Big primary election for mayor of New York City next week, people. Let’s take a look at what’s been going on. If you stick with me, I promise animal stories. Including kittens.

Right now the big news is on the Democratic side where Bill de Blasio, the current public advocate, has been shooting ahead in the polls. Skyrocketing!Perhaps this is because he has one of the most interesting families in the history of politics, including an African-American wife who says she only dated women until she fell in love with Bill de Blasio, and a 16-year-old son, Dante, who made a really lovely TV ad about his father. By now, more New Yorkers may be aware of Dante’s spectacular Afro than any other factor in the entire campaign. So it definitely could be the family.

It could also be because de Blasio is nearly six and a half feet tall. New Yorkers like to think big.

It would probably not be because of his work as public advocate. The New York City public advocate does not really have any work to do. His job is mainly to call press conferences and denounce things. We have quite a few elective posts like that around here.

But it could be the carriage horses. We will get to them in a minute.

When the race began, the two big names were Christine Quinn, the City Council speaker, and Bill Thompson, the former city comptroller. Thompson is low-key. So low that Chris Smith of New York magazine interviewed an enthusiastic woman at a Thompson rally who said that in 2009 she had voted “for the opposite of Bloomberg. The Democrat. Whoever that was.” It was Thompson.

Quinn, who would be both the first female mayor and the first openly gay mayor in city history, was the early favorite. But now the latest Quinnipiac poll has her struggling with Thompson for second place, while de Blasio is threatening to sew up the nomination in the first round by winning more than 40 percent of the vote.

It is possible that Quinn is having a hard time because she’s a woman. Really, unless you’re Hillary Clinton, New York is tough. Also, she is the candidate most identified with Mayor Bloomberg. We feel as if Bloomberg has been running the city since the signing of the Treaty of Ghent.

And don’t discount the Central Park carriage horses. Animal rights advocates have long yearned to abolish the industry, and Quinn is the only major Democrat who disagrees. The horses are very well-protected by regulation — they have to have five weeks of out-of-town vacation a year. French workers do not have as good a holiday package as the Central Park carriage horses. However, they do have to walk through traffic, which makes many people uncomfortable.

The horses became a huge issue early in the campaign, when there was an entire mayoral forum devoted to the subject of animal protection. In it, John Catsimatidis, one of the Republican candidates, described how his wife tried to save the family’s aged cat with mouth-to-mouth resuscitation.

Quinn did not attend the forum. Neither did Joe Lhota, the Republican front-runner, who made news the other day when he criticized transit officials for closing down two subway lines for more than an hour after two lost kittens wandered onto the tracks. (The other candidates said they would have shut down the lines to save the cats. Anthony Weiner claimed he would have thrown his body over the electrified rail. Anthony Weiner is still not going to be elected mayor.)But Quinn, who owns two rescue dogs, was identified by the carriage horse crusaders as Public Enemy No. 1. Meanwhile, de Blasio, who vowed to retire the horses “first day I’m mayor,” became their hero.

(De Blasio seems to be hedging on the timing issue, perhaps realizing that putting the carriage industry at the tiptop of your mayoral to-do list sounds a tad over the top. “It will not be my first act, but it’ll be something I’ll do right away,” the candidate said in a radio interview this week.)None of this is a big deal for the average New Yorker; it doesn’t come up on the campaign trail unless there are people waving “Christine Quinn Hates Animals” signs. What we have here is a lesson in intensity of preference. The animal rights folks started early, and drew a bunch of wealthy donors, some of whom had long-running issues with Quinn that had no relation to four-legged friends. They ran tons of ads, organized phone banks and showed up with their protest signs, throwing the campaign off-stride.

Then de Blasio popped up as the change candidate, running to everyone else’s left. New Yorkers may look loopy or out of control to the outside world, but when it comes to running the city, we generally pick candidates who are, one way or another, going to rein things in. Maybe this year, New York liberals are ready to party. If so, it’d be the first time, really, since John Lindsay. Who was 6-foot-4.