Oddly Wired
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influence

You agree to big requests to stay consistent.

A 1966 study found that people are more likely to accept a large favor if they first agreed to a small one.

Once you commit to a small action, you adjust your self-image to be the type of person who helps. Declining the second, larger request would create internal conflict between your new self-identity and your refusal, so you comply.

You are not helping; you are maintaining your own image.

Where this comes from

Study
Freedman and Fraser, 1966
What the check found
The study successfully demonstrated the effect as claimed. While the 'self-image' explanation is a common theoretical framework, it is just one of several competing psychological explanations for why the technique works.
Confidence
Well replicated

Related

One of these every day, and every one names the study it came from. When a finding is contested, it says so.