Makhshirin, Chapter Two, Mishnah Eight
1) If one found there lost property,
2) If the majority [of the inhabitants] were non-Jews, he need not proclaim it;
3) If the majority were Israelites, he must proclaim it;
4) If they were half and half, he must [also] proclaim it.
5) If one found bread there we must consider who form the majority of the bakers.
6) If it was bread of clean flour, we must consider who form the majority of those who eat bread of pure flour.
7) Rabbi Judah says: if it was coarse bread, we must consider who form the majority of those who eat coarse bread.
Section one: The issue here is finding lost property. The rabbis obligated one to declare lost property that was found and return it to the owner if the owner could identify it. These halakhot are found in the second chapter of Bava Metzia. This obligation is only to a fellow Jew. One is not obligated to return property to a non-Jew, at least not according to the Mishnah. Later halakhah rectified this discrimination, as it did in many cases.
Section two: If the majority was not Jewish, then he need not proclaim that he found a lost object because he can assume that it belonged to a non-Jew.
Section three: If the majority were Jews he must proclaim it and if a Jew claims it, he would have to return it to him. This would make for quite an awkward situation if he proclaimed it and then it turned out to belong to a non-Jew.
Section four: If the split is 50/50 he must assume that it could belong to a Jew and he must proclaim it.
Section five: The second half of the mishnah deals with bread that is found in the mixed city. The rabbis prohibited Jews from eating bread made by Gentiles, not because the bread is impure or not kosher, but in order to prevent assimilation. The first criterion is to follow the majority of bakers, as has been the rule in most of the previous mishnayot.
Section six: However, if the bread is of a special kind, such as bread made of clean flour, we need to look at who makes clean flour bread. This is more expensive so it will be made probably by the upper class.
Section seven: Today coarse bread is the most expensive type of bread, but back then (and probably not too long ago), it was for the poorer folk. So Rabbi Judah adds that if the bread is of poor quality, i.e. it is coarse, then we can assume it was made by someone poor and we follow the majority of poor people.