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Republicans also argue that the plan would favor large states and major metropolitan areas, where candidates are able to reach more voters with their advertising dollars. Since most big cities tilt leftward, the system would be more likely to pull candidates to the liberal end of the spectrum, they say.

Under the current system, say Democrats, candidates often end up concentrating their resources on the handful of close “battleground” states, which means that most voters receive little of the candidates’ attention.

In the 2008 election, said Mr. Koza, two-thirds of the campaign dollars were spent in six states, and 90 percent was spent in 15 states.

“When you’re in a non-battleground state, which is two-thirds of the states, you tend to get ignored,” Mr. Koza said. “People are figuring out that in most states, they don’t count. If anything, this presidential election reminded them that they don’t count.”

He predicted that a popular-vote system would force candidates to run national campaigns in which their focus is spread evenly through all 50 states. Opponents say that it’s more likely the campaigns would end up concentrating on places where the voters are, such as Los Angeles and New York City, and Republicans would take their chances with swing states in that case.

“Those swing states can actually be quite diverse,” Mr. Mitchell said. “It’s a slam-dunk that the 10 battleground states are more representative of the broad national interest than the 10 biggest metropolitan areas.”

Despite that argument, such current battleground states as Michigan and Colorado have had the measure go at least as far as approval by one chamber during a legislative session.

“That shows this isn’t kryptonite in battleground states, either,” Mr. Koza said. “This thing seems to have support all over the country.”

National Popular Vote was started by Mr. Koza, a self-professed elections geek who published an Electoral College board game in 1966. He went on to serve as founder and chairman of Scientific Games, where he co-invented the rub-off lottery ticket.

He and Barry Fadeem, NPV’s president and an attorney based in Lafayette, Calif., got their feet wet in legislative politics by lobbying on behalf of state-run lotteries. Mr. Koza now teaches courses in medicine and engineering at Stanford University as a consulting professor.