The youngest candidate at 43, Koizumi has vowed that in his first year as prime minister, he would pass a law allowing married couples to retain separate surnames. Koizumi, who made waves when he took a short paternity leave after the birth of his first child in 2020, is the only candidate who has promised to overturn the law.

The leading conservative candidate, Sanae Takaichi, 63, would become Japan’s first female prime minister. She has said that while she supports married couples’ use of different surnames in professional settings, the naming law should remain in place to preserve family unity and protect future offspring from confusion.

Both Shigeru Ishiba, 67, a four-time contender for the prime minister’s seat and a leading candidate in public opinion polls, and Yoko Kamikawa, 71, the current foreign minister and the other woman in the race, have said that more discussion is needed. Kamikawa said she “recognised the risk of division” over the issue.

For three decades, reformers both inside the party and from the opposition have proposed changes to the law. Two cases made it to Japan’s Supreme Court, with the justices ruling that Parliament ultimately must decide the matter. A third case is being heard before district courts in Tokyo and Sapporo.

Yukari Uchiyama, 56, a high school teacher and plaintiff in the current lawsuit on the issue, raised three children and is legally divorced from her husband, Yukio Koike, so that she can keep her original surname on legal documents. She said that giving up her surname made her feel as if “my very existence, which is the very foundation of my rights as a human being, is being ignored, or cut off from the roots.”

When “even something as simple as this doesn’t pass,” she said, “I think that various gender issues that are being raised are not acknowledged.”

Japanese media polls indicate that about two-thirds of the public supports a change in the naming law. This year, Japan’s largest business group issued a statement calling for the government to allow married people to keep their birth names in the official family registry.

Citing an issue that invokes gender equality helps a candidate like Koizumi define himself as breaking with the party’s traditional patriarchal leadership, said Mireya Solis, director of the Centre for Asia Policy Studies at the Brookings Institution in Washington.

“This is why this is really touching a nerve,” she said. “It’s an issue that signals an appetite for change.”

For Takaichi, taking the opposite tack is a way to signal her hard-line bona fides to the party’s small but powerful right wing.

While the debate is unlikely to sway the election on its own, it highlights a generational divide inside the party, with older voters supporting the status quo.

“I think a lot of senior politicians believe this in their bones,” said Kenneth McElwain, a professor of political science at the University of Tokyo and a visiting professor at Columbia University. “They are representing people in their 60s-plus for whom this is crucial.”

In the past, candidates for prime minister were likely to tussle most visibly over matters like defence and national security.

Liberals and conservatives were defined by how hawkish and dovish they were on foreign policy, Solis said. “But that doesn’t seem to be the cleavage any more,” she added.

Even politicians previously considered doves – like Kishida – have come to support an expansion of the Japanese defence budget and increased militarisation.

Takaichi has invoked some nationalist tropes that could spook Japan’s Asian neighbours, such as promising to visit Yasukuni Shrine, where Class A war criminals from World War II are enshrined. But her basic foreign and defence policies do not differ markedly from those of her more progressive rivals.

The candidates have discussed other policy positions, such as how to change the rigid labour market and whether to restart nuclear reactors that have been shut down since the 2011 earthquake and tsunami triggered a nuclear meltdown.

But they have been almost uniformly vague in addressing the scandals that have led to high voter dissatisfaction and declining trust in the governing party.

After the assassination of Shinzo Abe, the former prime minister, in 2022, the news media unearthed extensive ties between the fringe Unification Church and a group of conservative politicians. The killer had been angered by Abe’s ties to the church.

LDP MPs scurried to contain the political fallout, but party leaders have failed to persuade voters that they have fully purged the church’s influence.

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Since late last year, the party has also been contending with a financial scandal in which some LDP MPs were accused of taking kickbacks from sales of tickets to political fundraisers.

With none of the candidates offering clear plans to address the public discontent, the LDP election represents further stagnation, said Chiyako Sato, an editorial writer with The Mainichi Shimbun, a centrist newspaper.

The Liberal Democrats, she told reporters last week, are simply “changing faces to simulate a change in government.”