At the end of parshas Metzora the Torah discusses the halachos of when a woman becomes a niddah. The Torah says that a woman who becomes a niddah must count seven days from when she stops seeing blood, and then becomes tahor by immersing in a mikveh. The Gemara in Kesubos 72a says that a woman is believed when she counts the seven days on her own. Tosafos in Gittin 2b says that this is the source from the Torah for the rule that eid echad ne’eman b’issurim (one person is believed concerning issurim). Rashi in Yevamos 88a says that the source for this halacha is due to the fact that if the aforementioned rule was not so, no one would be able to eat from his fellow or even from his own household (and apparently that is not possible).
Testimony of two witnesses is always believed, even when it contradicts a chazakah – a halachic rule that states that when there is an unknown we should assume that everything remained status quo. There is a machlokes Rishonim whether the testimony of one person is accepted when it contradicts a chazakah. For example, a live animal is prohibited to be eaten since it is not shechted. If one person will testify that it was shechted, his testimony will contradict the chazakah that it was not shechted. Tosafos, the Rush, and the Mordechai hold that one witness is not believed against a chazakah. The Rashba believes that one witness is believed, even when contradicting a chazakah.
The Shev Shmeitza 6:7 asks the following question: the Gemara (Yevamos 119b) says that when determining a doubt one should follow the rov (majority) over a chazakah. This is known as ruba v’chazakah, ruba adif. Mathematically, since a rov is greater than a chazakah and a chazakah is greater than one witness (according to some Rishonim), we should infer that a rov is greater than one witness. Therefore if three pieces of meat get mixed up (two non-kosher and one kosher) and one witness says that he knows which is the kosher piece, he should not be believed. Since there is a doubt as to which piece is kosher and the halacha of following the rov is telling us that the selected piece is from the majority (non-kosher), one witness cannot contradict the rov and testify which piece is kosher. But today’s norm dictates that this is not the correct halacha. Why? Because it is common for marketplaces to contain a majority of non-kosher meat and only a minority of kosher meat, and the seller is to be believed when saying which pieces are kosher.
The Chelkas Yoev writes that there is an explicit tosefta in Pesachim at the end of the fifth perek that says that one witness is believed over a rov. The Pnei Yehoshua (Kiddushin 63b) also says that one witness will be believed over a rov. He explains that the rule that one witness is not believed against a chazakah only applies when the chazakah is foolproof. However when the chazakah is weakened prior to the testimony of the witness, the witness will be believed. The Pnei Yehoshua adds that a chazakah that is not weakened is even stronger than a rov. Based on this there is no longer any indication that a rov is stronger than one witness. Thus in the case of the marketplace that contains a majority of non-kosher meat, one witness will be believed.
The Shev Shmeitza disagrees with the Pnei Yehoshua and offers another suggestion. The only case where one witness is not believed against a chazakah is when even according to his testimony, the item was forbidden at one point and he is attempting to remove it from its current status. However, if according to his testimony the item was never forbidden, his testimony is not considered contradictory to the chazakah and thus he is believed. The same would apply when one witness testifies about a case that has a rov. As a result, in the case of the pieces of meat that were mixed up, the witness testified that he always knew which piece was kosher; therefore, according to his testimony, there is no mixture and thus there is no rov. If the pieces are not mixed, a rov does not apply since there is no doubt. Therefore his testimony is not contradicting the rov. Hence he is believed.
If a single witness would testify that he found an animal to be treif, his testimony would directly contradict the rov that states that the majority of animals are not treif. He may be believed on a different merit but, according to the Rishonim that say that a single witness is not believed against a chazakah, he would not be believed against a rov as well.