Sanae Takaichi is Japan’s fifth prime minister in as many years.

After weeks of political chaos and tense coalition negotiations, Japan’s parliament on Tuesday voted to elect Sanae Takaichi as the East Asian country’s first female prime minister, smashing a glass ceiling in a country that lags behind most developed nations in terms of women’s representation.

Ms. Takaichi won the leadership of Japan’s ruling Liberal Democratic Party earlier this month. But her rise to the premiership was thrown into doubt when the LDP’s longterm coalition partner, the centrist Komeito party, refused to join a government led by the conservative Ms. Takaichi, a protege of former Prime Minister Shinzo Abe and avowed admirer of Margaret Thatcher.

Without Komeito, the LDP was well short of a majority in t

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