The other three were the result of party coups—members of the governing party losing confidence in their serving prime ministers—first Rudd, then Gillard, and now Abbott—and booting them out. Since parliamentary systems work by electing a party rather than a presidential-style leader, and prime ministers thus serve at the pleasure of their parliamentary bloc, in theory this could happen frequently anywhere.
But in the rest of the world, and even in Australia until recent years, it’s been relatively rare. Usually a party changes leaders after some big general-election defeat. What makes it all the odder and cozier is that the Abbott-Turnbull switch has parallels to the Rudd-Gillard-Rudd sequence, in that Turnbull was the Liberal leader until Abbott unseated him as leader of the opposition, by a single vote, in 2009.
On the other hand, no nation whose past (and perhaps) future politics has been dominated by a sequence of Bushes and Clintons had better sound too self-righteous about a revolving cast of usual suspects in Australian leadership. I won’t even bother to write out the sentence that begins, “And no nation where Donald Trump dominates in the polls ...”
2) Americans can get some sense of the personality-politics here if they think of Tony Abbott as combining elements of U.S. Republicans Scott Brown, George W. Bush, and Ted Cruz. Like Scott Brown (who succeeded Teddy Kennedy as senator from Massachusetts, and eventually lost to Elizabeth Warren), Abbott has cultivated a beefcake image of The Body Beautiful. They are the only two male politicians I can recall willingly being photographed in Speedos.
Like George W. Bush, Abbott governed in a way seemingly at odds with his fancy educational background. In Bush’s case, that was a Yale undergraduate degree followed by Harvard Business School; for Abbott, the University of Sydney followed by a Rhodes Scholarship to the Queen’s College, Oxford. But the non-Ivy League, non-Oxbridge “go with my gut” governing style Americans recall from the George W. Bush era also characterized Abbott. Also in common with Bush-era Republicans, Abbott was a climate-change skeptic, and he began dismantling Australia’s previously ambitious climate-related policies.
Like the also-fancily-educated Ted Cruz (Princeton and Harvard Law School), and unlike Bush in his “compassionate conservative” phase and some others, Abbott governed in a dark, “things are getting worse” style rather than with a sunny “it's all getting better!” tone.
As for Malcolm Turnbull? It’s hard to draw a direct American parallel to him, because he comes from a tradition for which we have no in-office specimens any more, only history-book and museum-piece relics. He is internationalist, unashamedly intellectual, urbane. With apologies in advance for the differences between American and Australian politics and personal styles, you could start by thinking of Malcolm Turnbull as a “liberal Republican”—Rockefeller, Heinz, Hatfield, even Gerald Ford—of a type no longer found in the U.S.