Rav Yochanan presents 3 cases where we follow rov against a chazaka (tosafos d.h. achar, and on amud 2 d.h. l'mutei point out that we are only including and excluding cases where there is a chazaka fighting the rov). The gemara questions why doesn't he list the famous case of 10 stores, 9 selling kosher and one selling treif where we follow rov. The gemara says that we are only looking for cases of tu'mah, not issur. However, the fact that the gemara even suggests this as an option forces Tosafos to write that there is a chazaka of all meat starting off as issur prior to being shechted, fighting against the rov that it is kosher.
There is a very interesting machlokes between the Binas Adam (sha'ar ha'kavua #16) and the Chavos Da'as (y.d. 119) whether we follow the majority of stores that sell kosher meat, or the majority of kosher meat. The Binas Adam holds strongly that we follow the majority of meat, therefore if the one treif store sells more meat that the 9 kosher, the meat would be treif. His rationale is very simple, we don't know whether the meat fell from a seller or a buyer. The only factor that would incorporate all buyers and sellers would be the amount of meat available for sale. He proves this point from a Mishna in Shekalim (7) that says that when we find money and don't know whether it is from shekalim or from donations, we assume it fell from whatever it is closer to. The Bartenura asks, how can we follow "karov", since the rule is that Rov trumps Karov? He answers that we are speaking in a case where the amount of money in the shekalim is equal to the amount of money in the donation boxes, so there is no "rov" to speak about. This doesn't seem to make sense because there are 6 donation boxes, and only one shekel box, so even if the money is equal, we still have a rov? From here we see that rov depends on the amount of money, not from the amount of places it could have come from and since the amount of money in the shekalim box equals all 6 donation boxes, there is no rov. Similarly, we should follow the amount of meat being sold in the city, not the amount of stores that it could have come from.
The Binas Adam cites the Chavos Da'as in 119 who brings the exact same proof from shekalim which seems to support his own position, but the Chavos Da'as 110 takes for granted that we follow the amount of stores, NOT the amount of meat being sold. The Chavos Da'as (110) proves that we should follow the amount of stores, not the quantity of meat from the case where one finds an object in a city where most inhabitants are Jews. Why must he assume it fell from a Jew? Goyim are richer than Jews and have more items than Jews so if we follow the majority of the items it would be assumed to belong to a goy, yet we assume it belongs to a Jew! From here we see that we follow the amount of sources that it could have come from when designing the rov. The Binas Adam rejects this proof for two reasons: 1. Even though goyim own more objects than Jews, they all walk the streets carrying the same amount of items in their pockets, therefore the only rov to follow is the rov of people in the city. 2. The issue by hashavas aveida is WHO it fell from, so we focus on jews vs. goyim, but the issue by the meat and coins is what it's status is, so we should focus on the quantity of that item.
The Binas Adam proves his point from Tosafos in our sugya who says that the chazaka on the meat goes against the rov that it is kosher. If the rov is on the stores then the chazaka on the meat doesn't in anyway impact the fact that most stores sell kosher meat. However, since the rov is on the meat that it comes from the majority of kosher meat in the city, it makes sense for the chazaka of the meat to be fighting the rov.
The Binas Adam concludes that when he had the opportunity to visit the Chavos Da'as in Lisa (in the hakdama of the chochmas adam he also mentions visiting in the year 5570 and the chavos da'as advised that he organize the chochmas adam according to the order of shulchan aruch, which he did) he presented his argument to him and the chavos da'as was silent. He understood this to mean that the chavos da'as consented to him that we follow the quantity of meat in the city, not the number of stores from which to purchase meat.
The Pischei Teshuva (y.d. 110:2) cites the Beis Ephraim who says that if the question is on a chicken or piece of meat bought by an individual, the question is really which store he went into so we follow the majority of stores, not the amount of meat. However, if all the meat was sold in all the stores, then we follow the majority of the quantity that was put out on the market. He cites the Ran who writes explicitly that the fact that the shas makes no distinction between the amount of meat in the stores, it apparently makes no difference. This is also the way that the Nodeh B'yehuda leans, but is not תוקע עצמו on it to be lenient.
In short, the machlokes between the Chavos Da'as and Chochmas Adam seems to be whether we follow the source of where the item came from - רוב חנויות מוכרות בשר שחוטה, or the statistical chance of it being kosher - רוב בשר טריפה. The Binas Adam holds firmly that we follow the statistical chance of it being kosher and therefore disregard whether there are 9 kosher stores and 1 treif, or 9 treif and 1 kosher, since it is all dependent on the quantity of meat for sale in that city. The language of chazal - רוב חנויות, was assuming equal amounts of meat in all stores.
I once received a shaila that I consulted many gedolim on. One of the issues that were raised is whether rov is a realistic statistic or an invention of chazal in making assumptions. For example, when trying to determine the yichus of a child found in a city, if the city is inhabited by mostly gentile woman and a small minority of Jewish women, but almost all the gentile woman are post menopause whereas most Jewish women are of child bearing age, do we assume the child is a goy (blindly following the rov) or a Jew (statistically the mother is Jewish)? Rav Hershel Schachter (as reported by his son R. Shay) held strongly that rov is a statistical reality and therefore the child is Jewish, whereas Rav Asher Weiss held strongly that rov of the city is goyim so the child is a goy. To me it seems that if it were truly impossible for the gentile women to conceive, they wouldn't be part of the rov, but if it is possible albeit unlikely (for example the goyim were all in their 40's and the Jews all in their 20's), they should be part of the rov rendering the child a goy (Rav Hershel would maintain that we follow the statistical chance therefore if it were more likely that the child would be born from a Jewish woman, we would ignore the fact that most women in the city are goyim).
At first glance it would seem that the Binas Adam supports the approach of Rav Hershel Schachter - we follow the statistic reality that this meat comes from the majority of the meat in the city and don't get caught up in the language of chazal רוב חנויות. However, in truth even the Binas Adam may hold that we include in the rov all possible sources and we would not use statistics to limit who we allow into the rov. For example, if the issue were the wife of a kohein being raped and we had to determine whether the rapist was from the rov k'sheirim, or mi'ut p'sulim, we would include every rav, rosh yeshiva, and magid shiur in the rov kesharim since they are all potential albeit unlikely rapists. Statistics may say she was raped by someone who is passul, but we would still follow all the potential people who could have raped her, even those who are unlikely to have done so (my understanding is that Rav Hershel would hold that we follow the statistical evidence even in this case). The Binas Adam doesn't necessarily hold that we follow statistics to limit the pool, but rather if we are judging on the meat we have to look at all the meat around. If we are judging on people such as Jews vs. goyim for hashavas aveida or rape, we would look at the entire pool of people.
