Does a Ben Noach have the right to use a concept like rov? The Pri Migadim in Teivas Gomeh and Pesicha L'Taaravos Chakira 3 discusses the question of a piece of eiver min hachai that is mixed with other meats. Can a Ben Noach use bittul b'rov to eat the mixture? The Pri Megadim assumes that you can't use rov since the dinim of rov are learned from Sanhedrin and Kodshim/Korbonos. Since these halachos don't apply to a ben Noach, they have no mekor for rov. The Pri Megadim does have a safeik that maybe we still say mi ikka midi d'yisroel mutar u'ben noach assur and therefore the ta'aroves is muttar to a ben noach.
The Noda B'Yehuda (Mahadura Tanyana Even Ezer Siman 42) also holds like this. However, he does say we follow rov l'chumrah. Therefore, we use the rov of rov bi'ilos achar haba'al to say we know who a ben Noach's father is and therefore he is assur to his father's wife.
The Pri Yitzchak (Chelek 2 Siman 60) disagrees and says from the fact that dinei yerusha apply to a ben Noach and a son inherits his father, we see that we use rov and we say rov bi'ilos achar haba'al .
The Chasam Sofer (Yora Deia Siman 71) also holds we say rov by a ben Noach.
There are a few nafka minas.
1) The gemara in Avodah Zara 6B says a ben Noach can bring a korban but he can't bring a treifa as a korban. The only reason we don't say that every animal brought is a safeik treifa is because we use a rov of rov b'heimos k'sheiros. If a ben Noach can't use rov, maybe we should say that a ben Noach can never bring his own korbon on his private bamah beacuse maybe it is a treifa.
One approach to answering the kash ais to say that the only animal that a be nOach can not bring is an naimal that woul dbe posul for a Yisroel to bring. So since a stam animal is muttar for a Yisroel it is also muttar for a ben Noach. Only a definate treifa is a problem.
2) The Minchas Chinuch (Mitzva 32) says that an asufi who lives among rov yisroel can assume he is a yisroel. But if a ben Noach doesn't have rov how can he keep Shabbos since goy sheshavas is chayav misa.
3) The Rambam paskens if B'nei K'turah and B'nei Yishmael get mixed up you give the whole group a bris mila. The Sha'agas Aryeh asks, why don't we go after rov and rov are from Yishmael. His rayah that the Rambam holds we go after rov by a ben Noach is that the Rambam paskensthat if a ger from Amon comes to us we say Sancheirev mixed everyone up and since rov non Jews are not from Amon we can assume this ger is not from Amon and he can marry a Jew.
The Noda B'Yehuda answers that there is no rov by a ben Noach. But in the case of the ger, since he already converted he is a Jew and he can use rov.
The question on the Noda B'Yehuda is so why don't we say any ben Noach is chayav mila since maybe he is from B'nei Keturah and we can't use rov. Also, why did the Rambam only use a case of B'nei Keturah mixed with Yishmael.
One answer I saw is that since other goyim don't have a mesorah to do mila we can assume they are not b'nei Keturah. It is only Yishmael who also has a mesora for mila that we have to worry maybe they are b'nei keturah.