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Now that Robert J. Duffy has decided he will not stick around for another term as lieutenant governor, Gov. Andrew M. Cuomo and his top advisers must solve equations posed by New York’s political calculus.

Should they strive to balance the ticket with a woman or a minority to run with the Italian-American male governor?

Would a Western New Yorker help in the one region Cuomo failed to carry in 2010?

Or maybe from the downstate suburbs, where a Republican concentration always poses a challenge?

Several names already are being floated as a possible running mate, leading with Buffalo Mayor Byron W. Brown. Other locals mentioned include former Rep. Kathleen C. Hochul and Leecia R. Eve, a Cuomo administration veteran who is now a Verizon executive.

But other Democratic figures from across the state also are entering the picture, including Assembly Majority Leader Joseph D. Morelle of Rochester.

In addition, county executives, always desired because of their management experience, are mentioned. They include Suffolk’s Steve Bellone and Ulster’s Michael P. Hein.

Then there’s Onondaga County Executive Joanie Mahoney, a Cuomo favorite who would be the wildest of wild-card picks as the ultimate political balancer. She’s a Republican.

Duffy, 59, fulfilled the expectations of just about every Albany observer when he announced Thursday he would not run for a second term, adding another chapter to a string of seconds-in-command bailing out after a first term, dating from Mary Ann Krupsak leaving Gov. Hugh L. Carey in 1978.

Duffy, former mayor of Rochester, told the Rochester Democrat and Chronicle that the job took its toll on him, both physically from traveling the state in a car with a bad back and leg pain, and the time away from his family.

“It’s a life decision, not a political one. I have thoroughly enjoyed my four years,” Duffy told the paper.

Cuomo said Thursday that he owes Duffy “a tremendous debt of gratitude.”

“Bob has not just been a great partner in governing our state – he has also been a true friend,” the governor said. “I have said repeatedly that asking Bob to be New York’s lieutenant governor was the first and best decision I made since running for governor, and that statement remains true today.”

Now the Cuomo team must prepare for this fall’s election and the expectation of a second term, with scrutiny focusing on several candidates:

Brown – As mayor of New York’s second-largest city, Brown has a good portion of today’s political speculation swirling around him. He always has been considered close to Cuomo, cooperates with him politically, and reigns over the “capital” of the western region that favored Republican Carl P. Paladino in the gubernatorial election of 2010.

“He wants it,” said one local Brown ally who asked not to be identified.

Thursday, the mayor issued a statement about Duffy’s departure without addressing any questions about his interest or non-interest in the ticket’s second spot.

“I have a very good relationship with both Gov. Andrew Cuomo and Lt. Gov. Robert Duffy. I wish Lt. Gov. Duffy well,” Brown said. “Ultimately any decision regarding the next lieutenant governor will be made by the governor.”

Brown is considered an attractive candidate after his third consecutive mayoral victory featuring a campaign that constantly highlighted Buffalo’s “progress.” And with only one mayor in Buffalo history (James D. Griffin) successfully winning a fourth term, many observers say it is only natural for Brown to look beyond City Hall.

As an African-American, Brown would offer racial diversity to the ticket. And he could serve as an attraction to some black voters who still may be wary of Cuomo after his primary challenge to Democratic gubernatorial candidate H. Carl McCall – also African-American – in 2002.

Brown, 55, is also no stranger to Albany as a former state senator who is viewed as capable of filling the governor’s chair should the need arise.

Hochul – The former Erie County clerk who served a brief term in Congress is considered a formidable campaigner with the ability to attract Republican votes. She barely lost to Chris Collins in 2012 in the state’s most Republican congressional district.

Some who know her well say Hochul, 55, would like to hold public office again. But she is also settling in as vice president for government relations at M&T Bank, where friends say a hefty salary might deter a return to elective office.

“He has not called her, and she just doesn’t see it happening,” one Hochul associate said this week.

Her husband, U.S. Attorney William J. Hochul Jr., is also generating speculation as a candidate for a vacant federal judgeship in Buffalo.

Eve – At 49, the daughter of former Deputy Assembly Speaker Arthur O. Eve is also thriving in the private sector as vice president for government affairs at Verizon, following a stint in Cuomo’s economic-development office. Those who know her well say she is happy at Verizon while splitting time between Buffalo and New York City.

The Harvard Law School graduate also served as an aide to then-Sens. Joseph R. Biden Jr. and Hillary Rodham Clinton. Though Eve’s name has never appeared on a ballot, she has been around government and politics her entire life. She also publicly campaigned for the second spot in 2006 when Eliot L. Spitzer was nominated for governor, losing out to then-State Sen. David A. Paterson.

State campaign finance records indicate Eve maintains an account from the 2006 effort, with more than $71,000 on hand. She is viewed as experienced and well-connected to many in New York City’s Democratic hierarchy.

Morelle – He’s the second-ranking Democrat in the Assembly after Speaker Sheldon Silver of Manhattan, but it’s virtually impossible for an upstate Democrat to attain the top Assembly post because of the chamber’s overwhelming majority of New York City members. So Morelle, 56, could look beyond the Legislature to the executive branch.

Others question whether Morelle would want the job or whether another Italian-American male would add value to the Cuomo ticket. But, like Duffy, he has the advantage of coming from Rochester, an upstate-downstate balance that worked well for Cuomo four years ago.

In a move that may or may not prove coincidental, Morelle – always considered a close Cuomo ally – resigned last week as Monroe County Democratic chairman.

Mahoney – The Onondaga County executive would bring upstate flavor to the Cuomo ticket and, as a Republican, rare bipartisanship. An attorney and former prosecutor, Mahoney is 49 this year and has proved a popular candidate in Onondaga County.

But Cuomo is already riling up some on the political left who say he has not proved progressive enough, and the left-leaning Working Families Party has not yet granted its endorsement to the governor. If Working Families nominated someone else that would siphon votes from the Democratic incumbent, it could provide a ray of hope to Republican gubernatorial candidate Rob Astorino.

As a result, most handicappers rate a Mahoney candidacy as a “long shot.”

Bellone and Hein – The two downstate county executives bring managerial experience and have been mentioned as potential running mates. Bellone could prove attractive in vote-rich Suffolk County, which can vote Republican.

Hein is also considered a rising Democrat, but it is questionable whether his Ulster County base would prove “upstate enough” to provide regional balance.

email: rmccarthy@buffnews.com