Pe'ah, Chapter 4, Mishnah 2. In the previous mishnah we learned the law of pe'ah while the crop is still attached to the ground: the poor themselves come and take the pe'ah, competing with one another for it, and the owner is not permitted to distribute it among them. Distribution by the owner is done only where there is danger involved. From this comes the principle explained there: even if ninety nine of the poor ask that the owner distribute the pe'ah, and only one asks to compete and take it himself, we listen to that one, because that is the halachah in that case.
With a trained vine and a date palm, the ruling is reversed:
Against this stands the case of our mishnah: "b'dalis u'v'dekel eino chein" - with a dalis (a vine trained on a trellis) and with a date palm it is not so. Since climbing them and competing over them involve danger, a different law applies: "afilu tish'im v'tishah omrim la'voz v'echad omer l'chaleik, lazeh shom'in, she'amar k'halachah" - even if ninety nine say to grab it and one says to distribute it, we listen to that one, for he spoke in accordance with the halachah.
That is, even if ninety nine of the poor say that they wish to take it themselves and compete with one another, and one of them says that the owner should be the one to distribute the pe'ah, we listen to that one, since he said what is proper according to the halachah, and with a trained vine and a date palm the owner must indeed distribute it. We do not listen to the ninety nine who want to compete, because that is not the halachah in this case.
In summary: in both mishnayos the ruling is not determined by the opinion of the majority but by the halachah:
Attached to the ground: the poor take it themselves and compete, and therefore even if only one asks for this, we listen to him.
With a trained vine and a date palm: because of the danger, the owner is the one who distributes, and therefore even if only one asks for this, we listen to him, "she'amar k'halachah" - for he spoke in accordance with the halachah.