Australians ended six years of tumultuous Labor Party rule and gave the conservative Liberal Party and its allies a healthy majority in parliamentary elections held last weekend. Mr. Tony Abbott will assume the office of prime minister, the third to hold that post in three months. Mr. Abbott has his work cut out. Restoring political stability in Canberra should not be difficult. More pressing is winning over voters, who, despite backing his party, do not hold him in especially high regard, and regaining the footing of a slowing Australian economy. None are impossible, but all require a deft touch, one for which Mr. Abbott has shown little proclivity in the past.

Voting is compulsory in Australia, so the results of Saturday’s ballot provide an accurate reading of public sentiment. As expected, the Liberal-National coalition crushed the Labor Party, claiming 88 seats, an increase of 16 from the previous Parliament. The Labor Party dropped to 57 representatives, down from 71. (It had ruled with the support of independent and Green representatives since 2010 — the first minority government since World War II.)

For once, economic policy was not an issue. Australia’s economy has grown for 22 years, unemployment and interest rates are low, and household incomes have increased in real terms. Still, public dissatisfaction with Labor government has steadily increased over the six years it was in power. The causes of that disaffection are threefold. The first, and most important, was the bitter infighting within the party. Labor, led by Mr. Kevin Rudd, came to power in 2007, and Mr. Rudd assumed the office of prime minister. He was ousted three years later in a coup led by his deputy, Ms. Julia Gillard. The rebels had chafed under Mr. Rudd’s autocratic style, which alienated many in the party. Ms. Gillard kept Mr. Rudd by her side as foreign minister, using his experience and expertise to bolster her government and signal party unity after the coup.

While Ms. Gillard made history as Australia’s first female prime minister and proved a formidable debater in Parliament, her government proved less than steady. Forced to make deals with independents and the Greens in a minority government, the prime minister looked weak and her policies inconsistent. The realization that Ms. Gillard could not lead the party into elections obliged Labor to call a chastened Mr. Rudd back to the prime minister’s office at the beginning of the summer. The move made sense on a tactical level — Mr. Rudd was a far more popular figure — but it was both too late and reinforced the image of Labor as unstable.

The second reason for the party’s demise was its support for a carbon tax. When he first took office, Mr. Rudd reversed the policy of the previous government and signed the Kyoto Protocol on global warming. He also promised to introduce a carbon emissions trading scheme, a pledge that came up empty when the Senate failed to follow through. Still, Labor had said it would not impose a tax on the country’s biggest carbon polluters, the energy sector, a policy Ms. Gillard reversed to win the support of other legislators after Labor was shellacked in 2010 elections. That shift outraged voters. A similar reversal — the call by Mr. Rudd when he returned as prime minister to deny asylum seekers entry into Australia — also alienated voters. For die-hard Labor supporters it was a mean-spirited reversal; for others, it looked like an opportunistic shift. Mr. Rudd brought Labor back, but he could not close the gap.

Mr. Abbott, once deemed “unelectable” even by some of his supporters, will now take charge. He has promised to scrap the carbon tax by 2014, and replace it with taxpayer-financed incentives to reduce pollution. He has promised to repeal a 30 percent tax on the profits of Australia’s coal and iron ore mining companies, the engines of the country’s economic growth that have been slowing as China’s economy decelerates. At the same time, he has pledged to return the budget to surplus, a task made immeasurably more difficult by his campaign pledge to expand paid parental leave.

When it comes to foreign policy, Mr. Abbott has said that he will focus more on relations with Asia; not because of a de-prioritizing of Australia’s traditional allies, the United States and Great Britain, but because focus has to be on “relations that need the most attention.” He is confident that he understands thinking in Washington and London; he is less so about goings on in Jakarta, Beijing, Tokyo and Seoul.

Indonesia looms large in Australian foreign policy calculations. It is a huge neighbor with the potential to have a great impact on the country: if nothing else, it is the origin for most of the asylum seekers. China, too, is critical, given its demand for Australian exports. Japan once played that role, but it has been eclipsed by China’s insatiable appetite. But there remain many opportunities for Tokyo and Canberra to forge a still stronger relationship. Japan has worked closely with Australia to strengthen the institutions and norms of regional governance. The countries closely worked together, and with the U.S., to promote security and stability in the Asia Pacific. Indeed, after the U.S., Australia is Japan’s closest security partner. It is hoped that Japan and Australia under Mr. Abbott and his new government will deepen their relationship.

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