The opportunity to extend one’s ability to walk beyond the 2,000-ama limit in either direction that is described in the Mishna (36b) is based on the concept of beraira (literally “choice,” and here referring to retroactive designation). The idea of beraira is that when information becomes available, it can retroactively help decide what choice was made earlier. In the Mishna’s case, once we know which direction the non-Jews or scholar was coming from, we can retroactively decide that the eiruv should apply according to that – as yet unknown – reality.
The Gemara quotes a number of tanna’im who argue about the principle of beraira. Rabbi Yose, for example, is quoted as rejecting the principle with regard to tithes, but he seems to accept it in the case of sacrifices.
The case of tithes, as presented by the Gemara, is when wine is purchased that has not been tithed. When the purchaser says “I will set aside the appropriate amount of wine tomorrow for teruma, ma’aser and ma’aser sheni” can he drink the wine immediately, based on what will be done tomorrow? Rabbi Yose is among the tanna’im who forbid such tithing. The case of sacrifices involves two women who each bring a pair of doves to the kohen, without specifying whose sacrifices were whose or which one was for the Ola (burnt offering) and which one was for the Hatat (sin offering). The kohen decides which sacrifice is which, and Rabbi Yose rules that the sacrifices are valid for each of the women.
The Gemara quotes Rabba as explaining that in the latter case a clear statement was made giving the kohen the ability to decide which sacrifice was which.
Pigeons or doves are the common sacrifices brought by women who have given birth. Part of the process that completes their becoming tahor (ritually pure) and being permitted to partake in kodashim (holy things) or enter the precincts of the Temple is bringing these two sacrifices – an Ola and a Hatat (see Vayikra 12:1-8). There is an entire tractate – Massekhet Kinim – devoted to the issues that can come up when the doves are misplaced or confused with one-another.
Rabba’s explanation – that a condition was made giving the kohen the ability to decide which dove would be used for which sacrifice – is understood by the Meiri to mean that in general there is an assumed condition that the decision will be left to the kohen by the people bringing this sacrifice.