PHOENIX — When two winning tickets for a record $588 million Powerball jackpot were claimed from the Nov. 28 drawing, the world focused on the winners.

A Missouri couple appeared at a press conference and held up the traditional giant-sized check. The Arizona winner, however, skipped the press conference where lottery officials announced last month that someone had claimed the second half of the prize.

The differing approach to releasing information on the winners reflects a broader debate that is playing out in state Legislatures and lottery offices nationwide: Should the winners’ names be secret?

Lawmakers in Michigan and New Jersey think so, proposing bills to allow anonymity because winners are prone to falling victim to scams, shady businesses, greedy distant family members and violent criminals looking to shake them down.

Lotteries object, arguing that publicizing the winners’ names drives sales and that having their names released ensures that people know there isn’t something fishy afoot, like a game rigged so a lottery insider wins.

When players see that an actual person won, “it has a much greater impact than when they might read that the lottery paid a big prize to an anonymous player,” said Andi Brancato, director of public relations for the Michigan state lottery.

Holly Armstrong, spokeswoman for the South Carolina Education Lottery, said no privacy policy or law changes currently are in the works.

Now, winners complete a claim form before they collect prize money. They can agree to allow their name and likeness to be by lottery for publicity by checking a box on the claim form. If they don’t agree to publicity, the lottery won’t use or release their information, Armstrong said.

But, the lottery is a state agency subject to the state’s Freedom of Information law. If someone submits a request under the law for information on winners, the lottery must comply, she said. But, she added, the lottery doesn’t get very many of those requests.

Most states require the names of lottery winners be disclosed, albeit in different ways. Some states require the winner to appear at a press conference, like Missouri winners Mark and Cindy Hill did on Nov. 30.

Arizona and other states allow winners not to appear in public, but their names can be obtained through public records laws. The Arizona winner, Matthew Good, was not identified at the news conference a week after the Hills’ came forward, and has not given interviews or appeared in public.

When news media including The Associated Press learned of his name through records requests, TV crews and reporters flocked to Good’s neighborhood to get reaction from the winner of a lottery that captivated the nation.