Bava Metzia 2 - Two people are holding on to a tallith
If two people come to court, holding together a garment by its fringes and each one claiming that he found this garment first - how is the court to decide this matter? Being that there are no witnesses, the court suggests that they should both take an oath. Each one will swear that he owns at least half of the garment - and then they can divide or sell it and split the money.
They should have no problem taking this oath: since they claim to own the whole thing, they surely own half. If both were to swear that each owns the whole thing, it would sound like contradictory oaths.
A similar case is when two people bought an object, but one bought it first, and the other just forced the money into the hands of the seller. Since the seller does not remember who did what, they will have to take the same oath.
Both cases are needed. For the found garment, the one who grabbed it later can rationalize thus: "The other fellow just found this garment, I am making him lose nothing by getting a half of it!" And in a store, one can say, "I paid! Let the other fellow go and find it in another place." Knowing that one will have to take an oath, he will be hesitant to apply such self-justifications.