When It Comes To Birchas HaMazon A Levi Has Rights Too
The proper order which should determine who should lead bentching is:
A Talmud Chacham (unless there is a Kohen who is a Talmud Chacham even if he is not on the same level as the Yisrael Talmud Chacham). (Mishna Berurah 201:12)
A Kohen (Shulchan Aruch 201)
An Avel
A Levi (The Mishna Berura 201:13 explains that this applies to making a hamotzei and giving tzedaka as well. However this is only in instances in which the Levi is on the same level as the Yisrael in terms of being a Talmud Chacham).
The Levush (quoted in the Piskei Teshuvos 201:3) says that in this generation there are no halachos of kedima by bentching being that it will create too many fights. Therefore, when there is a meal served at the home of a baal habayis he can choose who he wants to lead bentching and does not need permission from the Talmud Chacham, Kohen or Levi to pass over them favor of someone else.
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