Isn’t this also illegal? He promised consideration (e.g. an entry in a sweepstakes) in exchange for specific performance (signing a petition), and is now claiming that the consideration he promised was not given, after people had already performed in accordance with his stated requirements. How is this different than if I tell you I’ll give you a lottery ticket if you give me $1, then after receiving the dollar, I decline to give you the ticket?

For reference: https://www.law.cornell.edu/uscode/text/52/10307

©False information in registering or voting; penalties Whoever knowingly or willfully gives false information as to his name, address or period of residence in the voting district for the purpose of establishing his eligibility to register or vote, or conspires with another individual for the purpose of encouraging his false registration to vote or illegal voting, or pays or offers to pay or accepts payment either for registration to vote or for voting shall be fined not more than $10,000 or imprisoned not more than five years, or both: Provided, however, That this provision shall be applicable only to general, special, or primary elections held solely or in part for the purpose of selecting or electing any candidate for the office of President, Vice President, presidential elector, Member of the United States Senate, Member of the United States House of Representatives, Delegate from the District of Columbia, Guam, or the Virgin Islands, or Resident Commissioner of the Commonwealth of Puerto Rico.