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From Bilvavi Mishkan Evneh (vol 1):
Chazal have said (Sanhedrin 7a) that a judge must imagine that a sword is placed between his thighs (and a small error would be dangerous).  Rav Yisrael Salanter zt”l has said that this applies to each person, for everyone is a judge over himself.

What this means is that, IMHO, just like a dayan’s job is more than just saying that one person is right and one person is wrong.  The job is really becoming a k’li (vessel) for emes (truth).  Our job is to stick to the emes.  It is much easier to judge others.  That same scrutiny with which we view our neighbors has to be applied to ourselves.