Final answer:
The man used the foot-in-the-door technique, a persuasion strategy where an individual agrees to a small request, which increases the likelihood they will agree to a larger request later.
Step-by-step explanation:
The technique the representative used to persuade Sylvia to place a sign on her lawn is known as the foot-in-the-door technique. This is a method of persuasion where a small request is made with the intention of getting the person to agree to a larger request later on. By initially asking Sylvia for a large request, a 30-foot sign, and then scaling down to a smaller sign, the representative effectively shifted her perception of the requests, making the smaller sign seem more reasonable. This approach leverages the principle of consistency, where once an individual agrees to a small action, they are more likely to agree to further actions to maintain their self-image as helpful or consistent.