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 themself and their household.
And the mehadrin, (those who are super strict 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 says: 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, they kindle one light.
And Beit Hillel says: On the first day one kindles one light, and from there on, gradually increases the number of lights until, on the last day, they kindle eight lights.
Ulla said: There were two amora’im in the West, (Eretz Yisrael). who disagreed with regard to this dispute, Rabbi Yosei bar Avin and Rabbi Yosei bar Zevida.
One said that the reason for Beit Shammai’s opinion is that the number of lights corresponds to the incoming days, i.e., the future. On the first day, eight days remain in Hanukkah, one kindles eight lights, and on the second day seven days remain, one kindles seven, etc.
The reason for Beit Hillel’s opinion is that the number of lights corresponds to the outgoing days. Each day, the number of lights corresponds to the number of the days of Hanukkah that were already observed.
And one said that the reason for Beit Shammai’s opinion is that the number of lights corresponds to the bulls of the festival of Sukkot: Thirteen were sacrificed on the first day and each succeeding day one fewer was sacrificed (Numbers 29:12–31).
The reason for Beit Hillel’s opinion is that the number of lights is based on the principle:
One elevates to a higher level in matters of sanctity and one does not downgrade. Therefore, if the objective is to have the number of lights correspond to the number of days, there is no alternative to increasing their number with the passing of each day.