A person who tries to increase compliance by inducing an individual to agree first to small request is using the technique known as
The question describes a persuasion strategy where an initial small request is made to increase the likelihood of compliance with a subsequent larger request. This specific technique is known as the Foot-in-the-door technique.
This technique relies on the principle of commitment and consistency. Once an individual agrees to a small, easy-to-fulfill request (the "foot in the door"), they feel a greater obligation or desire to remain consistent with that initial commitment. This makes them more likely to agree to a larger, related request that follows.
Therefore, the technique matching the description of starting with a small request to increase compliance is the Foot-in-the-door technique.