Would affirmative action help close Japan's notorious gender gap? That was one question raised at a Tokyo panel July 2 on the possibilities of "womenomics," featuring Facebook Chief Operating Officer Sheryl Sandberg. Ms. Sandberg's book "Lean In,'' released in Japanese last week, argues that women need to be more assertive in order to win leadership positions for themselves in government and business.

Ms. Sandberg and her fellow panelists -- Tomoko Namba, founder of mobile gaming firm DeNA Co. ; Goldman Sachs managing director and Japan strategist Kathy Matsui; and Yuko Kawamoto from Waseda University Graduate School of Finance – were somewhat skeptical of the idea of setting quotas or targets for women's participation in the public sector and private industry. That topic has been raised recently everywhere from Japanese TV shows to Prime Minister Shinzo Abe.

"Besides whether or not it's a man or a woman, the bigger difference is whether they can do the work," Ms. Namba said, in disagreeing with the quota idea. "With a quota system, it's difficult to know whether people are chosen because of their ability to do the job or just to fill the quota. It's disrespectful to the people who worked hard."

Ms. Sandberg more or less agreed, saying "Even with quotas, if we don't address some of the fundamental, underlying issues of gender, it won't be enough." She said that while she understands the cultural differences around the world and doesn't want to tell other countries what their public policy should be, establishing a quota system in government will not change Japan's workplace problems. She cited the example of countries in Scandinavia and Norway which have quotas for boards and government, but where less than 3% of the countries' top companies are run by women.

Ms. Kawamoto was in favor of trying a public quota system, but was doubtful whether it could work in the private sector, saying "I don't think any of the people on this panel actually understand how difficult a Japanese company can be."

If the government or companies do opt for a quota system, they should first implement a better system for evaluating work, Ms. Kawamoto said, noting that in Japan people are often judged by how long they work. It's possible that male bosses in the Japanese workplace just aren't seeing how hard women are working, she said.

Ms. Matsui said she had changed her position on Japanese quotas in recent years: "There aren't many other options, the clock is ticking, and the working population is declining; at least start at the public-sector level and try to set a quota or goal target." While acknowledging the problems that Ms. Namba pointed out, she said "If we can at least initiate the push at the government level, we can see where progress can be made."

Fixing the gender gap is a problem that Japanese Prime Minister Shinzo Abe has put near the top of his list of ills to reform, in order to promote growth in the world's No. 3 economy.

According to the World Economic Forum's 2012 Global Gender Gap Report, Japan ranked 101 out of 135 countries, just below Azerbaijan and Malaysia, but a hair above Cambodia. The Forum bases its rankings on gender-equality data from labor-force participation, education level, sex ratio and life expectancy, as well as political empowerment based on the number of women in ministerial or higher government positions.

While ranking high in health issues, Japan received poor ratings in economic opportunities and political empowerment for women. In northeast Asia, Japan sits slightly above South Korea at 108, but far below China at 69, and hasn't experienced any notable change since the report's creation in 2006, when it was ranked at its highest, at 80.

The same report notes that restricting job opportunities for women costs northeast Asia between $42 billion and $46 billion a year, and that closing the gap between male and female employment in Japan would boost the country's GDP by as much as 16%.

Prime Minister Abe has been trying to do his part in changing Japan's standing in the political-empowerment section of the index: He promised that his Liberal Democratic Party would create a society where 30% of leadership positions were filled by women by 2020. He's not doing too well so far: Only nine of the 79 LDP candidates for the upcoming election are women.

Work-life balance also poses a problem in Japan. When asked how the mother of two juggles the responsibilities of home and work at Facebook, Ms. Sandberg responded that it was a question that she has often been asked in interviews, but which men are never asked, and it was part of the reason why women are being held back. She argued that distribution of housework is a problem that needed to be addressed, noting that Japanese women spend five times more time on housework than Japanese men. The government has suggested that if women were pushed to go to the office, it could open an untapped market of housework services.

But Ms. Matsui noted that while working mothers can never find a perfect 50-50 balance between career and life, one of the reasons working is tough for women in Japan is because families aren't able to hire help as easily as they can in many other countries.

Ms. Matsui's assessment falls in line with a special report that aired on NHK last week, on "maternity harassment" in companies, where full-time working mothers were pressured to resign from their positions because they had to leave work early to take care of their children.

But cultural attitudes may have an impact on female employment as well. While Ms. Sandberg's book urges women to "lean in" to work, and asks men to help with housework, a survey by Japan's Cabinet Office in 2012 shows that Japanese women may actually be looking to "lean back."

Almost half -- 48.4% -- of 1,600 women surveyed said they more or less agreed when asked whether "a husband should go to work and a wife should protect the home." Together with men, some 51.6% more or less agreed women's role was to stay at home. That's an almost 10% increase from when the same question was asked in 2009. Of the younger, prime job-hunting population of men and women in their early-to-late twenties, around 50% agreed that a married woman's place was in the home.