The Pnei Yehoshua on daf 15a in Sukka
gives an excellent explanation to our gemara (15b
in Eruvin) which answers a bunch of questions. First a list of some of the questions:
Our gemara paskens like Rav Pappa that if parutz k'omed it's ok as long there isn't more open space than closed space. Tosafos d"h v'hilchasa asks why we pasken here that half and half is ok but in chulin 29a
we pasked that half and half is not considered like rov. He "answers" that you could differentiate between mechitzos vs. isur and tumah.
How could the gemara bring a reaya to either Rav Pappa or Rav Huna Brei D'rav Yehoshua from sukka? They each said that the basis of their opinions is the wording of the halacha l'moshe misinai. The halacha was said regarding mechitzos not regarding schach of a sukka.
How can our gemara pasken like Rav Pappa despite the tyuvta?
Is the machlokes really based on a halacha l'Moshe Misinai? Are they really arguing historically what exactly Hashem told Moshe?
He says this also answers some of Tosafos' question in the gemara over there in sukka.
The Pnei Yehoshua says that their machlokes is really based on a much broader machlokes which is actually a machlokes Rishonim. They say that if it's 50-50 then it's treated like a safek. Rav Pappa believes that a safeik d'oraysa is l'chumra but that's only m'drabonnon. Therefore, in this case where it's a d'rabonnon and it's a tircha the Rabonnon allowed you to be meikil and say 50-50 is enough. R Huna Brei D'Rav Yehoshua holds that it's d'oraysa so we will be machmir even in this d'rabonnon by hilchos Shabbos where we will be machmir because of k'eyn d'oraysa tikkun. The gemara asked a question from Sukka because it's a d'oraysa yet we pasken that 50-50 is enough. The truth is that it would have been a question on Rav Pappa also but it was a more obvious question on RHB"Y. Rav Pappa would agree in other cases where it's an isur d'oraysa that we would be machmir. The tyuvta on Rav Pappa was from a case that might have been a reshus harabim d'oraysa in which case even Rav Pappa would agree.