I wanted here to deal with Maimonides [Nizkei Mamon chapter 2] [When the string is owned the owner of the string pays .5 damage and the owner of the chicken nothing] and the Talmud in Bava Kama page 19b.
The Gra said this statement of Maimonides is not understandable. And he goes with the approach of the Rosh
But before I do I want to say over the Gemara and Rosh [Rabbainu Asher]. This will give us some perspective.
The Mishna says when chickens that get a string attached to them and then a vessel gets tangled in the string and gets dragged along and breaks the obligation is half damages.
The idea is the damages that comes in an unusual way that they owner could not have suspected he is obligated only in half damages. [Damage directly by means of foot or pit or fire are all stated openly in the Torah itself in Exodus.]
Rav Huna says the Mishna refers a string that gets attached by itself but if someone ties it, it is full damage.
The Talmud asks, "Who can he be referring to? If the owner of the string, then if he covered it, it is is no fault of his. And if he did not cover it he should pay full damage. So it must be he means the owner of the chicken and it is a case that tit was flying, and Rav Huna was referring to a case of a string that was not owned."
The Rosh is thinking here: "OK, so full damages when someone tied it? That must mean like Rabbi Natan in the case of a stone on the edge of a pit. (Bava Kama 53 and page 13)"
I have two points to make. One is if the first approach of the Gemara was correct, then it never would have said that Rav Huna was not referring to the Mishna. [This idea was stated by the Migdol Oz. It is not my original idea.] Just think about it. If, in fact, the owner of the chicken pays half damage when it got tied by itself and when it is flying, why in the world would the Gemara resort to the radical step of changing Rav Huna's statement?!! You don't do such a thing unless you have be backed against a wall.
Now Rashi and Tosphot do I admit try to deal with this issue, but clearly the evidence is on the side of the idea that the Gemara throws out the first approach completely. This turns the tables around completely and makes the Rambam seem to be the reasonable one over here.
The only thing left is to show why the Rambam says this--not just how he sees it in the Gemara but the reasoning behind it.
And this is my answer: I say that Rabbi Nathan was referring to cases of full damage. In our case here it is half damage. And in such a case R. Natan would never have said you get half damage from one and half damage from the other. That would have to be considered ridiculous.
The other idea is that this is not a case of two people causing damage. One is direct and the other indirect.
Like two owners of a pit. One walks by and does not cover it. then the other walks by and does not cover it. the second one is obligated. There is a lot more to talk about here but let this suffice for now.