OLYMPIA — Supporters of the affirmative-action measure Referendum 88 have conceded defeat, as Washington’s counties began tallying and posting the bulk of their remaining ballots.

With King, Pierce, Snohomish, Kitsap and other counties reporting late Tuesday afternoon, the statewide measure trailed 49.6% to 50.4%.

Down by roughly 15,000 votes, the measure fell comfortably outside the number needed to trigger a mandatory recount.

If approved, Referendum 88 would have implemented the affirmative-action measure known as Initiative 1000. Approved by state lawmakers this spring, I-1000 reinstated affirmative action for public contracting, employment and education.

“After a week of ballot counting it is clear that I-1000 will fall just short of approval,” Cherika Carter, campaign manager for the WA Fairness Coalition, said in a statement. But, “With nearly 50% of voters voting to Approve I-1000, it’s clear that many Washingtonians want a better, more fair and equitable state with opportunities for all.”

After lawmakers passed the measure, opponents of the new law — led by a group of Chinese immigrants — gathered signatures to get it on the ballot. The group, known as Let People Vote,  argued the policy was “divisive” and essentially created a system for racial quotas that would allow state government to discriminate.

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“Our coalition of volunteers from across the political spectrum defeated the Pro-88 campaign because voters didn’t want a new system of quotas based on race, nor did they want a massive new unaccountable government bureaucracy to implement it,”  Linda Yang, one of the group’s leaders, wrote in a statement Tuesday evening.

Even before Tuesday’s results, the measure looked unlikely to pass, with two large vote counts from King County on Friday failing to keep it in the lead. On Saturday, after Snohomish County posted more results, Referendum 88 trailed by almost 13,000 votes.

A majority of voters in at least four counties were approving the measure: Whatcom, Jefferson, San Juan and King. Most of those votes have come from King County, where the measure was passing Tuesday with 63%.

But voters in other counties rejected the measure, often by wide margins. Referendum 88 Tuesday trailed by 12 points in Pierce County and nine points in Snohomish County.

In Thurston County, which hadn’t posted updated results Tuesday evening, the measure trailed by about 200 votes.

The vote sparked the first public conversation over that affirmative-action policy since Washington voters in 1998 decisively cast ballots to ban affirmative action with Initiative 200.

Supporters of affirmative action have called the policy necessary to make up for longstanding discrimination against women and people of color in education, jobs and other spheres of life.

One example cited is data showing a drop in state contracts for certified women- and minority-owned businesses since the affirmative-action ban.