(Shmuel): If two people judged (instead of three), their judgement is valid, but they are called "a brazen Beis Din".

(R. Yochanan and Reish Lakish): Their judgement is not valid.

Question (Mishnah in Maseches Bechoros): If a person was judging a case and he found the guilty party innocent or the innocent party guilty or he declared a tahor item to be tamei or a tamei item to be tahor, his judgement is valid, but he must compensate from his own money. (This shows that the judgement of an individual is valid.)

Answer (R. Ba citing R. Abahu): It refers to when the litigants told the judge, "We accept you as if you were three judges".

What was the case? If he made a mistake and decided based on his own judgement (and there was no explicit source to answer it), how could you say that the judgement is valid (when they did not accept him upon themselves)? If he made a mistake over an explicit law, how could the judgement be valid and he must pay from his own property? (The judgement should be cancelled!)

So R. Ba citing R. Abahu explained that it was when they told the judge, "We accept you as if you were three judges". And they said that it was on condition that he judges them according to the Torah and he made a mistake and instead he just used his judgement. He must pay from his own property, since he was brazen enough to judge a Torah case alone.

As the Mishnah (in Pirkei Avos) teaches - one should not judge alone, as the only One who judges alone is Hash-m.

(R. Yehudah ben Pazi): Even Hash-m does not judge alone, as the pasuk says (Melachim I 22:19), "and all the host of heaven were standing by Him on His right and on His left" -these ones tipping to the side of merit and these to the side of liability.

Even though Hash-m (therefore) does not judge alone, but he seals it alone, as the pasuk says (Daniel 10:21), "Indeed, I will tell you what is inscribed in a true writing" (and truth is the seal of Hash-m).

(R. Yochanan): Hash-m will only do something in His world after consulting with the Heavenly Beis Din. Why is this? Because the pasuk says (Daniel 10:1), "and the word was true, and for a long time"

When is truth Hash-m's seal? When He consults with the Heavenly Beis Din.

(R. Elazar): Wherever a verse says the words "and Hash-m" - it refers to Him and His Beis Din, and the most explicit source is (Melachim I 22:23), "And Hash-m spoke bad about you"

Question: What is the seal of Hash-m?

(R. Baybei citing R. Reuven): Truth.

Question: What is truth?

Answer (R. Bun): That He is the Living G-d and the eternal King. (The letters of emet - truth are Alef-Mem-Taf - which stand for Elokim Melech Tamid - G-d, King, eternal.)

(Reish Lakish): The letter Alef is the beginning of the alphabet, Mem is in the middle and Tav is at the end - to teach you that "I am Hash-m the first, who did not receive from another and aside from me there is no god; as I have no partner and I am the last, that I will not give it to another.

R. Ba and R. Binyamin bar Yefes were being judged before R. Yitzchak and R. Binyamin won the case.

R. Ba came and wanted to complain to R. Ami that R. Yitzchak was judging alone. R. Ami told him that if an expert judge wishes to judge alone, he may.

R. Abahu was sitting and judging alone at the gates of the city of Kisarin. His students said to him, "Didn't you teach us that one may not judge alone?"

(R. Abahu replied): Since you see that I am judging and litigants are still coming to me, it is assumed that they accepted to follow my ruling nevertheless.

Support (Beraisa): When can an individual not judge? When the litigants did not accept him as if he was three judges; but if they did, he may judge alone.