Questions: Is a judge permitted to take a payment from a litigant with the stipulation that the judge be as fair as he possibly can?
The Torah prohibits bribes of any kind because it will ultimately have an affect on the way that the judge views the case.
It is even forbidden to give a bribe that comes with the stipulation that the judge should conduct a fair trial.
The Gemara in Ketubot says that a bribe is forbidden because it makes the judge empathize with the litigant and feel somehow that they are connected to one another.
As soon as a man receives a gift from another he sees the giver as an extension of himself and nobody can see himself as guilty.
The Hebrew word for bribe is shochad. according to the Gemara it means shehu chad - he is one with you.