The chances of Uber choosing a woman as its next CEO are about the same as getting a cab in midtown Manhattan in the rain at rush hour.

As a woman who has built her career in and around tech, I strongly suspected this even before this week’s report that the field has been narrowed to four men, all CEOs. Just over 5 percent of chief executive roles at Standard & Poor’s 500 Index companies are women — and a string of recent departures means that number is on the decline. As much as many people would like to see a female take the lead at a troubled Silicon Valley company that has come to epitomize all the gender problems that have long troubled tech, I know as much as the next business person that the numbers just aren’t in our favor.

And that’s a shame. Despite what the numbers tell us, there are many, many qualified women who could drive Uber into the future.

One name that immediately comes to mind is the amazing Diane Green, the senior executive of Google‘s booming cloud business. Greene has a long history in tech — starting with her founding Vmare — and software she developed to help companies manage job applications is opening new doors for Google in its constant battle for market supremacy with Microsoft.

Also important — she’s deeply committed to advancing women in tech, and knows first-hand the kinds of issues they’ve faced and isn’t afraid to address them, evidenced by her telling a tech conference crowd of mostly men in March that she wished more women were in the room.

Jen Fitzpatrick from Google Maps, who started at the company as an intern in 1999 and climbed her way up to her current role of vice president of Local & Maps, would also be a smart choice, as her experience managing geographic data is something Uber could use to advance its system.

Nearly half of Google’s management team is women, so both Fitzpatrick and Greene are coming from an environment where women are taken seriously and accustomed to being promoted — a culture shift that Uber would most certainly benefit from.

Although this might seem like an out-of-the-box choice, I’d also suggest Sheri McCoy, the former CEO of Avon Products who stepped down on Thursday after facing a barrage of criticism from activist shareholders.

True, McCoy had problems while at the helm of the company, including a 35-percent drop in its stock price this year. But McCoy also took innovative steps to try and right the company after taking it over in 2012, including selling off a large portion of its North American operations to a private equity firm.

Although people tend to think the “gig economy” started with Uber and Airbnb, in truth Avon has been doing it for decades with its part-time, majority female sales force. Uber has said it wants more women drivers, and McCoy likely will be able to tap into that workforce better than most.

McCoy was likely also hurt by a dangerous trend that hinders many top women executives. Studies show that women are more likely than men to be tapped to turn around companies and are frequently shown the door when they don’t quickly succeed.

One doesn’t have to look far to find other examples.

The day before Avon announced McCoy’s departure, Irene Rosenfeld, the chief executive at Mondelez International, most famous for being the maker of Oreo cookies, announced her retirement after her own battles with investors, and Marissa Mayer of Yahoo left after a bumpy five years in her post after she was unable to fix the company’s declining fortunes.

If one has any doubts about the unconscious bias that women leading companies face, you can look no further than the headline of the CNN Money story announcing McCoy’s departure — “Ding dong! Avon’s CEO is leaving.” Not exactly subtle.

Whoever leads Uber, it will be a challenge. The truth is, a woman could do it, but picking her as some kind of window-dressing exercise only hurts us all in the long run by using them as props to masquerade a reluctance to address deep internal issues. All of the leadership at Uber was complicit in what had been happening at the company for years, and if they didn’t know what was going on, that’s a different kind of failure that should also be recognized and admonished.

No woman created this problem, but qualified women should certainly be among those considered to try and fix it.

Tracy Chadwell has worked in finance for 15 years and is the founder of 1843 Capital, a venture-capital firm that seeks to fund women-owned tech companies. She was partner of a growth-capital fund, Baker Capital, which had more than $1 billion under management. As a frequent speaker and start-up competition judge, Tracy has developed a broad network in the female founder community. She speaks conversational Japanese and restaurant French. Follow her on Twitter @TChadwell.

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