We're indebted to many researchers and thousands of salespeople for this one. It's been extensively field-tested.
It can be used in dodgy, manipulative ways, but you can use it honourably. The ethics depend on the context, so I'll have to leave the ethical issues to you to mull over.
It's the consistency principle, known to salespeople as the 'foot-in-the door technique'.
Here's how it works.
We don't really persuade people. They persuade themselves. But here's a way to influence their thinking.
'Put yourself in the other person's shoes' might be a cliched instruction, but it should be in your persuasion toolkit.
Make it a habit in your team.