Mr. Wu recognizes this difference, and he says he wants to use the lieutenant governor’s job as a pulpit, to become the state’s de facto public advocate, particularly in support of consumer issues, Internet access and economic development zones.

Mr. Cuomo chose Ms. Hochul this spring to balance his ticket with a conservative woman from upstate. Ms. Hochul now supports his gun control bill, but when she ran unsuccessfully for re-election to Congress in 2012, her campaign featured the endorsement from the National Rifle Association. The N.R.A. said at the time that she had “a proven record of defending the Second Amendment.”

She also boasted repeatedly that she had voted many times against “Obamacare.” She strongly opposed allowing undocumented immigrants to have drivers’ licenses. And during her short time in Congress, environmentalists criticized many of her votes, including those to repeal emission standards for cement manufacturers and to allow fewer controls on open pit mines and other polluting industries.

She undoubtedly embraced those views to try to win re-election in a district that had become a stronghold for Republicans. But her willingness to shift politically does not suggest she would offer any kind of independent judgment. Nor does her record give any real clue about what would happen if she took over as governor. In the meantime, she has promised to “support the administration.”

Although he lacks time in politics, Mr. Wu has an impressive record in the legal field, particularly in Internet law and policy. Widely known for coining the phrase “net neutrality,” he has been an adviser to the Federal Trade Commission as part of his efforts on behalf of consumers to keep the Internet from “becoming too corporatized.”