Three million people live in the city of Chicago. But just 20 of them made all the difference in determining who would have control of the city government. Last month voters in seven Chicago wards redistricted by a federal court went to the polls and chose between candidates supported by Mayor Harold Washington and those loyal to Alderman and Cook County Democratic Chairman Edward Vrdolyak. Last week the last of several courts ruled on the result in the 26th ward, upholding the 20-vote margin by which Luis Gutierrez was reported ahead of Manuel Torres. Since his election in 1983, Mr. Washington has been on the short end of a 29-21 split on the board of aldermen. With the winners of the recent elections, including Mr. Gutierrez, he now has 25 votes. His own tie-breaker gives him control.

That means, even in old-style Chicago, less than it used to. A federal court order that is itself getting quite old forbids elected officials from hiring and firing city employees, even those not covered by civil service, for political reasons. This flies in the face of what every Chicagoan knows: that there is a Democratic and a Republican, a regular and a reform, way to sweep the streets and keep the Sanitary District operating. Patronage politics continues in some quarters, however. The Vrdolyak 29 refused to confirm the mayor's appointments to commissions that control the Chicago Park District, the Regional Transit Authority, the city colleges board and other agencies. The Washington 25 plus the mayor will now confirm them and thereby get control of perhaps 20,000 jobs.

More important is what Mr. Washington's victory does for the quality of government and of public discourse in the city. Chicago's politics has been plagued by racial animosity of an intensity not seen in most big cities for a decade, and both the mayor and his opponents have, at different times and to varying degrees, contributed to that mood since 1983. Now Mr. Washington has a chance to set a more positive tone. As blacks cheer the victory of the city's first mayor and whites sulk in fear that their interests and safety will be ignored by City Hall, the mayor must prove he can govern fairly and well. Next year he must run again, in a city in which blacks are still not a majority even in the Democratic primary, and then he will have to balance the need to motivate his mostly black core constituency against the need to mollify the hesitant whites whose votes he must have. He has proved he can win elections, but he -- and those citizens anywhere who think their votes don't count -- might keep in mind that in the most recent and crucial of them the margin of victory was just 20 votes.