Bava Metzia, Chapter 3, Mishnah 3. Two cases are brought in this Mishnah, and the ruling in both is identical. Both deal with a person who wishes to do the right thing and rectify his action, but does not know to whom exactly he owes the money:
The robber: A person who committed a transgression and robbed money, and now wishes to return it to its true owner - but does not know which of the two is the victim.
The negligent watchman: A watchman who was negligent in his responsibility, and now wishes to resolve the matter - but does not know to which of the two he owes the money.
The parameter of the case must be emphasized: there is no one here claiming money from him. The man committed an improper act, and now voluntarily wishes to fulfill his obligation towards Heaven - to rectify his account Above so that he will not be punished for his actions. The only problem is that he does not know to whom he should give the money he owes.
The language of the Mishnah:
"Amar lishnayim: Gazalti le'echad mikem maneh ve'eini yodea eizeh mikem" - He says to two people that he robbed one of them of a maneh (one hundred dinars), and he does not remember or is unsure which of the two it is, but he wants to return the money.
"O aviv shel echad mikem hifkid li maneh ve'eini yodea eizehu" - This is the second case, in which the halachah is identical in principle: one who served as a watchman says that the father of one of the two deposited a maneh with him for safekeeping, and he does not know which one it is.
"Nosen lazeh maneh velazeh maneh, shehodah mipi atzmo" - Since his intention is to certainly fulfill his obligation towards Heaven, he gives a maneh to each of the two people. It turns out that he loses an additional maneh - the maneh he took and is returning, plus a second maneh - and this is to ensure that the one harmed by his negligence or robbery will receive his full amount back.
The novel teaching of the Mishnah:
To understand the significance of this law, we must compare it to other cases. If the two people were claiming the money from him, and each one claims, "The one hundred is mine," what would he have to do? In a regular case, where the person did not do anything improper and no guilt hangs over him, he could say: "Here is the one hundred before you, work it out between yourselves," and a beis din intervening in the matter would divide the sum between them half and half due to the doubt.
However, the case of our Mishnah is not like this. Here the person committed an improper act - either he was negligent in his duty as a watchman or he was a robber - and therefore the Sages imposed a penalty upon him. They say to him: True, had you not committed an improper act, you could have returned the one hundred and left the two men to work it out between themselves (since one of them is certainly lying), but since you acted improperly - whether as a negligent watchman or as a robber - you are penalized to pay twice.
In practice, in a case where both of them make a claim, each of the two who claims he is owed the one hundred is required to swear that the money is his, for one who exacts money from his fellow and does not have absolute proof - is obligated to take an oath. After both have sworn, he pays both of them. This double payment is a penalty and a punishment for having acted improperly to begin with; had he not been negligent, he would not bear the responsibility and would not pay twice.
Why the Mishnah specifically stated "the father of one of you":
Our Mishnah deals with a person who wishes to do the right thing and rectify the situation even according to the laws of Heaven, and therefore it specifically used a case where the father of one of the two deposited the money with him. For had it been the two men themselves who had deposited it, each of them would know the truth: when he says, "I do not know which of you," one of the two should have said, "I know that it is me." And in such a situation he would not be considered completely negligent, and therefore he would not be obligated to pay twice.
But in the case before us, since he was negligent, he is penalized, and he must pay twice if he wishes to fulfill his obligation towards Heaven - and this is true even if those men do not swear that the money belongs to them.
In summary: The Mishnah presents two cases - a robber and a negligent watchman - where a person voluntarily seeks to fulfill his obligation to Heaven but does not know to which of the two men he owes the money. The ruling is "noten lazeh maneh velazeh maneh, shehodah mipi atzmo" - he gives a maneh to this one and a maneh to that one, since he confessed on his own: because he acted improperly, the Sages penalize him with a double payment, and he cannot settle for placing the one hundred before the two of them to sort it out between themselves. We also discussed the reason the Mishnah specifically used the case of a deposit made by the father of one of them - so that it would be a case where neither of the two men knows the truth for certain.