Did anyone ever convince you by overwhelming you? Probably not. You may have kept quiet or avoided the discussion, but you probably stuck to your point of view or stayed by your opinion. Convincing someone by pushing or arguing often has the opposite effect.
It is much smarter and more effective to do things differently. Listen to the other person with respect. Let them give their opinion first. And listen sincerely to this opinion, without going on the defensive. Even if you don't agree with this person or if you have a different vision.
Research shows that using the same reasoning as the person you are trying to convince is much more effective than using another one.
For example, if the other person applies a logical reasoning, use logic yourself. If someone is more likely to make decisions based on emotions, it is better to use an emotional argument to convince.
Take for example the fact that you want to convince a customer to consider you as their supplier. They have been working with their current supplier for 10 years and want to keep it that way because the cooperation is pleasant.
Because 'pleasant cooperation' is more of an emotional feeling, there is little point in launching a logical argument: "Switching to our product will reduce production time by 10%". This will probably not find much resonance.
Instead, you could say, "I fully understand. We try to provide that same level of support and trust to our customers. That's why we want our best account manager to look after your business".
If you really want to convince others, it is especially important to understand the needs of these people. The SCAN method is extremely effective in this respect.
In this video you will discover the 4 steps of the SCAN-technique to convince others.
More information: Training Persuasive Communication