OLYMPIA — With Referendum 88 trailing by a slim margin, Washingtonians appeared like they might, for the second time in two decades, vote against affirmative action.

With most counties reporting results Tuesday, voters were rejecting the measure 51.3% to 48.7%, in an election that tested ideas of fairness and discrimination. Many more votes remain to be counted.

Supporters of affirmative action have said the policy is necessary to combat discrimination that determines who gets access to universities, government jobs and public contracts.

But throughout the campaign, opponents of affirmative action — led by a group of Chinese immigrants — said the policy gives the government the power to discriminate.

They criticized a commission that would have been created to oversee diversity efforts at state agencies, and they argued existing benefits for veterans were at risk.

“I think when you add all those together, voters don’t like it,” Linda Yang, a leader of the anti-affirmative-action campaign, Let People Vote, said Tuesday night.

Supporters of affirmative action on Tuesday kept hope blazing for a shift in their direction, with many ballots still to be counted in King County, where 60% so far were favoring affirmative action.

“I’m looking toward the last-minute ballots coming in,” said Cherika Carter, campaign manager for the Washington Fairness Coalition, the campaign supporting Referendum 88. “I recognize that young people and people of color like to take their time voting.”

In addition to King County, the measure Tuesday night was passing in Jefferson, San Juan and Whatcom counties.

But voters in the Western Washington counties of Pierce, Snohomish, Clark and Thurston joined with Eastern Washington in rejecting the measure.

Referendum 88 put to a vote the affirmative-action measure known as Initiative 1000, which Washington state lawmakers passed this spring after a signature-gathering campaign brought the measure to the Legislature.

The campaign has been the biggest public conversation on an emotional and highly charged issue since Washingtonians in 1998 banned affirmative action by a vote, and has served as a barometer for feelings about the state of equity and discrimination here, 20 years on.

I-1000, the measure passed by lawmakers, aims to increase diversity in public contracting, employment and education, while barring the use of quotas or preferential treatment.

The measure defines preferential treatment as using a single factor — such as gender, race, age or sexual orientation — to choose a lesser-qualified candidate over a better-qualified candidate.

Affirmative-action supporters say such measures are necessary to address longstanding and broad discrimination against women and people of color. One example they cite is data showing a drop in contracts with the state for certified women- and minority-owned businesses.

The effort to put the measure reinstating affirmative action before the Legislature gathered nearly 400,000 signatures. The campaign, led in part by former state lawmaker Jesse Wineberry, spent into debt along the way, however, and is now being sued for not paying its signature-gathering firms.

Once it hit the Legislature, opponents of affirmative action strongly protested the new measure.

They and other critics say I-1000 adds up to what is effectively a quota system by creating diversity goals and timetables to reach them.

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