Based on my personal experiences, primarily in sales roles, I have synthesized four techniques that will enable you to persuade other person to change their mind.
Conduct an interview
People often assert a position and then dig in. Asking open-ended questions with the notion of understanding the underlying sentiments behind a position will often lead to mutually agreeable situation. For instance, you and your spouse disagree on vacation plans: One wants to go camping and other prefers a nicer hotel. Asking questions as, what’s important about camping? What do you love about it? Will you rather have separate camping trip with friends? This might lead to a good compromise solution with vacation split between camping and hotels
Re-frame the debate
Find a way to recast the subject at hand so that the person is prompted to think about things differently. Most people sometimes get lost in proverbial trees and loose the vision of the forest. Down at the tree-level, the dominant psyche is driven by fear or scarcity. Re-framing and painting a holistic vision, often leads to new ways of the thinking about a problem that will likely make a long-term impact.
Point holes in your own argument
If you are up-front about drawbacks in your argument, it sends a signal to other person that you understand different facets and complexity of the argument and that you are honest. This helps you gain trust and credibility, which is crucial in having other person be patient and listen to your argument with all sincerity.
Make it their idea
The goal is to make the other person believe that it was his idea. It’s much easier said than done. The process involves planting clues, so that the other person can reach the conclusion you want them to reach (your idea) without you explicitly laying it out to them and hence, make them believe that it was their idea.
The key is to be patient, because if you rush through your “clues” it will be obvious. If you take it slow, the idea will form naturally in their mind all by itself. It’s akin to surfing, where you patiently wait for the wave, and once you are into the wave, keep on paddling and the wave will automatically carry you. Or, as in Soccer, patiently building an attack by keeping the ball rolling around the defense and wait for that break.