According to many Rishonim an eid echad cannot testify against a chazakah (see Yevamos 88). Would an eid echad be believed against a rov? For example, if I have three pieces of meat in front of me and only one is kosher, can I trust an eid echad who identifies the kosher piece?
As a general rule halacha tells us ruba v'chazakah -- ruba adif. When there is a clash between the evidence of rov and the evidence of chazakah, the evidence of rov is considered superior and more authoritative. It would stand to reason therefore that if an eid echad is not believed against the inferior form of evidence of chazakah, he would certainly not be believed against the superior evidence of rov.
The Achonim are bothered by this conclusion because it flies in the face of common practice. As the Pnei Yehoshua points out in a few places (e.g. see Kidushin 63b), we buy meat trusting an eid echad (the butcher) that it's kosher even though most of the meat in the world (rov) is treif.
My son brought to my attention an interesting sevara of R' Naftali Trop. One of the other proofs of the Pnei Yehoshua (quoted by R' N"T, but which I have not found in the Pnei Yehoshua yet) that an eid echad is believed is from the fact that we would accept an eid echad's testimony as to who the rightful owner of a lost object is even though there are many more people in the world (rov) who are not the owner than who are.
R' Naftali says this case is not a proof --this case of returning a lost object is completely different than the case of the mixed up pieces of meat that we started with. Can you figure out the difference?