Aside from the cases described in the first Mishna (2a) where two people were both holding a cloak and claiming ownership, the Mishna also describes other situations in which ownership claims are made. If two people are riding an animal, for example, or if one was riding and one was leading the animal, the Mishna rules that we will treat their claims of ownership the same way we treat people who are each holding an object.
The ruling of the Mishna notwithstanding, Rav Yosef quotes Rav Yehuda as having a tradition from Shmuel that in a case where one person is riding the animal and another leading the animal only one of them can claim ownership – unfortunately he did not remember which one it was. Does the rider have a stronger claim because he is holding the animal, or does the leader have a stronger claim because the animal is directed by his actions? Ultimately Rav Yehuda suggested to Rav Yosef that they can clarify this question based on a Mishna in Massekhet Kilayim (8:3), where according to Shmuel’s reading of the Mishna, if two animals that cannot be harnessed together for work are pulling a cart, only the person leading the animals will be held liable; the person sitting in the cart will not. Thus we can conclude that Shmuel’s position is that someone riding an animal cannot claim ownership – certainly not when someone else is leading the animal.
The obvious question that is raised by the rishonim is that our Mishna comes to a clear conclusion that offers credence to the claims of the rider, as well – how can the amora’im Shmuel, Rav Yosef and Rav Yehuda suggest otherwise?
One suggestion that is raised is that Rav Yehuda is examining different kinds of “riding.” Will the Mishna’s ruling be true only if the rider is actively driving the animal, or even if he is passively riding on it? The Ran suggests that we cannot reach any conclusions from the Mishna where the case is that the rider claims to have already taken possession of the animal before he began to ride it.