Increase the Light
תנו רבנן מצות חנוכה נר איש וביתו והמהדרין נר לכל אחד ואחד והמהדרין מן המהדרין בית שמאי אומרים יום ראשון מדליק שמנה מכאן ואילך פוחת והולך ובית הלל אומרים יום ראשון מדליק אחת מכאן ואילך מוסיף והולך
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.
אמר עולא פליגי בה תרי אמוראי במערבא רבי יוסי בר אבין ורבי יוסי בר זבידא חד אמר טעמא דבית שמאי כנגד ימים הנכנסין וטעמא דבית הלל כנגד ימים היוצאין וחד אמר טעמא דבית שמאי כנגד פרי החג וטעמא דבית הלל דמעלין בקדש ואין מורידין
Ulla said: There were two amoraim 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.
פרי החג - מתמעטים והולכים בקרבנות דפרשת פנחס:

The bulls of the festival: decreasing and following the sacrifices (described) in parashat Pinchas.

מעלין בקדש ואין מורידין - מקרא ילפינן לה במנחות בפרק שתי הלחם (מנחות דף צט.):

One ascends to a higher level, and does not descend: This principle is derived from a verse, as explained in Menachot 99a.

והמהדרין מן המהדרין - נראה לר"י דב"ש וב"ה לא קיימי אלא אנר איש וביתו שכן יש יותר הידור דאיכא היכרא כשמוסיף והולך או מחסר שהוא כנגד ימים הנכנסים או היוצאים אבל אם עושה נר לכל אחד אפי' יוסיף מכאן ואילך ליכא היכרא שיסברו שכך יש בני אדם בבית:
And Mehadrin of the Mehadrin (beautiful of the beautiful)... It seems to R"I that Beis-Shamai and Beis- Hilel refer only to "Man and his household" (i.e. to fulfilling the Mitzvah of Chanukah candles by the head of the household alone on behave of his entire family), because in this way there is more beautification of the Mitzvah because there is something recognizable when he keeps adding or leaving out (candles) which corresponds to days that are entering (the days of Chanukah still to come, i.e. position of Beis-Shamay) or exiting (the days of Chanukah that have already passed, i.e. position of Beis-Hilel). However, if he makes a candle for each one (i.e. each member of his household gets his own candle), even if he adds (candles) from this moment and onwards, there is nothing recognizable, because (the people) would think that so is the number of people in the household. (i.e. in this case, instead of attributing the increase or decrease in candles to the intention of the owner to match the corresponding day of Chanukah, people would attribute it to the intention to match the number of people in the household.)
כַּמָּה נֵרוֹת הוּא מַדְלִיק בַּחֲנֻכָּה. מִצְוָתָהּ שֶׁיִּהְיֶה כָּל בַּיִת וּבַיִת מַדְלִיק נֵר אֶחָד בֵּין שֶׁהָיוּ אַנְשֵׁי הַבַּיִת מְרֻבִּין בֵּין שֶׁלֹּא הָיָה בּוֹ אֶלָּא אָדָם אֶחָד. וְהַמְהַדֵּר אֶת הַמִּצְוָה מַדְלִיק נֵרוֹת כְּמִנְיַן אַנְשֵׁי הַבַּיִת נֵר לְכָל אֶחָד וְאֶחָד בֵּין אֲנָשִׁים בֵּין נָשִׁים. וְהַמְהַדֵּר יוֹתֵר עַל זֶה וְעוֹשֶׂה מִצְוָה מִן הַמֻּבְחָר מַדְלִיק נֵר לְכָל אֶחָד בַּלַּיְלָה הָרִאשׁוֹן וּמוֹסִיף וְהוֹלֵךְ בְּכָל לַיְלָה וְלַיְלָה נֵר אֶחָד:
How many lights do you kindle on Chanukah? It is a commandment that one light be kindled in each and every house whether it be a household with many people or a house with a single person. To exalt the mitzvah, one may kindle light according to the number of people in the household, a light for each and every person, whether they are men or women. One who wishes to further glorify this and performs the mitzvah in the most choice manner kindles a light for each person on the first night and adds on following nights one light.
כֵּיצַד. הֲרֵי שֶׁהָיוּ אַנְשֵׁי הַבַּיִת עֲשָׂרָה. בַּלַּיְלָה הָרִאשׁוֹן מַדְלִיק עֲשָׂרָה נֵרוֹת וּבְלֵיל שֵׁנִי עֶשְׂרִים וּבְלֵיל שְׁלִישִׁי שְׁלֹשִׁים עַד שֶׁנִּמְצָא מַדְלִיק בְּלֵיל שְׁמִינִי שְׁמוֹנִים נֵרוֹת:
How does this work? Suppose the people of the house were ten. On the first night, one lights ten candles; on the second night, twenty; and on the third night, thirty; until the result is that one lights on the eighth nigh eighty candles.
כמה נרות מדליק בלילה הראשון מדליק אחד מכאן ואילך מוסיף והולך אחד בכל ליל' עד שבליל אחרון יהיו שמונ' ואפי' אם רבים בני הבית לא ידליקו יותר: הגה וי"א דכל אחד מבני הבית ידליק (רמב"ם) וכן המנהג פשוט ויזהרו ליתן כל א' וא' נרותיו במקום מיוחד כדי שיהיה היכר כמה נרות מדליקין [מהר"א מפראג]:
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)