We will learn this week or next of Donald Trump's choice for secretary of state, perhaps the most important of all cabinet posts. But after the events of the past few days, surely the question is: Why would anyone in their right mind want the job?

Several respectable candidates are in the mix to represent the Trump administration's foreign policy, plus Rudy Giuliani. Which way Mr. Trump goes could signal whether he wants a secretary of state who will clean up after him, or who will double down on whatever he says.

Whichever the choice, provoking outrage seems to be the one constant of Mr. Trump's approach to global affairs. This man will go down in history as the first American president to foment a slew of international incidents while he was waiting to be inaugurated.

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His phone call with Taiwanese President Tsai Ing-wen on Friday – the first by an American president or president-elect in four decades – took China hands by surprise and alarm, throwing into question 40 years of America's One-China policy and earning rebukes from both Beijing and the Obama White House.

Some Sinophiles detected method in Mr. Trump's apparent act of madness. "As a businessman, Donald Trump is used to looking for leverage in any relationship," Jon Huntsman, who served as ambassador to China for Barack Obama, told the New York Times. "A President Trump is likely to see Taiwan as a useful leverage point."

That Mr. Huntsman, a former governor of Utah who is viewed as a paragon of moderation within the Republican Party (which explains the miserable failure of his 2012 presidential nomination campaign), would take Mr. Trump's side is intriguing, given that he is reportedly in the running for secretary of state. Mr. Trump is apparently not fully satisfied with any of the current contenders and wants to do more interviews.

This must be disheartening news for the long-suffering Mitt Romney, the 2012 Republican presidential nominee who has gone from worst critic to BFF of the president-elect, and whose wan, embarrassed smile in a photograph of the two having dinner last week spoke gigabytes.

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Mr. Romney, Mr. Huntsman, former CIA director and retired general David Petraeus and Tennessee Republican Senator Bob Corker are at the top of the list of contenders, which also includes John Bolton, who was George W. Bush's UN ambassador, and Exxon Mobil president and chief executive officer Rex Tillerson.

Any of them would be charged with explaining, defending and ameliorating Mr. Trump, which would be a full-time job, and then some.

Last week, apart from the Taiwanese affair, the president-elect chatted enthusiastically with Pakistani Prime Minister Nawaz Sharif, calling that country "amazing," offering any help Mr. Sharif might need and promising to visit sometime. Since Pakistan would very much like help in winning its chronic dispute with India over Kashmir, the Indians were none too pleased. And visit a country that's half reluctant ally, half terrorist haven? It's something Mr. Obama managed to avoid doing.

Mr. Trump also had a pleasant phone call with Kazakhstan's President and Ruthless Dictator Nursultan Nazarbayev. As for allies? He off-handedly told British Prime Minister Theresa May, "If you travel to the U.S., you should let me know," while Whitehall diplomats listened in, agog. Earlier, he tweeted a recommendation that she appoint Nigel Farage, former leader of the anti-European party UKIP, as ambassador to Washington, which was offensive in just so many ways.

Why such respectable figures as Mr. Romney, Mr. Huntsman or Gen. Petraeus would want to have anything to do with a president who is so thoughtless and disruptive on Twitter, and who is a positive menace when on the phone, is a mystery, unless they feel a sense of duty to limit the damage to America's reputation that is sure to come.

Senior Trump aide Kellyanne Conway told reporters that the next secretary of state's task would be "to implement and adhere to the president-elect's America First foreign policy, and to be loyal to his view of the world." Which of these men shares that view of the world?

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If the president-elect wants someone who will offer full-throated support, Mr. Giuliani is the obvious choice. In the days when no one outside Mr. Trump's inner circle (and perhaps few in it) thought he would win, the former New York mayor was his most stalwart ally.

But Mr. Trump doesn't always reward loyalty. (Can anyone remember what happened to Chris Christie?) Mr. Giuliani's foreign business connections are problematic. (As though Mr. Trump's aren't.) And apparently Mr. Trump is annoyed at Mr. Giuliani's overt lobbying for the job. So the search continues.

But anyone who wants to be Mr. Trump's secretary of state should remember: The president-elect offered these tweets Sunday night: "Did China ask us if it was OK to devalue their currency (making it hard for our companies to compete), heavily tax our products going into.. their country (the U.S. doesn't tax them) or to build a massive military complex in the middle of the South China Sea? I don't think so!"

Imagine being secretary of state and waking up to that sort of thing every day.