Gemara

(Rav Yehudah): The judges who made decrees in Yerushalayim received stipends from the Shekalim brought to buy Korbanos.

Karna used to receive a Sela from both parties when he judged a case.

Question: It says "Don't take a bribe"!

Answer #1: That is only when a judge takes only from one party, lest it bias his judgment. Karna took from both parties, so he would be unbiased.

Rejection: Even a bribe to give an unbiased judgment is forbidden!

(Beraisa): "Do not take a bribe" does not discuss one who intends to acquit the guilty and convict the innocent. It already says "Do not pervert judgment"!

Rather, bribes are forbidden even with intent to acquit the innocent and convict the guilty!

Answer #2: Karna did not take the money for a bribe, rather for wages.

Question (Mishnah): If one receives wages for judging, his judgments are void.

Answer: That refers to one who takes wages for the verdict. Karna took Sechar Betelo (compensation for what he could have earned in the time he judged).

Question (Beraisa): If a judge takes wages to judge, this is repulsive, but his ruling is valid.

If the wages are for the ruling, the ruling is void! Rather, he takes Sechar Betelo, and it is called repulsive!

Answer: It is repulsive when it is unclear what he could have earned in the time. People used to pay Karna a Zuz to smell wine and evaluate it (how long it will be before it spoils), so his Sechar Betelo was clear.

When people would come to Rav Huna for judgment, he would ask them to get someone to draw water in his stead.

Kidushin 58b (Mishnah): If one was Mekadesh a woman with water or ashes of the Parah Adumah, she is Mekudeshes.

Contradiction (Mishnah): If one takes wages for a Mitzvah, the Mitzvah is invalid.

Answer (Abaye): One may take wages for the exertion of transporting and drawing the water. One may not take wages for sprinkling or sanctifying.

Bechoros 29a (Beraisa): "(Re'eh Limadti Eschem) Ka'asher Tzivani Hash-m Elokai" - just like Moshe taught Torah for free, we should do so.

Rishonim

Rif and Rosh (Sanhedrin 2a and 1:10): Karna used to receive a Sela from both parties when he judged a case. We conclude that he took Sechar Betelo. Karna used to receive a Zuz to smell wine and evaluate it. He requested the Zuz that he could have earned had he not judged. When people would come to Rav Huna for judgment, he would ask them to get someone to draw water in his stead. We permit Sechar Betelo only if it is clear, like this.

Rambam (Hilchos Sanhedrin 23:5): If one takes wages for judging, his judgments are void. This is if it is not evident wages. But if he was working and people came for judgment, and he said 'give me someone to work in place of me while I judge, or give to me the wages I will lose', it is permitted. This is if it is evident that he takes no more than Sechar Betelo, and they pay equally in front of each other.

Kesef Mishneh: Rav Huna would say 'get (plural) someone to draw water in my stead', i.e. he spoke to both of them together. Also, if one pays not in front of the other, perhaps he will suspect that the other paid more than him, or that only he pays and that it is a bribe.

Hagahos Mishneh l'Melech: Mutzal me'Esh cites the Mishneh l'Melech to say that if he took wages after judging, the verdict stands. Mutzal me'Esh says that the Gemara in Kidushin disproves this. (It did not answer that he took wages afterwards.) This is no disproof! Surely, the Mishneh l'Melech only said that the judgment stands. Surely one may not take wages afterwards - 'just like I (Moshe) taught for free, also you.' The Gemara asked why one may take wages, therefore it could not answer that he took wages afterwards! Beis Yakov (128) forbids promising to pay afterwards for testimony or judgment. If he paid, it disqualifies the verdict retroactively, but not testimony. I do not know his source to distinguish these.

Ran Kidushin (23a DH umid'Tanan): The Mishnah says that his judgments and testimonies are invalid, to teach that every one is invalid unless we know that he was not paid for that case. A Tosefta in Bechoros (3:5) explicitly says so about testimony, and the Yerushalmi says so about judgments

Rosh (Bechoros 4:5): The judges who made decrees in Yerushalayim received stipends from the Terumas ha'Lishkah. It was not Sechar Betelo, for they had no profession. Rather, they judged all the time, so they needed to take in order to eat. The Rambam says that if he did not take wages for a particular judgment, it is valid. This is reasonable, but if one is suspected, how can we know through witnesses that he did not take?

Ma'adanei Yom Tov (40): Perhaps witnesses did not leave his side from the time the litigants' argument began!

Poskim

Shulchan Aruch (CM 9:5): If one takes wages for judging, every judgment of his is void, unless it is known that he was not paid for that case.

Shulchan Aruch (ibid.): One may take Sechar Betelo. This is if all know that he takes only Sechar Betelo. E.g. he has a known job to do at the time he judges, he asks for the earnings he will lose while judging, and they pay equally. If it is not evident, e.g. he says 'perhaps I would have profited through buying merchandise or wholesaling', it is forbidden.

Beis Yosef (DH u'Mah she'Chosav v'Im): The Rosh (56:5) says that people came to Rav Huna while he was drawing water, therefore it was evident. If he says 'perhaps I would have profited through business', it is forbidden. If he would take more than what he lost, this is wages for judging, and the judgment would be Batel. If he forced one to pay the other, this is theft!

Drishah (10): There are three laws. If the judge was working at the time and it is evident how much he lost, he may take Sechar Betelo l'Chatchilah. If he has no job, but perhaps he could profit in a way that depends on others and occurs rarely, this is wages for judging. The verdict is Batel. If he has a job that is not well known, or he was not working now but he could if he wanted, it is repulsive to take Sechar Betelo, but b'Di'eved his judgment stands.

Bach (9): If a party paid the judge and said 'do not obligate me if I innocent', since he mentioned his innocence, this is a bribe. It must be returned. If each party paid without mentioning his innocence, even if he said 'in order that you will vindicate the innocent and obligate the guilty', this is wages for judging. The judgment is Batel, but the judge may keep the money. The Gemara says that if one cannot find a Rebbi to teach him for free, he should pay.

Rebuttal (Ritva Kidushin 58b DH Omar): Since the judgment is Batel, he did not do anything for them, so he must return the money!

Bach (10): The Rosh (56:5) says that whether the judge takes more than he would have earned, or the proper amount but it is not evident, his ruling is Batel. If so, when is it valid, but repulsive? Rather, whether or not he takes more, if he refuses to give the verdict without pay, this is wages for judging and it is Batel. If he gives the verdict but requests money, the verdict is valid, but it is repulsive if it is not evident what he would have earned. Even if they give extra, it is a mere gift; the verdict stands. One may refuse to make a compromise for free; the Isur applies only to judgment. However, both must pay equally and together; the Isur to tilt judgment applies also to compromise.

SMA (14): If he stipulated from the beginning, he receives the full wage he would have earned - "Efes Ki Lo Yihyeh Becha Evyon." If he did not stipulate, and after judging he requests evident Sechar Betelo, they need to pay only what one would take to be idle from his job, like one who returns an Aveidah.

Darchei Moshe (2, citing Ramban Kidushin 58b DH Ha): His verdict is Batel automatically, without an announcement that he is Pasul. However, if he returns the money, his verdict or testimony is valid. This is not like other Pesulim which require announcement, and Teshuvah (to return to Kashrus). Rather, Chachamim fined to invalidate his deeds as long as he takes wages.