The split over a proposed joint ticket bolsters the governing party candidate’s chances in the coming presidential election. That won’t please Beijing.For weeks, Taiwan’s two main opposition parties were edging toward a coalition, in a bid to unseat the island democracy’s governing party in the coming presidential election, an outcome that Beijing would welcome. The election, one elder statesman from Taiwan’s opposition said, was a choice between war and peace.This week, though, the two parties — which both argue that they are better able to ensure peace with China — chose in spectacular fashion to go to war against each other. An incipient deal for a joint presidential ticket between the long-established Nationalist Party and the upstart Taiwan People’s Party unraveled with the speed, melodrama and lingering vitriol of a celebrity wedding gone wrong.A meeting that was opened to journalists on Thursday seemed to have been meant as a show of good will within the opposition. But it featured sniping between rival spokesmen, a long-winded tribute to the spirit of Thanksgiving by Terry Gou — a magnate turned politician trying to cajole the opposition toward unity — and mutual accusations of bad faith between the two presidential candidates who had been trying to strike a deal: Hou Yu-ih of the Nationalist Party and Ko Wen-je, the founder of the Taiwan People’s Party.Mr. Gou tried to break the icy tensions at one point by saying that he needed a bathroom break.“I don’t want a silent ending on this Thanksgiving Day,” he later told journalists after Mr. Hou and his two allies had left the stage. “But unfortunately it looks like it will be a silent ending.”Friday was the deadline for registering for Taiwan’s election, which will be held on Jan. 13, and by noon both Mr. Hou and Mr. Ko had officially registered as presidential candidates, confirming that there would be no unity ticket. Mr. Gou, who had also thrown his hat in the ring, withdrew from the race.Taiwan’s young, vigorous democratic politics has often included some raucous drama. Yet even experienced observers of the Taiwanese scene have been agog by this week, and baffled as to why the opposition parties would stage such a public rupture over who would be the presidential candidate on a unity ticket, and who would accept the vice presidential nomination.“It really defies theories of coalition building,” Lev Nachman, a political scientist at National Chengchi University in Taipei, said of the week’s bickering. “How do you tell undecided voters ‘still vote for me’ after having a very publicly messy, willfully uninformed debate about who ought to be first and who ought to be second?”The collapse of the proposed opposition pact could have consequences rippling beyond Taiwan, affecting the tense balance between Beijing — which claims the self-governing island as its own — and Washington over the future status of the island.The situation also makes it more likely that Taiwan’s vice president, Lai Ching-te, the presidential candidate for the governing Democratic Progressive Party, or D.P.P., will win the election — a result sure to displease Chinese Communist Party leaders.Mr. Lai’s party asserts Taiwan’s distinctive identity and claims to nationhood, and has become closer to the United States. China’s leaders could respond to a victory for him by escalating menacing military activities around Taiwan, which sits roughly 100 miles off the Chinese coast.A victory for the Nationalists could reopen communication with China that mostly froze shortly after Tsai Ing-wen from the Democratic Progressive Party was elected president in 2016. And a third successive loss for the Nationalists, who favor closer ties and negotiations with Beijing, could undercut Chinese confidence that they remain a viable force.Lai Ching-te, Taiwan’s vice president, and a candidate from the Democratic Progressive Party. A split between Mr. Hou and Ko Wen-je of Taiwan People’s Party may benefit his campaign.I-Hwa Cheng/Agence France-Presse — Getty ImagesTaiwan’s first-past-the-post system for electing its president awards victory to the candidate with the highest raw percentage of votes. Mr. Lai has led in polls for months, but his projected share of the vote has sat below 40 percent in many surveys, meaning that the opposition could claw past his lead if it coalesced behind a single candidate. Mr. Hou and Mr. Ko for months sat around the mid- to high 20s in polls, suggesting that it could be hard for either to overtake Mr. Lai unless the other candidate stepped aside.“This may scare off moderate voters who might have been into voting for a joint ticket for the sake of blocking the D.P.P.,” Mr. Nachman said of the falling out between the opposition parties. “Now those moderate voters will look at this team in a different light.”For now, many Taiwanese people seem absorbed — sometimes gleeful, sometimes anguished — by the spectacle of recent days. “Wave Makers,” a recent Netflix drama series, showed Taiwanese electoral politics as a noble, if sometimes cutthroat, affair. This week was more like the political satire “Veep.”Last weekend, the Nationalist Party and Taiwan People’s Party appeared poised to settle on a unity ticket, with each agreeing to decide on their choice of joint presidential nominee — Mr. Hou or Mr. Ko — by examining electoral polls to determine who had the strongest shot at winning.But teams of statistical experts put forward by each party could not agree on what polls to use and what to make of the results, and the parties became locked in days of bickering over the numbers and their implications. At news conferences, rival spokespeople brandished printouts of opinion poll results and struggled to explain complex statistical concepts.The real issue was which leader would claim the presidential nominee spot, and the quarrel exposed deep wariness between the Nationalists — a party with a history of over a century that is also known as the Kuomintang, or K.M.T. — and the Taiwan People’s Party, which Mr. Ko, a surgeon and former mayor of Taipei, founded in 2019.“The K.M.T., as the grand old party, could never make way for an upstart party, so structurally, it was very difficult for them to work out how to work together,” said Brian Hioe, a founding editor of New Bloom, a Taiwanese magazine that takes a critical view of mainstream politics. On the other hand, Mr. Hioe added, “Ko Wen-je’s party has the need to differentiate itself from the K.M.T. — to show that it’s independent and different — and so working with the K.M.T. would be seen by many of his party membership as a betrayal.”A supporter of Kuomintang, or the long-established Nationalist Party, holding a flag outside the Central Election Commission in Taipei on Friday.Annabelle Chih/Getty ImagesMa Ying-jeou, the Nationalist president of Taiwan from 2008 to 2016, stepped in to try to broker an agreement between his party and Mr. Ko. Hopes rose on Thursday when Mr. Hou announced that he would be waiting at Mr. Ma’s office to hold negotiations with Mr. Ko.But it quickly became clear that Mr. Ko and Mr. Hou remained divided. Mr. Ko refused to go to Mr. Ma’s office, and insisted on talks at another location. Mr. Hou stayed put in Mr. Ma’s office for hours, waiting for Mr. Ko to give way. Eventually, Mr. Hou agreed to meet at the Grand Hyatt hotel in Taipei, and party functionaries announced with solemn specificity that the talks would happen in Room 2538.Dozens of journalists converged on the hotel, waiting for a possible announcement. Expectations rose when Mr. Hou entered a conference room where the journalists and live-feed cameras waited. But he sat with a fixed smile for about 20 minutes before Mr. Ko arrived, glowering. Mr. Gou, the magnate, opened proceedings with his tribute to Thanksgiving and calls for unity, recalling his wedding ceremony in the same hotel. But it soon became clear that Mr. Hou and Mr. Ko were no closer.On Friday, Taiwanese people had shared images online and quips ridiculing the opposition’s public feuding. Photographs of Room 2538, a suite at the Grand Hyatt, circulated on the internet. Some likened the spectacle to “The Break-up Ring,” a popular Taiwanese television show that featured quarreling couples and their in-laws airing their grievances on camera.Some drew a more somber conclusion: that dysfunction on the opposition side left Taiwan’s democracy weaker.“In a healthy democracy, No. 2 and No. 3 will collaborate to challenge No. 1,” said Wu Tzu-chia, the chairman of My Formosa, an online magazine. “This should be a very rigorous process, but in Taiwan, it’s become very crude, like buying meat and vegetables in the marketplace.” More