I just learned about this din of Smoch miuta l?chazakah v?hava lei palga u?palga.My understanding is the din says if you have a rov l?hatir and you have a miut to be choshesh, but if there is also a chazakah that says asar; you put together the chazakah that says asar with the tzad of the miut and then rov loses it?s koach of rov. And it basically turns into a safeik of 50/50.
Thank You for your question! The concepts of Rov and Mi'ut, and Semoch Mi'uta in particular, are -- as you probably know -- very wide and deep topics throughout Shas, but I can try to shed a little light on the topic.
At first, since it seems that the Gemara is saying that the Mishnah is according to Rebbi Meir, we need to know why do we need to add the Chazakah to overpower the Rov, while Rebbi Meir holds that we are Choshesh for the Mi'ut in any case, so it is Asur either way.
(I must add that the Rambam and the Rif and some Rishonim in the name of Rav Hai Gaon say that Semoch Mi'uta is brought down here also according to the Rabanan who usually would rely on the Rov to be Matir. These Rishonim need to reconcile their opinion with the Gemara in Kidushin 80a, which seems to say that the Rabanan do not agree with the rule of Semoch Mi'uta.)
Tosfos here (in the name of Rabeinu Elchanan) says that we do not really need the rule of Semoch, and it just comes to teach that if there is a Chazakah on the Rov's side -- where we might have thought that we add the Chazakah to the Rov and permit the matter even according to Rebbi Meir -- there is a Chazakah on the other side, too, and the Chazakos' cancel each other out.
Tosfos in Bechoros (20a) seemss to disagree with the Tosfos here. Tosfos there says that the Chashash that Rebbi Meir usually has regarding the Mi'ut is just mid'Rabanan, while when the Chazakah is added, it turns the case into a Safek d'Oraisa. It is interesting, since this would imply that we can take the Chashash mid'Rabanan that Rebbi Meir has and combine it with a Chazakah to turn the case into a Safek mid'Oraisa. The Acharonim elaborate on this, but this is a side issue. (See Beis ha'Levi II, 29b, and Kovetz He'oros 66.)
By the way, we find in some cases that we may add a Chazakah to the Mi'ut according to Rebbi Meir even l'Kula (see Kidushin 80a), which is a proof that Semoch Mi'uta is much more than the regular Chashash which Rebbi Mei has for the Mi'uta, and might even give more power than 50/50, but this is a long discussion in itself.
There is more to this Sugya, but this is a good start.
Kol Tuv,
Aharon Steiner