Demai, Chapter 3, Mishnah 1. This mishnah deals with certain leniencies in the laws of demai: to whom one may feed produce whose tithes have not been taken.
Rashi in Berachos explains the basis for these leniencies: even though we suspect that an am ha'aretz did not separate tithes, there is nevertheless an established principle that "most amei ha'aretz do tithe" - that is, the majority of amei ha'aretz do in fact separate tithes, and the entire law of demai is no more than a stringency. For this reason we find that the Sages were lenient with it in various cases.
Feeding the Poor and Achsanya:
The mishnah opens: "Ma'achilin es ha'aniyim demai v'es ha'achsanya demai" - one may feed demai to the poor, and likewise to achsanya. Two explanations are given for 'achsanya':
According to Rashi: achsanya refers to soldiers whom the government has billeted to lodge in people's homes, and one may feed them demai.
According to the Rambam: achsanya means guests in general, and one may feed demai to any guest.
The Dispute Between the Bavli and the Yerushalmi:
According to the Bavli in Berachos, the mishnah is to be understood at face value: one may feed them demai, and they themselves may eat the demai.
In the Yerushalmi, by contrast, the Amoraim disagree:
One Amora holds that the poor whom one may feed demai are specifically chaveirim who will go on to tithe: they are informed that this is demai, and they tithe it themselves. But poor people who are amei ha'aretz may not be fed demai.
The other Amora holds that this applies even to a poor person who is an am ha'aretz, for if we distinguish between one poor person and another, the ultimate result will be that the door is closed before amei ha'aretz. Donors will not want to give food to a poor person who is an am ha'aretz, since when giving to a chaver they are not required to take the tithes from the food, whereas when giving to an am ha'aretz they are required to do so. Therefore the two cases must be treated equally.
Rabban Gamliel and His Workers:
The mishnah continues that Rabban Gamliel "hayah ma'achil es po'alo demai" - he would feed his worker demai. We do not rule this way, but some understand that this refers to food he was not obligated to give them, and his giving it was an act of charity - and therefore it falls into the category of the poor.
Charity Collectors:
The mishnah deals with charity collectors, who collect food in order to feed people, such as for the communal soup kitchen.
Beis Shammai say: "Nosnin es ham'usar l'she'eino m'aser, v'she'eino m'usar lam'aser, nimtze'u kol ha'adam ochlin m'sukan" - the food collected from chaveirim and from Torah scholars, which is known to have had its tithes separated, should be given to poor people who do not tithe, that is, to amei ha'aretz who will not separate tithes. And the food that is untithed, received from donors who are amei ha'aretz, should be given to poor people who are Torah scholars, who will separate the tithes from it. In this way everyone eats properly tithed food, from which the tithe of demai has been separated: the Torah scholars will separate demai from the food they received from amei ha'aretz, and the amei ha'aretz will be given food that came from chaveirim.
The Sages disagree: "Govin s'tam um'chalkin s'tam, v'harotzeh l'saken y'saken" - they collect without distinction and distribute without distinction, to amei ha'aretz and chaveirim alike, and whoever wishes to tithe may tithe, and whoever does not wish to does not tithe. The reason is once again that same principle: if we begin to make distinctions, the ultimate result will be that the charity fund will manage to collect less. People will feel that they are not being treated equally, and will not want to donate to charity. For this reason the Sages rule that no distinctions are made, and whoever wishes to separate demai may separate it.
In summary: in this mishnah we learned the basis for the leniency in demai, which is only a stringency built on the concern for the minority who do not tithe. One may feed demai to the poor and to achsanya (soldiers lodged in the home according to Rashi, or guests in general according to the Rambam); according to the Bavli this is to be taken at face value, while in the Yerushalmi they disagreed whether it is permitted even for a poor person who is an am ha'aretz, out of concern for closing the door. We saw that Rabban Gamliel fed his worker demai as an act of charity, and we saw the dispute between Beis Shammai and the Sages regarding charity collectors: whether to distribute the tithed and untithed food with a distinction, or to collect and distribute without distinction - and in both reasons the same consideration returns, not to harm the poor or the giving itself.