If you’re trying to sell something to someone, you can sometimes get a metaphorical foot in the door by getting them to agree to a small thing before going after the big one. A smaller agreement sets up the relationship, and going from $25 to $80 is a lot less intimidating than going from $0 to $80.
But sometimes, instead of going for the foot in the door, you might go for a door in the face.
I don’t know if they exist where you are, but in my neighborhood we used to get teens trying to sell small items or candy door-to-door. Sometimes, they’d open with a big request instead of a small one — maybe a year’s subscription to a magazine. When we said no, they’d ask instead for maybe just a small purchase of a single candy bar. Since they didn’t push it, and a dollar candy bar seems almost negligible compared to a magazine subscription, the temptation to make their sad face go away was much more tempting.
That’s a door in the face. If you swing for the fences, you might make it, but if you don’t you still seem unusually reasonable by offering a much smaller counteroffer. Then your customer feels like the reasonable thing to do is accept it.
Robert Cialdini writes about a similar door-in-the-face experience in his book Influence. It’s a quick read, with a lot of great stories about identifying and resisting social influence techniques.