Chris was the lead hostage negotiator for the police, was part of high stake negotiations with kidnappers and large threats to society.
Empathise with their situation first and then get them to empathise with your situation.
Sincere empathy will make them feel like they were treated fairly; this is why psychiatrists can get the guard down from a patient by just listening to them.
1. Get them to agree with you
You have to agree with something in terms of a compliment if you notice they have a passion for something in the argument. Listen to their speech or body language to look out for a deep emotion being shown while they are talking a certain topic and use that for them to agree with. Once theres an agreement of such it would be easier to put across your points as their guard will then be down. Arguments or meetings like this will make both parties feel tense which causes the guards to go up.If you can get them to say "That's right" in this stage then you have made them feel heard. Chris says a negotiation does not start without them other side saying "That's right".
A good way of getting them to agree with a statement would be to use sentences like "It seems like you're really concerned about..." or "It sounds like ... is really important to you" to agree with them. If you got this wrong and they get defensive, emphasise that you did mention it seems like, not that they are.
2. Get them to empathise with you
Use calibrated questions, these are open ended questions that start with "how" or "what". This will get their thoughts off them and focus on you by problem solving the question. A way of asking this would be "how am I supposed to do..." if you have to start paying more rent then possibly "... pay that much when I earn less than what is required". Common responses to these types of questions will make the other side to raise/lower the demand to help or come to an agreement from both sides. If they only raise/lower the demand then respond with a different calibrated questions, thank them for their generous offer but then again ask them a calibrated question with another point e.g. "Sorry, I don't see how I am supposed to pay that much when the houses nearby cost less than my budget".
When you want something out of a negotiation don't get the other side to disagree with you, instead use empathy to get them to agree to you first and then ask open ended questions to get them to empathise your position.