What did R. Gamliel expect R. Akiva to bless?

Tosfos: He will bless Birkas ha'Mazon, like R. Gamliel's opinion. This is why he authorized him to bless for everyone. We are not Mezamen (one blesses for everyone) for Peros. Since R. Akiva blessed me'Ein Shalosh, he blessed only for himself.

Why does it say Kafatz?

Rav Elyashiv, from Tzlach: He did not want R. Gamliel to stop him, for then to continue would be overt disobedience.

Chashukei Chemed citing Ben Yehoyada: He jumped from where he was sitting at the table, and went elsewhere, past the table, for he did not want to do unlike his Rebbi right in front of him.

If one was obligated to bless Birkas ha'Mazon, and he blessed me'Ein Shalosh, was he Yotzei?

Daf Al ha'Daf: The Ra'ah, Ritva, Shitah Mekubetzes, Beis Yosef, Ginas Veradim and Birkei Yosef say so. Rav O. Yosef (Me'or Yisrael) proved from here that he was not Yotzei! If he was, why did R. Gamliel say 'why do you enter arguments?' It was good to bless me'Ein Shalosh, for then he was Yotzei according to both opinions! Chafetz Hash-m (of the Ohr ha'Chayim) asks, what was R. Gamliel's objection? In any case, R. Akiva must do like one opinion! He answered, if one said me'Ein Shalosh in place of Birkas ha'Mazon he was not Yotzei. If he said Birkas ha'Mazon in place of me'Ein Shalosh, he was Yotzei. Therefore, he should have blessed Birkas ha'Mazon, for then all agree that he was Yotzei!

Why does the Halachah follow the majority?

Ha'Boneh: Rabim do not agree about Sheker. The Torah said "Acharei Rabim Lehatos" - an individual or minority could err, (NOTE: but we assume that the majority would not. It can occur that the majority errs. We bring Par Helam Davar if most of the Sanhedrin erred, and most if Yisrael sinned due to this! - PF)

Here R. Akiva said 'Yachid v'Rabim, the Halachah follows the Rabim.' In the Tosefta, he said "Acharei Rabim Lehatos"!

Chashukei Chemed citing Maharatz Chayos: There are two ways of following the majority. (a) If they argued with each other, and voted, the minority is Batel to the majority - Acharei Rabim Lehatos. (b) If they did not argue face to face, and did not hear the other side's proofs, Acharei Rabim Lehatos does not apply. Even so, the Halachah follows the majority. So was the argument of R. Gamliel and Chachamim. (NOTE: R. Gamliel was the Nasi - why would he not debate the matter with Chachamim? - PF)

Chashukei Chemed: We find that Yehudah ben Dortai left Yerushalayim before Erev Pesach that fell on Shabbos, for he held that Chagigah of the 14th overrides Shabbos (Pesachim 70b. Chachamim say that it does not; they would not allow him to offer it.) Since the Halachah follows the Rabim, why did he need to go away? We can say that they never took a vote about this; he holds like R. Gamliel that in such a case, we do not say that the Halachah follows the Rabim.