CHICAGO — History was made in Chicago’s wide-open mayoral race last night. Bill Daley, the son and brother of the city’s second-longest and longest-serving mayors, finished a close third behind Lori Lightfoot, a Democratic former federal prosecutor, and Toni Preckwinkle, chairwoman of the Cook County Democratic Party. After a runoff in April, one of the two women will be the city’s first black female leader. Long dominated by a white patriarchal machine, Chicago should celebrate its milestone.

But after a convoluted and at times chaotic race, the winning women will move forward having each won less than 20 percent of the vote amid a record-breaking field of 14 competitors.

With 1,999 of 2,069 precincts reporting, Mr. Daley had collected 14.8 percent of the vote, Ms. Preckwinkle 16 percent, and Ms. Lightfoot 17.5 percent. However, the candidates Jerry Joyce, Amara Enyia, Susana Mendoza and Willie Wilson all got between 7.4 percent and 10.5 percent of the vote, and their constituencies’ support placed in any other candidate’s bucket would have swung the vote in any number of directions.

Various people reported struggling to make the complex strategic calculus that runoff systems force electorates to make: Should you vote your heart, for the candidate with whom you most agree? Or do you go with one of the candidates you don’t like but that you at least like more than the person who you fear has the best chance to win? If so, who’s that candidate?