What you think a no will do
In chapter 3 I put off an objection. The yes doesn't only end a few seconds of tension, you said. It also saves you from what a no would have caused. She'd be hurt, she'd think you selfish, things would be cool between you, and you'd feel guilty for a week.
That's a forecast, made in about four seconds. Forecasts can be checked, and researchers have checked this kind.
Julian Givi and Colleen Kirk ran a series of studies on people turning down invitations to things like a meal, a match or an evening watching television together. They compared what the person declining expected with what the person who'd done the inviting said they felt. The decliners got it wrong in a consistent direction. They overestimated how angry the inviter would be. They overestimated how much the no would signal that they didn't care about the inviter, and how likely it was to cost them future invitations. Givi and Kirk say in so many words that this is part of why saying no is hard, and that it leads people to accept invitations they'd sooner refuse.
They also found a reason for the mistake. The person declining assumes the other will fix on the bare fact of the no. But inviters gave more weight than expected to what had gone through the decliner's mind. They thought about the other person's circumstances and reasons, as you would if a friend turned you down. You expect them to see a rejection and what they see is a busy person.
This fits an older finding. Kenneth Savitsky, Nicholas Epley and Thomas Gilovich had people commit or imagine small social blunders and public failures, and then predict how harshly observers would judge them. People expected harsher judgments than they got. The researchers' explanation was that the person who slips up is fixed on the slip. The observers take in everything else about them and the situation as well, and the slip is a small part of their view.
As for your own week of guilt, Daniel Gilbert and colleagues showed in six studies that people overestimate how long they'll feel bad after things go wrong. Their events were far bigger than a tombola. They included a break-up, a rejected job application and being turned down for tenure. People recovered faster than they'd predicted, because they didn't allow for how quickly the mind makes its peace with things. Carrying that over to the guilt after a refusal is my step, not theirs. But if people overestimate how long they'll grieve a job, I think it's likely you overestimate how long you'll brood over a neighbour's fair.
I should be honest about the limits of all this. Givi and Kirk studied invitations to enjoyable things, and a request for help isn't the same. Someone who needs a tombola run has a problem to solve, and your no leaves her with it. I still think the finding carries over, and here's why. You can check it against your own experience from the other side.
Think of the last time you asked someone for something and they said no. Perhaps you asked a colleague to swap a shift, or a friend to come to something. What did you feel? I'd guess a flicker of disappointment, then "fair enough", then you asked someone else. I doubt you concluded that they were selfish, and I doubt you remember it now without effort. You had a list of other people to ask, and so has your neighbour. You were one of fifteen doors to her, but the conversation felt like the only one happening in the world, because it was the only one happening to you.
There's an objection that I take seriously. "Some people do take it badly. My sister sulks for a fortnight." Yes. Some people do, and chapter 15 is about them. But notice how the habit treats everyone as though they were your sister. You give the mild neighbour, the reasonable colleague and the friend who'd never think twice about it the same automatic yes. You're paying to insure against a reaction that most of them would never have.
The unwilling yes is a trade made on a forecast, and the forecast is wrong in a known direction. It expects too much anger, too much judgment and too much guilt, lasting too long. None of this makes the four seconds comfortable. It does mean that what you're buying your way out of is smaller than it looks from inside them.