Australia’s prime minister, Anthony Albanese, never styled himself as an anti-Trump figure in his pitch for re-election.

       He said that he trusted President Trump, and that he respected the United States’ democratic process. He rarely invoked Mr. Trump by name, redirecting questions about him to discussions of budget surpluses or a comment that he was focused on Australia. He was measured and opaque in any criticisms of Mr. Trump, and vowed not to retaliate against his tariffs.

       But the global tumult set off by Mr. Trump’s return to power made him a factor in Australia’s election. And in the end, Mr. Albanese and his center-left Labor Party appear to have been bolstered by a wave of anti-Trump sentiment, pulling off a stunning landslide victory on Saturday.

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       Australia hasn’t been subject to the body blows that Mr. Trump has delivered to other longstanding U.S. allies, and that have become a factor in at least one recent election — like threatening Canada’s sovereignty and calling into doubt the future of military alliances with Europe.

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       A polling station on Saturday in Sydney. Many voters said they were concerned by the high cost of living.Credit...Mridula Amin for The New York Times

       The effects of his tariffs are likely to be less severe in Australia, whose biggest trading partner is China. So neither Mr. Albanese or the leader of the conservative opposition, Peter Dutton, were compelled to directly address the issue of Mr. Trump.

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