The Tanna Kama and Rabbi Yosi argue about the number of divisions in the Torah portion of Tisha B'av. The Rambam (Tfilla 12, 16) and Tur and Beis Yosef (Siman 559) follow the opinion of Rabbi Yosi. Why do they pasken like a minority view?
The view of Rebbi Yosi is not a minority view. The anonymous Beraisa at the beginning of the Amud says that there are three Aliyos on Tisha b'Av, and it does not differentiate based on what day Tisha b'Av occurs. Thus, the Halachah follows Rebbi Yosi, because an anonymous Beraisa supports his view.