The San Francisco Board of Supervisors tilted a bit more to the left after Tuesday’s election. How much that shift will impact its approach to issues such as homelessness and the housing crisis will reveal itself as the dynamics of the new group take shape.

On top of that, dealing with a board with a progressive majority could be dicey for Mayor London Breed, as she tries to carry out key parts of her agenda before her run for re-election in 2019, political observers say.

Three candidates likely to join the board after last week’s final results are tallied — Gordon Mar in District Four, Matt Haney in District Six and Shamann Walton in District 10 — are all largely considered to be progressives. During the campaign, each said he would push for high levels of affordable housing and supported Proposition C, which set taxes on big businesses to raise money for homeless services. It received overwhelming support from voters but probably faces legal challenges.

Mar, who has long worked as a neighborhood and labor activist, helped lead a group that pushed for free tuition at City College and worked to raise the city’s minimum wage to $15. His campaign also received staunch support from labor unions.

Walton is the executive director of the Young Community Developers, a nonprofit that provides job training and develops affordable housing.

On the school board, Haney led initiatives to build future affordable housing for teachers and helped plan a school to be built in Mission Bay.

But political analysts and some of the current supervisors are having a hard time neatly defining Walton for his wide range of endorsements spanning the political spectrum — from Sen. Scott Wiener to various labor groups to the San Francisco Building and Construction Trades Council. The same fingerprinting problem goes for Haney for some of his campaign platforms, including his desire to increase pressure on police officers to arrest more drug dealers in the Tenderloin.

Add them to current Supervisor Rafael Mandelman — who is considered progressive on some issues, but is also is spearheading legislation with Breed to expand the city’s conservatorship laws — and the board will have a mash-up of members who could act as swing votes.

While having so many swing votes could lead to a sense of unpredictability, Jason McDaniel, a political science professor at San Francisco State University, said it could also lead to a more cooperative board that’s willing to compromise with one another.

“It will be up to them (the board) on an issue-by-issue basis to decide where they want to govern,” McDaniel said. “It becomes more about alliances and coalition building. ... If you think of it in terms of left versus right, it gets very, very confusing.”

The blurry political lines are different from earlier iterations of the board, when Chris Daly, John Avalos, Tom Ammiano and David Campos wore their progressive labels proudly. But now, ask nearly any current supervisor what they consider themselves — progressive or moderate? — and they’ll likely as not duck the answer. Walton and Haney did the same during the campaign, too.

“I feel like it’s overblown,” Mandelman said.

“I haven’t really felt that divide,” said Supervisor Ahsha Safaí, considered a moderate, but who said he doesn’t “embrace political labels.”

“At the end of the night, my job is to work with all of my colleagues,” said Supervisor Aaron Peskin, a progressive. “Not everyone fits into convenient buckets.”

Both District Five Supervisor Vallie Brown and District Two’s Catherine Stefani — who will probably win the seat for a full term — are also considered part of the moderate faction because of their backgrounds and policy stances. On the progressive side are Supervisors Sandra Lee Fewer, Norman Yee and Hillary Ronen.

David Latterman, a political consultant, doesn’t buy the idea that the progressive and moderate labels have been diluted. He said the divides will really show during the budget season, a time when the supervisors sometimes quarrel over where exactly the money should go.

“It’s not exactly what it was in the early 2000s when you had self-defined progressives and a movement and a cause, and they all ran together,” he said. But “the fact remains that you have six to eight progressive-leaning board members, maybe a few swing voters who will be there sometimes, and sometimes not.”

There are certain issues, however, where the progressive-majority board will use its weight.

Up first is electing a new president, the person with the power to fast-track legislation and make committee assignments. Given the new board, that person will probably be someone who leans left. Supervisor Hillary Ronen, vividly progressive, said she is gunning for the job.

Based on their campaign rhetoric, Haney and Walton will probably demand the highest rate of affordable housing possible in new development projects in SoMa and Bayview-Hunters-Point.

Another issue will be the “Twitter tax break,” which lured tech companies to the city with a payroll tax break in 2011 and has been cited by some as a reason for the San Francisco’s soaring housing prices and traffic problems. It’s set to expire next year, but the board could renew it.

With a progressive-majority board, “there is a less than zero chance that that would go anywhere,” political analyst Jim Stearns said. “That thing is deader than dead.”

It remains to be seen how a progressive-majority board will work with Breed. The outcome of the races put into question how many allies Breed will have on the 11-member board when it comes to fulfilling key parts of her agenda, such as building more Navigation Centers and adding homeless services in parts of the city aside from the Tenderloin, the Mission and Bayview-Hunters Point.

But the fact that the candidates who are likely to win didn’t run on an “anti-Breed” platform is perhaps a sign that she will be able to forge connections on the board, McDaniel said.

“It’ll be harder for Breed to govern on the agenda she campaigned on,” McDaniel said. But “there is space for Mayor Breed to find areas of governance. ... It’ll be up to the mayor to see if she can forge allies.”

Trisha Thadani is a San Francisco Chronicle staff writer. Email: tthadani@sfchronicle.com Twitter: @TrishaThadani