נר איש וביתו

The Sages taught in a baraita: The basic mitzva of Hanukkah is each day to have a light kindled by a person, the head of the household, for himself and his household. And the mehadrin, i.e., those who are meticulous in the performance of mitzvot, kindle a light for each and every one in the household. And the mehadrin min hamehadrin, who are even more meticulous, adjust the number of lights daily. Beit Shammai and Beit Hillel disagree as to the nature of that adjustment. Beit Shammai say: On the first day one kindles eight lights and, from there on, gradually decreases the number of lights until, on the last day of Hanukkah, he kindles one light. And Beit Hillel say: On the first day one kindles one light, and from there on, gradually increases the number of lights until, on the last day, he kindles eight lights.

And the mehadrin of the mehadrin (those who seek to beautify, among those who seek to beautify): It seems to RI that Beit Shammai and Beit Hillel refer only to "a man and his household" (i.e. the head of the household alone lighting on behalf of his entire family). Because in this way, there is more beautification; since there is something recognizable when he keeps adding or removing [lights], corresponding to the days that are entering (the days of Channukah still to come) or exiting (the days of Channukah that have already passed). However, if he makes a light for each one (i.e. each member of his household gets his own light), even if he adds from now onwards, there is nothing recognizable, because [people] would think that this is the number of people in the household (i.e. instead of attributing the increase or decrease in lights to the intention of the owner to correspond to the day of Chanukah, people would attribute it to the intention to correspond to the number of people in the household).

How many candles should one light on Chanukah? The mitzvah is that a single candle should be lit in each and every house, regardless of whether there are many members of the household, or merely one person [lives] there.
A person who performs the mitzvah in a beautiful and conscientious manner should light candles for every member of the household, whether male or female.
A person who is even more conscientious in his performance of the mitzvah than this and observes the mitzvah in the most desirable manner should light candles for every member of his household, a candle for each individual, whether male or female, on the first night. On each subsequent night, he should add a candle [for each of the members of the household].

It is common custom in all of our cities in Spain that a single candle is lit for all the members of the household on the first night. We proceed to add a new candle on each and every night, until on the eighth night eight candles are lit. [This practice is followed] regardless of whether there are many members of the household or only one man [is lighting candles].

How many lights should one kindle? On the first night, he kindles one [light]. From then on he continues to add one each night, until on the last night they are eight. And even if the household members are many, they should not kindle more. Rem"a: And some say that every one of the household members kindles (Maimonides) and such is the widespread custom. And they should take care to each place their lights in a unique place, so that it will be apparent how many lights they are kindling. (Abraham Kara of Prague)