But regardless of a mixed-gender race, there is already plenty of talk about stereotyping or even sexism when it comes to how Ip and Lam are viewed, both by ­voters in Hong Kong and decision makers in Beijing.

At the same time, there is also the possibility that gender could work to their advantage in their run for the top job, with the ­so-called “soft-touch” expected of women in positions of power. In the case of Ip and Lam, though, shattering stereotypes is everyday business because of their strong personalities and reputation for toughness.

When Ip was interviewed by the Post at the weekend and asked about the open hostility – even hate – towards her from some quarters, she made it clear that she felt her being a woman had “a lot to do with it”. She has been known to lament about being ­belittled or underestimated ­because of her gender.

Watch: Regina Ip takes questions on her leadership bid

Ip knows what it’s like to have people fixate on her looks and ­appearance. When she was ­probably the most hated minister as the former security chief spearheading the unsuccessful drive to introduce national security legislation back in 2003, she was often mocked and derided in public as “Broomhead” for a bushy hairdo at the time.

During one radio show, she said: “Many people have looked down on me. They think that I am just a woman without the support from tycoons and consortiums.” She summed up the attitude ­towards her: “She’s just a woman, what can she do?”

Women can be hard on their own gender as well: Ip once ­referred to Lam as her “junior sister apprentice” – the suggestion being that while the chief secretary might be “a good fighter”, Ip was the superior candidate to lead Hong Kong.

Stereotypes may abound, but some formidable critics the Post spoke to agreed that most Hongkongers were sensible and open-minded enough, and would ultimately judge candidates by their qualities and abilities rather than gender.

“I think Hong Kong people are very fair. They won’t judge you by your gender. No one will think that just because you are a woman you’re not qualified to be the chief executive,” said former Democratic Party chairwoman Emily Lau Wai-hing, who enjoys a reputation for toughness similar to that of Lam and Ip.

“By the same token, it doesn’t mean that people will be particularly lenient to women just ­because of their gender. What matters most is whether the ­candidate is brave and capable enough of speaking up for Hong Kong and fighting for its best ­interests.”

Former civil service minister Joseph Wong Wing-ping agreed that Hongkongers did not have a gender bias, but he could not say the same for Beijing, given mindsets on the mainland where women have traditionally played a far smaller role than men in politics.

“In the end, the elected chief executive shall be appointed by the central government; whether there is a gender bias in Beijing’s officialdom culture is still unknown,” he said.

“But in Beijing, so far no woman has ever sat in the Politburo Standing Committee. I don’t know whether our leaders have doubts about women or whether their male counterparts are more outstanding.”

Andrew Fung Ho-keung, director and chief executive of the Hong Kong Policy Research Institute, echoed Ip in suggesting that the city’s tycoons and big businesses had reservations about women’s abilities, especially when vying for the highest office.

“For Hong Kong, facing so many issues such as social divisions, I don’t think Beijing will care about gender as long as the eligible candidate fares well in the areas of competence, popularity and problem-solving,” he said. The city was actually ready for picking a female leader, he added.

“Rather, I am afraid the business sector and tycoons have doubts about women as both Regina Ip and Carrie Lam advocate policies that smack of socialism, which is not their cup of tea,” Fung argued. “In Hong Kong, it’s hard for the male-dominated business sector to see eye to eye with woman leaders.”

When it comes to leadership styles, Ip is often perceived in ­public as the hardliner next to Lam, but it is no secret among civil servants that the chief secretary is not on good terms with many ­administrative officers working under her, while Ip, in contrast, enjoys strong support from her former colleagues, especially those in the disciplined services.

“Many AOs hate Carrie ­because she is such a harsh ­workaholic, requiring others to work like her. Also, she is very ­obstinate and unwilling to listen to the opinions of others,” a ­government source said.

Emily Lau is particularly highly critical of Lam, who has been dubbed a female version of the unpopular chief executive, who is nicknamed “689” in a derogatory reference to the number of votes he won from the 1,200-strong Election ­Committee that crowned him leader in 2012.

A day after Leung’s declaration not to seek a second term, Lam made a surprise U-turn on her earlier claims that she was not ­interested in the top job, saying she had “no choice” but to reconsider running because of the “drastic change” caused by Leung’s pullout.

The pan-democrats expect her to continue where Leung left off in terms of governance and policies if she wins.

“Carrie Lam is really dishonest with her election bid. If she wants to run for the CE election, just say it. Why she has to link it with Leung is really beyond me,” Lau said, even going so far as to label the No 2 official as “a wolf in sheep’s clothing” – again, an ­unflattering reference to another nickname for the chief executive.

Describing both Lam and Ip as ill-tempered, Lau alleged that Lam had become arrogant over the past two years.

She cited Lam’s refusal to communicate with the pan-democrats, especially after the Occupy movement of 2014 and the failed political reform process.

During that period, Lam had tried to lobby opposition lawmakers to “pocket” Beijing’s rigid framework for electing the chief executive by universal suffrage, which was voted down.

“If she is so hostile to us, how can she be able to communicate with us as the chief executive?” the veteran politician said.

Wong, the former civil service chief, also agreed that, as Leung’s top aide, Lam’s popularity might, to a certain extent, be “tainted”.

But Starry Lee Wai-king, chairwoman of the pro-establishment Democratic Alliance for the Betterment and Progress of Hong Kong (DAB), holds Lam in high ­regard.

She remarked earlier that Lam believed in a “big government” and was committed to serving Hong Kong people, compared with John Tsang, who seemed to favour a “small government” ­approach.

University of Hong Kong academic Nelson Chow Wing-sun, commissioned by Lam in 2013 to study the city’s retirement protection issues, said the chief secretary put plenty of effort into welfare policies, but was too “conservative” in dishing out money. He has advised the government on welfare issues since the 1980s.

In 2014, Chow’s team put ­forward a proposal to give senior citizens aged 65 or above – rich or poor – a pension of HK$3,000 a month without imposing a means test. Lam rejected it as a heavy financial burden on the government’s coffers, and even suggested Chow did not have a good grasp of public finance.

“Of course I felt upset at that time. Our team’s study showed that the government was capable of coping with the additional ­expenses. But it is undeniable that Lam really put her heart into ­welfare policies,” he said.

Ip, by contrast, seemed more interested in security than ­welfare, he added.

“Carrie seems to hold on to a belief that welfare policies should only benefit the poor, not the rich,” Chow said.

“But as a taxpayer, a rich elderly person makes his or her contribution to society and deserves a pension.

“Also, she is very conservative about public finances, afraid of ­incurring recurrent expenditure for a long-term policy.”

As for Ip, who recently threw a tantrum at a reporter for asking about her stance on introducing national security legislation in the next five years, Wong said she had lost credit in such a response.

Still, ­Policy Research Institute chief Fung said they were both loyal in the eyes of Beijing but their “tough” personalities might make it harder for them to resolve political conflicts and bridge crippling social divisions.

“I am worried that they are ­getting too tough. Politics requires a balancing act of compromise. As a political leader, he or she should know how to put on a charm ­offensive to achieve the desired results or turn the situation around,” he said.

At the end of the day, Hong Kong is not unfamiliar with strong women at the helm. The most famous example is Baroness Lydia Dunn, who was once hotly tipped to be Hong Kong’s first chief executive.

Dunn was dubbed the most powerful woman politician in Hong Kong under British rule in the 1980s and was also successful in business, becoming deputy chairwoman of HSBC.

Her decision to resign from the Executive Council and return to Britain brought her Hong Kong political career to an end in June 1995.

Another famous female leader was former chief secretary Anson Chan Fang On-sang, the first woman and the first ethnic ­Chinese to hold the No 2 government post from 1993 to 2001.

Chan was often described as an “Iron Lady”, with “an iron fist in a velvet glove”.

She was once lauded as the most powerful woman in Asia for her role as the deputy of former British governor Chris Patten, and later chief executive Tung Chee-hwa.

However, amid rumours that she was at odds with Tung and also Beijing, Chan announced her resignation in early 2001 and ­officially stepped down that year.

Women’s talk

Regina Ip

On Article 23 draft bill: “Are you seriously telling me that taxi drivers, restaurant waiters and workers at McDonald’s will want to discuss these proposals with me? A draft bill is for the experts.” (September 26, 2002)

On democracy: “Don’t believe democracy will be a panacea. Adolf Hitler was returned by universal suffrage and he killed seven million Jews.” (October 28, 2002)

On July 1 protest: “We cannot rule out the possibility that some citizens may join it as a kind of activity because it’s a holiday ... many people taking to the street will not necessarily mean that they are against Article 23.” (June 29, 2003)

On Filipino maids: “Apart from reporting on the misconduct of Hong Kong employers, shouldn’t the international media pay more attention to the issue of a large number of Filipino maids being turned into sexual resources for male foreigners?” (April 17, 2015)

On wearing mink: “Wearing fur is actually the same as eating beef … Mink farming can be more humane than rearing chicken or cattle.” (January 27, 2016)

Carrie Lam

On legitimacy of problematic oaths at Legco: “Although I am here to answer questions, it does not mean I recognise the status of some people as legislators.” (November 9, 2016)

On CE election: “I know that when I talk about reconsidering [the election] today I will immediately attract criticism, accusing me of a U-turn and eating my own words.” (December 10, 2016)

Religious conviction: “The 8th Beatitude says, ‘Blessed are they that suffer persecution for justice’s sake’. It fits me very much because there is a place reserved for me in heaven. In fact, nowadays, as you work in the government, you are often criticised for doing what is just.” (November 1, 2015)