In a historic election Saturday, Taiwanese voters gave Mr. Chen Shui-bian of the opposition Democratic Progressive Party a convincing victory. In electing Mr. Chen, the Taiwanese people defied threats from Beijing and brought an end to 50 years of Nationalist rule in Taiwan. His win in Taiwan’s second democratic elections — the most freely contested and the most competitive in China’s history — changes the political dynamic in China and poses important new challenges for the governments in Beijing, Tokyo and Washington. But the new president in Taiwan faces some unchanging realities as well, and they are as important as his history-making victory.

Mr. Chen, former mayor of Taipei, took 39 percent of the votes, beating Mr. James Soong Chu-yu, an independent, who won 37 percent, and Vice President Lien Chan of the Nationalist Party, who got only 23 percent. Mr. Chen can claim a mandate. Turnout was high: Nearly 83 percent of Taiwan’s 15.46 million eligible voters cast ballots.

Their willingness to court Chinese anger testifies to the first immutable fact of this election. The Taiwanese people want to be the masters of their own destiny. Taiwan has developed the most democratic political system in Chinese history, and the Taiwanese are not going to give it up. After 50 years of Nationalist rule, the people of Taiwan demanded change. The voters wanted an end to the excesses and the corruption. They do not want war, but they are not going to be intimidated either.

Mr. Chen recognizes that mandate. Although the DPP originally called for Taiwan’s independence, both he and the party have retreated from that position. Throughout the campaign, he said that he would not unilaterally change Taiwan’s status and extended several olive branches to Beijing. Within an hour of his victory, he said that he hoped to make a “journey of reconciliation” to the mainland before his inauguration on May 20. He also invited Chinese President Jiang Zemin and Premier Zhu Rongji to Taipei.

Beijing’s response has been guarded. In a statement released after the results were in, the Chinese Cabinet said that it was “listening to the words and watching the actions” of Taipei’s president-elect. It even extended an olive branch of its own, saying that “China is willing to exchange views on cross-strait relations and peaceful reunification with all Taiwan political parties who approve of the one-China principle.” But it also reiterated the second unchangeable fact in Taiwanese politics: Any thoughts of independence are beyond the pale.

The language of the statement suggests that China’s leadership has learned something in the past few weeks: Threats backfire. Beijing’s dire warnings during the campaign did not scare Taiwan’s voters. They might even have helped Mr. Chen. The DPP usually claims about one-quarter of the votes in an election; the 39 percent Mr. Chen won on Saturday means his base extended beyond the party.

The most important factor, however, is the third unchanging fact: the economic relationship between Taiwan and the mainland. Threats notwithstanding, the two economies are increasingly intertwined. Taiwan has invested over $40 billion in China, and bilateral trade last year reached $25.7 billion. The Taiwanese people want stability and economic progress. The Beijing government wants Taiwanese investment to help stimulate its own economy as well as to increase its leverage over Taipei. Cross-strait tension makes all those objectives more difficult to achieve.

Mr. Chen knows that relations with Beijing must be dealt with, but his first task is governing Taiwan. He must unite the island’s 23 million people and put together a government that can deliver on the hopes that propelled him into office. His party has little experience in national government and tensions between DPP loyalists and bureaucrats, who have known only Nationalist rule, must be overcome. The cozy relationship between the Nationalists and the business community will also create problems for the new government. The makeup of the new Cabinet will reveal much about Mr. Chen’s priorities. If Mr. Lee Yuan-tseh, a Nobel Prize winner and a favorite of Beijing, is appointed prime minister, as many anticipate, it would send positive signals to all concerned.

The administrations in Tokyo and Washington must make it clear to their counterparts in Beijing and Taipei that talk of war does no one any good. Beijing’s fears that others are encouraging Taiwanese thoughts of independence must be assuaged. And Taipei must be encouraged to resume a dialogue with Beijing. But patience is essential. Solving the Taiwanese question will take time. That is another immutable fact in Chinese politics.

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