All sacrifices which have been slaughtered for a designation other than their own are valid, but they are not credited to the owner as fulfillment of [his] obligation; except for the pesach- and chatas-offerings — the pesach-offering in its [proper] time, and the chatas-offering at all times. R’ Eliezer says: Also the asham offering — the pesach offering in its [proper] time, and the chatas- and asham offerings at all times. Said R’ Eliezer: The chatas offering comes [to atone] for sin, and the asham offering comes [to atone] for sin — just as the chatas-offering is disqualified [if it is intended] for a designation other than its own, so too the asham offering is disqualified [if it is intended] for a designation other than its own.

A Kohen takes precedence over a Levi, a Levi [takes precedence] over a Yisrael, a Yisrael [takes precedence] over a mamzer, a mamzer [takes precedence] over a Nesinite, a Nesinite [takes precedence] over a convert, and a convert [takes precedence] over a freed slave.  When is this? When they are all equal. But if the mamzer is a Torah scholar and the Kohen Gadol is ignorant —- the mamzer who is a Torah scholar takes precedence over the Kohen Gadol who is ignorant.