table, not by the window (Rema in the previous sif), and the whole reason for the move to light inside was due to the danger of visible performance of the mitzvah.
R. Moshe Feinstein (Igros Moshe Orach Chaim 4:105:7) rules pretty definitively that one should light with a bracha, even if there are no other people present to allow pirsumei nisa.
He is not particularly concerned with the Magen Avraham's chumra of waking up other members of the household in order to light late at night.
See Beur Halacha on O.C. 571:1. He cites the Gemarah (I don't recall where in the Gemarah this is mentioned) that says the mitzvah is to have one candle each night, and that suffices for himself and his household. If you live alone, you are the household. So, the fact that there are no others around is irrelevant. It seems that you can light and make the bracha as you are fulfilling the mitzvah.