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.

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.

Jeff Hatch-Miller, executive director of the Arizona Lottery, said he understands winners’ desire for privacy, but he argues they are essentially entering into a large contract with the government that is public. Others argue that appearing at a news conference helps defuse media interest because the winner is available to answer questions that satisfy the media’s interest in telling their stories.

In Michigan, Republican state Sen. Tory Rocca pushed a lottery bill that allows winners to remain anonymous. It didn’t pass, but in arguing for it, he cited cases where lottery winners were shot and killed because of their newfound wealth.

A Florida woman was convicted last month of first-degree murder after she befriended a man who won a $30 million jackpot in 2006. Prosecutors said she took control of his assets, killed him, buried him in her yard and poured a concrete slab above the grave.

An effort in New Jersey by Democratic Sen. Jim Whelan took a middle ground between public release and privacy, calling for a one-year delay in releasing winners’ names. It also didn’t make it out of the Legislature last year, but he said he’ll keep pressing to get it passed.

Whelan said a one-year delay would give winners a chance to adjust while still keeping the public disclosure lotteries say they need. However, Whelan said he doesn’t really buy the agencies’ arguments for public disclosure.

“I’m not sure how many people are spurred to buy a lottery ticket because they see a picture of someone in the paper holding up a big check - and I don’t think people don’t buy a ticket because they think the whole thing’s fixed,” Whelan said.

Of 44 states participating in Powerball and 33 in Mega-Millions, only Delaware, Kansas, Maryland, North Dakota and Ohio allow blanket anonymity, said Chuck Strutt, executive director of the Multi-State Lottery Association, which oversees the games.

“Obviously, it is a law that is designed to ensure an open and transparent process, so that the public can be ensured that insiders are not winners,” Strutt said. “But in today’s world, most of us can understand the wish to remain anonymous.”

The most famous modern lottery fraud case happened in 1980 when Pennsylvania Lottery district manager Edward Plevel and TV announcer Nick Perry were convicted of fixing the result of the Daily Number drawing.

Authorities found that some of the ping pong balls used in the game were injected with paint to make them too heavy to float up the winning slots. The result paid $3.8 million, a record at the time, and eight people involved in the fix won a total of about $1.2 million.

Former Missouri child services worker Sandra Hayes shared a $224 million Powerball jackpot with a dozen co-workers in 2006 and said she understands the push for anonymity.

Hayes said she received many requests for money or to make investments, both at work (she kept her job another month) and at home, where she’d find people waiting on her porch. Her lump sum payout after taxes was more than $6 million.

Even if people are allowed to remain anonymous, it’s often inevitable that their identities will become known.

Steve Thornton, a lawyer in Bowling Green, Ky., has helped two big lottery winners shield their names through corporations despite rules in his state that require disclosure of winners. Even though they were kept out of the public eye, one winner couldn’t stay hidden.

“It was not many months later that lots of people knew who won, even though it was not released, because of their gifts and their spending.” Thornton said.