Paul Vallas, a former public school executive, has called for a crackdown on crime, while Brandon Johnson, a county commissioner, wants to expand social programs.CHICAGO — After rejecting the incumbent mayor, Lori Lightfoot, in the first round of balloting in February, Chicago voters were set to choose on Tuesday between two candidates with starkly different visions for the country’s third-largest city.Paul Vallas, a former public schools executive, has run on a more conservative platform, calling for a larger police force, a crackdown on crime and more charter schools. His opponent, Brandon Johnson, a county commissioner and union organizer, has campaigned as a proud progressive who wants to expand social programs, spend more on neighborhood schools and add new taxes.The runoff election comes as Chicago fights to regain its prepandemic swagger. In recent years, the city has been confronted by rising crime rates, an emptier downtown and census estimates showing a loss of residents. Ms. Lightfoot, who missed the runoff after receiving only 17 percent of the vote in February, presided over two teacher work stoppages and civil unrest during her single term in City Hall, leaving many voters frustrated and frightened.“This city needs a lot — it needs safety,” said Shermane Thompson, who voted for Mr. Johnson and said she was scared to let her 9-year-old son play outside. “Jobs, mental health — it’s a lot of things that need to be done. But I want it to be done in a way that is long-lasting and that works for everyone, not just for select people.”The election in Chicago is the latest race in a large, liberal American city in which crime has been a primary issue. In New York City, Mayor Eric Adams, a Democrat and former police captain, defeated progressive candidates in his party’s 2021 mayoral primary by calling for a crackdown on crime. And in Los Angeles last year, Karen Bass, a liberal congresswoman, was elected mayor in a race in which her more conservative opponent, Rick Caruso, a billionaire real estate developer, ran on a law-and-order message.Mr. Vallas, 69, made public safety the focus of his campaign, calling for tougher prosecutions of minor offenses and a rapid expansion of the Chicago Police Department, which is operating under a consent decree in federal court and without a permanent superintendent. That platform helped Mr. Vallas finish in first place in the first round of the election in February, though well short of the outright majority he would have needed to clinch the job without a runoff.In a heavily Democratic city, Mr. Vallas has faced criticism for past comments that he considered himself to be more of a Republican than a Democrat, and for an endorsement from the local chapter of the Fraternal Order of Police, whose leaders frequently use brash rhetoric and support Republican politicians. Still, his description of Chicago as a city in crisis and his pledge to get crime under control resonated with many voters.“I’m tired of looking out my window and watching drive-by shootings,” said Sherri Ortiz, a West Side resident who said this week that she was leaning toward Mr. Vallas, who she believed was more likely to fix things quickly.Mr. Johnson, 47, qualified for the runoff by defeating several better-known candidates competing for the same liberal voters. A former social studies teacher, Mr. Johnson has spent the last dozen years as an employee of the Chicago Teachers Union, a powerful but polarizing political force that contributed heavily to his campaign. In recent weeks, he has described a public safety vision that goes beyond law enforcement, but has tried to distance himself from past support for defunding the police.In a West Side campaign stop on Monday, Mr. Johnson pitched an upbeat vision for the city, saying “a better, safer Chicago is possible if we actually invest in people.”“We deserve to have a leader that’s prepared to bring people together,” he said, “and that’s what my candidacy reflects.”Earlier on Monday, outside a South Side doughnut shop in the neighborhood where he grew up, Mr. Vallas said his record leading “institutions in crisis” made him the right candidate for the moment.“It’s about leadership, it’s about somebody with the experience,” said Mr. Vallas, who led the school systems in Chicago, Philadelphia and New Orleans, and was surrounded by Black politicians who had endorsed him.Race has often played a role in elections in Chicago, which has roughly equal numbers of white, Black and Hispanic residents. Mr. Vallas, who is white, made it to the runoff with strong support in the city’s downtown and in majority white areas of the Northwest and Southwest Sides, where many municipal workers live. Mr. Johnson, who is Black, performed well along the city’s northern lakefront, home to many white progressives, and in predominantly Hispanic areas northwest of downtown.With polls suggesting a tight race, both candidates touted support from Black and Hispanic politicians as they sought to win over voters who supported Ms. Lightfoot or Representative Jesús G. García, another mayoral candidate, in the first round of balloting.Whoever wins the election, it will mark a decisive shift from the policies of Ms. Lightfoot, with Mr. Vallas running to her political right and Mr. Johnson well to her left.Four years ago, Ms. Lightfoot, also a Democrat, carried all 50 wards in the runoff election, becoming the first Black woman and first gay person to serve as Chicago’s mayor. But her tenure was bumpy from the start. Soon after she took office, the teachers’ union went on strike. And after less than a year in office, the coronavirus pandemic upended every aspect of daily life. As the virus spread, the Loop business district emptied out and homicides rose to generational highs.On the campaign trail this year, Ms. Lightfoot emphasized investments in long-neglected parts of the South and West Sides and noted that homicide rates, though still higher than before the pandemic, had started to decline. Voters, however, decided to move on.Michael Gerstein More