1)
How does a lottery cease feuds?
1.
R. Yonah: One will not desire his colleague's share, for he will say that he got it from Hashem - "b'Cheik Yutal Es ha'Goral ume'Hashem Kol Mishpato" (16:33).
2.
Malbim: If you have a Safek and argument about who will take which portion, the lottery ceases the feud.
2)
What Atzumim does it separate?
1.
Rashi: These are the litigants, like "Hagishu Atzmoseichem" (Yeshayah 41:21), 'Shenayim she'Nis'atzmu b'Din' (Sanhedrin 31a). Because their feuds are Atzumos (awesome), they are called Atzumim. It is an expression of strength or of sealing, like "v'Otzem Einav" (ibid., 33:15).
2.
Malbim: Each litigant thinks that his claims are great and Tzedek is with him.
