Curtis Gans, director of the Center for the Study of the American Electorate in Washington, said the idea of a voter lottery had come up in other states, but he could not recall any moving forward with it. And he’s glad.

“People should not go vote because they might win a lottery,” Mr. Gans said. “We need to rekindle the religion of civic duty, and that is a hard job, but we should not make voting crassly commercial.”

Editorial writers, bloggers and others have panned the idea as bribery and say it may draw people simply trying to cash in without studying candidates or issues.

“Bribing people to vote is a superficial approach that will have no beneficial outcome to the process, except to make some people feel good that the turnout numbers are higher,” said an editorial in The Yuma Sun. “But higher numbers do not necessarily mean a better outcome.”

The initiative calls for financing the award through unclaimed state lottery prize money, private donations and, if need be, state money. A spokeswoman for the Arizona Lottery Commission said its unclaimed prize pot fluctuated greatly, but it now stood at more than $1 million.

Mr. Osterloh said private donors could add their own incentives, like a car dealership offering a new car to a random voter.

But he may be getting ahead of himself. There is the not-so-small matter of whether such a voter lottery is legal.