A few weeks ago, I received a phone call from Cancer Research UK telling me about their organization followed by a request to make a small donation... A few days later I got another call....
Agreeing to the first small request increases the likelihood of you subsequently complying to the second, larger request. This technique works only if the second request is consistent or has a similar nature to the first one, for example asking for a donation both times. Since you have already invested into this particular situation, it causes a change in your feelings towards becoming the kind of person who complies with such requests. It creates a new self image that you never thought you possessed, caring about the event or cause. Therefore when asked for another donation, instead of simply shutting off, you are more open to agree to the larger request than you would have been, if you were not asked before.
This form of compliance has stemmed from Freedman & Frasers' (1966) "Foot in the Door Technique". They show that a small request paves the way for compliance to a larger request. In their experiment they asked people to sign a petition or place a small card in their home windows or cars about keeping California beautiful or safe driving. When asking the same people after 2 weeks for a larger request, adherence was higher compared to people who were previously not asked for the small request, regardless of it being quite invasive a request.
Table 1 indicated that carrying out a small request increased the likelihood that the subject would agree to a similar larger request made by the same person.
Table 2 shows that this effect was quite strong even when a different person made the larger request and they were dissimilar in nature showing the high rate of compliance when following the "Foot in the Door Technique".
Freedman, J. L., & Fraser, S. C. (1966). Compliance without pressure: the foot-in-the-door technique. Journal of personality and social psychology, 4(2), 195