The students of Beis Shamai outnumbered those of Beis Hillel on that day and were able to use their majority number to enact decrees in accordance with their own opinions. One question is how it happened that Beis Shamai outnumbered Beis Hillel. The Mechilta (cited in a footnote by Rav Reuven Margolios in YESOD HA'MISHNAH, Bi'ur #12) says that the son of Chananya ben Chizkiyah ben Garon was a member of Beis Shamai, which implies that his father was as well. If so, it makes sense that more members of Beis Shamai than Beis Hillel gathered in Chananya Ben Chizkiyah's attic to discuss enactments.

The big question is what happened the next day. That is, the fact that on that day the students of Beis Shamai outnumbered those of Beis Hillel implies that the next day was back to normal, when Beis Hillel outnumbered Beis Shamai. If so, why didn't Beis Hillel merely re-enact the decrees in accordance with their opinion?

The answer is that on that day, Beis Hillel first argued and in the end agreed with Beis Shamai (in order to make peace; they agreed to them because they realized that Beis Shamai was in the majority). Once those involved in a vote have issued their opinions, they can no longer retract them. Therefore, even though the next day Beis Hillel was back in power, they could not re-enact the decrees that were made the day before in accordance with Beis Shamai's opinions.

See YESOD HA'MISHNAH by Rav Reuven Margolios (Bi'ur #12) for a lengthy discussion on the issue.

Below is what we wrote in the INSIGHTS to Daf 17.

Shabbos 17a

(1) THE DAY THAT HILLEL'S OPINION WAS OVERTURNED

The Gemara says that the day that Shamai overruled Hillel was as "difficult for the Jews as the day that the golden calf was made." What does the day that Shamai overruled Hillel have to do with the day that the golden calf was made?

RASHI explains that it was a difficult day for the Jewish people, because Hillel was the Nasi, the leader of the generation, and he was exceedingly humble. The CHASAM SOFER explains that Rashi means that just like the will of the people at the sin of the golden calf overruled the leader (Aharon ha'Kohen; Moshe, at the time, was upon the mountain receiving the tablets of the law) and made him join them, so, too, the opinion of the contending school of thought overruled the ruling of the authority, Hillel, and subjected him to their will by having him agree with them against his reasoning.

We might take the comparison between Hillel and the sin of the golden calf one step further. We find in Avos (1:12) that Hillel said, "One should be of the disciples of Aharon and constantly pursue peace." He said "disciples of Aharon " and not of " Moshe ," because it was Aharon's special trait of peace-loving and kindness that Hillel taught that people should follow. Moshe's trait was that of strict justice (Sanhedrin 6b), which Hillel felt was not the trait that the masses should cultivate in themselves for the sake of peace among men. Thus, it was Hillel's opinion that Aharon's traits be emulated. This was consistent with his opinion elsewhere, where the Gemara (Shabbos 30b) says that one should be patient, forgiving, and humble like Hillel, and not stand on one's honor like Shamai. We indeed find that Hillel almost always gives the more lenient opinion, and Shamai the more strict one.

The day that Aharon was overruled by the people building the golden calf was the day when the traits of Aharon were conquered, and the traits of Moshe, of strict justice, ruled, as we find that punishment was wrought upon the Jewish people. Similarly, when Shamai overruled Hillel, the traits of Hillel were conquered and Shamai's traits of strict justice ruled. It was difficult for the Jewish people to live in a state of strict justice, just like it was difficult for them to live in that state when Aharon's traits were conquered at the sin of the golden calf.