However, Ohio has not hosted a national political convention since 1936, when it boasted 26 electoral votes as the nation's fourth most populous state. Today, located in the slow-growing Midwest, Ohio has 18 electoral votes and is on track to lose one more by 2020.
The three cities, compared to some of the others that submitted bids, also may have a somewhat weaker network of hotels and transportation.
In interviews, Republican National Committee Chairman Reince Priebus and other officials have stressed the importance of $55 million in private fundraising, as well as hotel space and creating a good "delegate experience" in choosing a convention city.
Downplaying swing-state status, they pointed to 2012, when Democrats picked Charlotte, N.C., and Republicans selected Tampa, Fla.; neither party won its respective host state.
"As far as Republicans, the decision will be based more and more as a business decision," said Steve Scheffler, Iowa's Republican National Committeeman and one of two Midwest representatives on the nine-member RNC selection committee, citing a longer-term shift from decisions based primarily on political considerations. "It has to be about what's best for the party."
Ohio has added political complexities: Its core voters are older and working-class whites at a time when the Republican Party is working to attract younger minority voters.
Enid Mickelsen, who chairs the selection committee, stressed that a city's bid must meet the "four corners" of the RNC's request involving business factors: The city must raise $55 million in private funds; have a convention area with a capacity of at least 18,000; be able to supply 16,000 hotel rooms, plus 1,000 suites; and provide adequate accommodations to media.
When those requirements are addressed, other factors may be taken into consideration, including swing-state status and a candidate's ability to appeal to a state's voters and demographics, she said.
"We are encouraging everyone to review the written submissions and come up with an idea of what is most important," Mickelsen said. "You're looking at the totality."
The cities vying for 2016 include one other Midwest location Kansas City as well as four in the South and West, which boast emerging Hispanic voting populations: Dallas, Denver, Phoenix and Las Vegas. Las Vegas is presumed a front-runner because of its 150,000 close-in hotel rooms and the backing of major donor Sheldon Adelson.
At stake are a national convention that brings in as many as 45,000 visitors and up to $200 million for the local economy
Since 1980, the Midwest has been host to a national convention just three times, compared to four in the West, five in the Northeast and six in the South.
"With the exception of Chicago, the Midwest is flyover country, so in Ohio there is a general cynicism. Politicians talk about Midwest values, Midwest sensitivities, and then you don't see them for another four years," said Ned Hill, a dean at Cleveland State University.
"It's almost like Charlie Brown, who doesn't get a shot at the convention football," Hill said.
Cleveland was a convention runner-up for Republicans in 2008 and Democrats in 2012, bested by St. Paul, Minn., and Charlotte.
Cities don't always come out ahead after holding a convention. Democrats ended theirs in Charlotte millions in debt on a loan secured by Duke Energy, while Philadelphia grappled with lawsuits for years after clashes with protesters during the 2000 GOP convention.
Still, officials in Ohio say the weeklong crush of national media attention offers a chance to boost economic development.
A wild card is basketball and hockey playoffs that could run into June. The RNC wants to hold its convention between late June and mid July 2016 and needs about six weeks in advance to set up. Of the eight cities, only Cincinnati, Las Vegas and Kansas City do not have sports teams that could pose schedule conflicts.
Officials in Cleveland and Columbus say they will also apply to host the 2016 Democratic National Convention.
Columbus Mayor Michael Coleman, a Democrat, is making a first-time bid for a national convention that he says will show the world the growing metropolitan area has "swagger"; he touts Columbus as a swing city that could tilt Ohio in a candidate's direction.
Cincinnati, which has the support of Republican House Speaker John Boehner, says it is home to some of the nation's most generous GOP donors.
In Washington, D.C., to give his pitch, Cleveland's Democratic mayor, Frank Jackson, made clear his city was ready to finally host a convention.
"We went at this hard eight years ago," Jackson said, stressing that Cleveland had learned its lesson and submitted an improved 300-page bid that highlighted the city's fresh supply of hotels and restaurants. "This is the year to win it. We deserve it."
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