The policy differences among the four leading candidates for San Francisco mayor are not profound. Each is a San Francisco Democrat and experienced legislator who checks all the requisite boxes: support for sanctuary city, advocate of affordable housing and tenants’ rights, and champion of the causes of income inequality, civil rights and ending bias in the criminal justice system.

Two of the candidates, Supervisor Jane Kim and former state Sen. Mark Leno, want to push a progressive agenda with decidedly regulation-heavy approaches to buffering the side effects of a tidal wave of prosperity that is making life difficult for many residents, small businesses and arts and cultural endeavors of modest means.

Angela Alioto, who served on the Board of Supervisors from 1988 to 1997, rhapsodizes about recapturing a bygone era when homelessness was nonexistent, the streets were clean and crime was less prevalent. “The soul of the city is being torn away,” she told our editorial board.

One candidate stands out for both her commitment to address the concerns she shares with her opponents and her willingness to listen to competing arguments and come up with adjustments that achieve a progressive ideal in a more workable and reasonable manner. This sensibility is one of the most important attributes in a mayor, and the candidate who most demonstrates it is London Breed, president of the Board of Supervisors.

Perhaps the most critical issue facing San Francisco is the celestial cost of housing, which is straining the ability of working families to get by, aggravating landlord-tenant relations, contributing to the homelessness crisis and severely complicating the ability of employers to recruit and retain workers. As workers migrate to suburbs they can afford, housing costs also are inextricably linked with the traffic headaches that are becoming common at times and in places never seen before in the Bay Area.

Among the top four candidates, Breed has been most pronounced in acknowledging that the affordable housing problem is not going to be cured by City Hall mandates alone. She is willing to say out loud that San Francisco has a housing shortage at all levels, as it undeniably does.

Leno, and Kim particularly, emphasize government controls as their primary solutions to housing costs and tenant protections — as if the law of supply and demand does not really apply here. It does, like it or not.

The differences in approach are most evident in the candidates’ responses to a bill by state Sen. Scott Wiener, D-San Francisco, to compel development around transit hubs. The concept of his SB827 is sound: require higher-density development along major transit hubs, such as BART and Caltrain stations, and to a lesser extent along popular bus lines and light-rail stops.

None of the candidates would argue with the need for more transit-oriented development, but the prospect of losing some local control makes the issue easy to demagogue against — as Kim and Alioto did, hyperbolically and a bit disingenuously, to robust applause at a Monday night debate. Kim called it “a giveaway to developers” that doesn’t ask for anything in return. Alioto warned that it would “destroy who we are as a city.”

Breed was the candidate who seemed actually to have read the Wiener plan. For example, it does not preempt local design standards, affordable housing requirements, demolition rules or the ability to charge impact fees. Breed did suggest that more amendments may be required for her full support, but she came across as the candidate who was willing to work to achieve a difficult but important objective.

Her solution-aimed approach is, in a word, mayoral.

On homelessness, the city’s seemingly intractable issue, Breed has made plain it is “definitely at the top of my priority list,” and her multifaceted plan is both compassionate and tough-minded. She has pledged to end tent encampments within her first year in office. She has advocated conservatorship legislation that would allow courts to appoint guardians for individuals whose mental illnesses leave them incapable of caring for themselves. She has ambitious plans for expanding housing available to people without homes.

At 43, Breed has emerged as one of the dynamic new leaders in the city. Elected to the Board of Supervisors in an upset over an appointed incumbent in 2012, Breed was re-elected handily in 2016 and selected by her colleagues as board president.

Her leadership skills were demonstrated again in December when she assumed the role of acting mayor after the death of Mayor Ed Lee, and assumed the duties with an aura of grace, calm and fitting humility. That did not stop progressive factions, fearful that her title would give Breed an edge over Kim and Leno in the June special election, from plotting to replace her with Supervisor Mark Farrell.

The leftist faction succeeded, but its scheme may yet backfire, especially if the anger expressed by women and African American leaders translates into votes in June.

Breed has a remarkable personal story she invokes at almost every campaign forum: raised by her grandmother in a roach-filled apartment in the Western Addition, with spotty plumbing and a shower that never worked, in a neighborhood surrounded by poverty and violence. Her younger sister died of a drug overdose; her older brother is in prison.

Against all odds, Breed persevered. She graduated from UC Davis, interned in Mayor Willie Brown’s Office of Housing and Neighborhood Services, and ultimately became the executive director who revitalized the African American Art & Culture Complex in her old neighborhood.

No one has to lecture Breed about the challenge of living hand to mouth in this city. And no one in this field has a better firsthand appreciation of the importance of creating opportunity for those who are left behind. Anyone who thinks London Breed is going to be a pawn of power brokers has never been on the receiving end of a dissenting London Breed phone call.

She is fearlessly independent, as tough as she is charismatic.

An election necessarily involves choices, and this race is among appealing ones. Mark Leno distinguished himself as one of the most gracious, tenacious and effective legislators during his 14 years in the State Capitol, author of 161 laws and well respected across the aisle. Angela Alioto, daughter of the late Mayor Joe Alioto, was a pioneering supervisor on issues such as smoking bans and led Mayor Gavin Newsom’s efforts on homelessness. She is second to none in her expressed passion for the city. Jane Kim is proving to be a smooth and forceful campaigner and the definitive voice for progressives who are hoping to reclaim power.

It is no small feat for London Breed to emerge from this talented field as the right candidate at the right time to bring together a city whose ability to meet big challenges is too often derailed by petty politics and provincial forces. San Franciscans should vote on June 5 to return her to the mayor’s office.

This commentary is from The Chronicle’s editorial board. We invite you to express your views in a letter to the editor. Please submit your letter via our online form: SFChronicle.com/letters.