When you get into a disagreement with someone, it can quickly escalate into an argument if preventive measures aren’t taken. Once it turns into an argument, there is very little you can do to resolve it, as both you and the other party involved are likely to be too heated to come to a rational conclusion.
So, to ensure that the disagreement remains a discussion, and not an argument, let the other party know that you consider them honest, upright, and fair. You will compel them to act in a fair manner and you will likely get the outcome you desire.
Make it clear that you understand how you have failed the other person.
Do not put the blame on them, no matter how much you think they are the one in the wrong.
Be unbiased and sympathetic.
Truly listen to what they have to say.
Tell them that you are impressed with how patient and fair they have been up to this point.
Let them decide how to resolve the situation.