While at the United Nations the race to replace Antonio Guterres as secretary general gets in gear this month, some at the iconic building in Manhattan’s Turtle Bay region are asking whether at its current state of irrelevancy the institution itself can survive.   

One of the leading candidates to become the new UN chief on January 1 next year, the Argentine director of the International Atomic Energy Agency, Rafael Grossi, all but acknowledges the sorry state of the organization as it celebrates its 80th anniversary this month. 

“We all agree that the United Nations needs change,” Mr. Grossi told UN reporters on Wednesday. “We all agree that we all care a lot for the UN, and we all agree, I believe, that the UN is not in a good moment at this particular juncture, that there are many things that should change, should evolve, should be adjusted.”

The Sun’s handicapping of the race is to follow, but as even the UN chief’s selection needs a bit of adjustment, we first need to tell the uninitiated how this Rube Goldberg machine is rigged, and what are some of the assumptions that might, or might not, determine the outcome.    

Some of Mr. Grossi’s detractors claim he is overlooking one crucial piece of needed change: Although the UN endlessly claims to promote gender equality, it never chose a woman as its leader. A resolution passed by the General Assembly last month “notes with regret” that fact, and encourages states to “strongly consider nominating women as candidates.” Yet, the resolution declined to mandate a female secretary general. 

“We need action to ensure women’s full, equal and meaningful participation and leadership in decision-making at every level and all walks of life,” Mr. Guterres said in March, addressing the UN’s Commission on the Status of Women. “We need women leading in government and policy-making.”

That was also true ten years ago, the last time a race to occupy the executive suite on the UN building’s 38th floor was contested. Several women, especially from Europe, were lobbying governments to back them as secretary general. Yet, one person managed to convince the powers that be that he, more than any of the other candidates, is their man: Mr. Guterres. 

Beyond gender, the leadership position is traditionally rotated among the UN regional groups. Following two Africans, Boutrous- Boutrous Ghali and and Kofi Annan, an Asian, Ban ki-Moon, held the position that is now occupied by Mr. Guterres, a European. So now is the turn of the Latin America group, which last fielded a UN chief, Perez de Cuéllar, in the 1980s. 

America, though, is making clear it would rather have an ally at the helm of Turtle Bay than bend to unwritten UN traditions. “We believe the process for selection of such an important position should be purely merit-based with as wide a pool of candidates as possible,” the American deputy ambassador, Dorothy Shea, told the Security Council last week.  “With this in mind, the United States invites candidates from all regional groupings.”

“Americans can say that, but they have to convince 192 other UN members,” a UN official told the Sun. Yet, one other key player in the nomination process, agrees with America.

“Latin Americans have all the moral reasons to claim this term, but it does not prevent candidates from other regions to step in if they want to,” Russia’s UN ambassador, Vassily Nebenzya, told Reuters recently, adding, too, “I don’t mind a woman who will win it on merit, but merit comes first. Merit comes before gender.” 

The process of selecting a UN secretary general, like much else at Turtle Bay, is byzantine, secretive, and resembling no other election process in established democracies. And in reality, the decision is made far away from New York’s First Avenue, at key capitals. According to the UN Charter, the organization’s chief will be  “appointed by the General Assembly upon the recommendation of the Security Council.”

And that “recommendation” is key. Candidates mostly need to convince the five permanent, veto wielding council members — and especially America, Russia, and increasingly Communist China — that he or she will refrain from harming their interests.

The latest procedural format dictates that the race will start in the last quarter of this year and end by next fall, so the new chief has time to prepare for the role. Each candidate must be backed by at least one country and, in a new twist, must present a financial disclosure. 

The council traditionally conducts secret straw polls, designed to thin out the candidates list. In those, a candidacy can be doomed if the veto powers consistently express opposition to it. Following the secret polls, the Council finally votes publicly, and the General Assembly then rubber-stamps its recommendation. A secretary general then serves for five years, with an option to gain a single second term.    

Based on conversations with diplomats, UN officials, and other observers, Mr. Grossi is currently leading the race. Yet, as one official noted to the Sun, “Sometimes it’s better to be the runner-up, as the leading candidate might be targeted for objections in the straw polls by one or more of the council members.” 

With that in mind, here is the Sun’s handicapping of the race as it currently exists, including assets and weaknesses to each of the known candidates. It is based on wide ranging conversations at the UN, where sources decline to speak on the record in fear of publicly affecting the race. 

Rafael Grossi

The head of the Vienna-based nuclear agency told Turtle Bay reporters on Wednesday that as UN chief he’d do “exactly what I’m doing at the IAEA.” Mr. Grossi named successes such as his mediation between Moscow and Kyiv on safeguarding Ukrainian nuclear plants. His attempt to renew inspections of Iran’s nuclear facilities after the joint Israeli-American strikes in June, though, are less successful. Tehran claims that his earlier assessment of Iran’s failure to comply with its treaty obligations led to the attack.

That, though, could coalesce Western powers around Mr. Grossi’s candidacy. Three of the council’s permanent members used his reports to employ the “snapback” option that revived global sanction on Iran. One of these powers, though, Britain, might oppose his candidacy in early straw polls. President Javier Milley of Argentina is strongly contesting London’s sovereignty over the Falklands-Malvinas islands. 

Rebeca Grynspan

A former Costa Rican vice president and current chief of the UN Conference on Trade and Development, she is widely considered to be the race’s runner up. Ms. Grynspan is known as a mild, tactful diplomat who could allay the main powers’ concerns that she might go against their interests. Her country is an American ally, and has another huge asset: In 1948, following a bloody civil war, Costa Rica became one of the world’s only nations to ban a national armed force. No army is perfect for an organization that sports a sculpture of a tied-up pistol in its entrance. Beside being a woman, she could also become the first Jewish UN chief.  

Michelle Bachelet

The former Chilean president is widely admired in the UN halls, where many consider her a front runner. She embodies much of the institution’s pieties, including women’s rights, climate activism, and the like. “At first, I thought China wouldn’t support Bachelet, but foreign minister Wang Yi had a very positive conversation with her recently, so anything’s possible,” a close follower of Beijing tells the Sun. That is unlikely to help her, though. “The Americans will never agree to someone as far left as Bachelet,” a UN official opined. 

Alicia Barcena

A former Mexican foreign minister who has served in various roles as a UN official, Ms. Bárcena’s candidacy for the top job seems to lag behind other female Latin candidates. “Her time has come and gone,” a Mexican diplomat said. 

Achim Steiner

The administrator of the UN Development Program is both German and Brazilian. His gender might hurt his candidacy more than that of Mr. Grossi. 

Vuc Jeremic

A former Serbian foreign minister and president of the UN General Assembly, Mr. Jeremic’s candidacy is based on the notion that unlike the Latin group, the Eastern European bloc never occupied the UN’s 38th floor. Yet, as a UN-based diplomat said, he is “a candidate in his own eyes only.”

Kristalina Georgieva

The Bulgarian director of the International Monetary Fund is another Eastern European in the race. She ran to be secretary general in 2015 and was one of the most impressive women in the race. She lost to Mr. Guterres, and her candidacy is yet to gain wide support now. 

Jacinda Ardern

Another world zone, known as Oceania, also had tried to vie for the top role based on the fact that it never had one. New Zealand’s former prime minister, Ms. Ardern would be in that category. Yet, her country is a member of a group known as “Western Europeans and Others,” which also includes Mr. Guterres’s Portugal. 

Most UN secretary generals are from countries that are far from the top of the globe’s power structure. The five permanent council members are unlikely to ever challenge that dogma and promote their own candidate. That takes such UN-admired Americans as President Obama out of the race.

In 2015 Mr. Guterres managed to convince each of these powers that he would be on their side, and also that he speaks many of their languages fluently. The UN under him, though, became so irrelevant in world affairs that some wonder if anyone could bring it back to the world’s center stage — or even if such a goal is advisable.

“In five years, by the end of the next SG’s term, there won’t be a UN,” a senior Turtle Bay official predicted.