Shankar Vedantam

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As the mayor of New York City, Rudy Giuliani was a proponent of a controversial policing philosophy known as "broken windows." It calls for police to go after small crimes, in hopes of preventing bigger problems.

At first, it appeared as if violent crime dropped in the neighborhoods where "broken windows" policing was in force. The statistics, however, told a different story.

But the idea remains popular, despite evidence it likely had only modest effects.

The election of Donald Trump came as a shock to many Americans, but perhaps most of all to those in the business of calling elections. The pollsters on both the left and the right had confidently predicted Hillary Clinton would walk away with the race. They got it wrong. But one man did not: Allan Lichtman.

On Sept. 23, Lichtman, a historian at American University, declared that Trump would win, and he stuck by that call through the tumultuous final weeks of the campaign.

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It's no secret that this presidential campaign season has been tense, with disagreement and rancor even louder than usual.

(SOUNDBITE OF ARCHIVED RECORDING)

Fewer than 1 in 5 members of Congress are women. At Fortune 500 companies, fewer than 1 in 20 CEOs are women. And if you look at all the presidents of the United States through Barack Obama, what are the odds of having 44 presidents who are all men?

If men and women had an equal shot at the White House, the odds of this happening just by chance are about 1 in 18 trillion.

Magic.

That's what it feels like when you bump into your childhood friend on the first day of college ... or meet someone at a party in Paris, only to discover she lives in your dad's childhood home in Poughkeepsie, N.Y. But, says mathematician Joseph Mazur, these coincidences are not as extraordinary as we might think.

"People think that their address book is essentially the people they know, and it turns out any address book is about one percent of the people they know in some way," Mazur explains.

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Note: The audio for this story was updated on September 20th, 2016. On September 8th, Airbnb released a report on its efforts to combat discrimination and bias on its platform, and announced several changes to its policies surrounding issues of discrimination and diversity.

Quirtina Crittenden was struggling to get a room on Airbnb. She would send a request to a host. Wait. And then get declined.

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There's an old saying that if you want to get something done, always ask a busy person. Researchers have scientifically tested that theory. And NPR's social science correspondent Shankar Vedantam joins us now to explain what they found. Hey ya.

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