A measure that would have given San Francisco police officers more latitude in when they can shock suspects with Taser stun guns was defeated Tuesday.

Proposition H, put forward by the officers’ union, garnered 40 percent of the vote with nearly all precincts reporting.

“I think the biggest takeaway is that the police officers association as a political force is clearly fading in the city,” said Alex Post, an attorney with the state public defender’s office who co-chaired the opposition committee.

Tony Montoya, president of the union, was disappointed but said, “The voters have spoken.”

“We will still work with the Police Commission” on implementing rules for Tasers, he said. “We want a policy out there that’s going to be smart and effective.”

Takeaway: Whether city officers should carry the shock weapons has been a source of debate for years. That question was settled by the Police Commission, which approved the devices in November and adopted a policy regulating their use in March. Officers are supposed to get them around the end of the year.

The union, however, was frustrated by the commission’s pace in setting the rules. Its ballot measure would have established less restrictive guidelines for when Tasers may be deployed. Opponents saw it as usurping the Police Commission’s power. The measure was a clear test of the police union’s citywide clout.

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Background: Tasers fire a pair of electric darts intended to strike and incapacitate a person. Supporters of the devices say they help officers subdue suspects without resorting to lethal force, and note that the SFPD is one of the last major departments in the country without them.

Critics of Tasers have questioned whether the weapons are effective, pointing out that in some cases, officers have shot people after they cannot subdue them with a Taser. In some cases, shocks from stun guns have led to deaths.

Under the Police Department’s use-of-force policy, officers will be permitted to deploy Tasers on suspects who are “violently resisting.” The union-backed measure called for lowering the standard to when a suspect is “actively resisting.” Under Prop. H, that standard could have been amended only at the ballot box or by a four-fifths vote of the Board of Supervisors.

Under the commission-backed policy, officers can use Tasers only when a person is “armed with a weapon other than a firearm, such as an edged weapon or blunt object” and is injuring or intending to injure another person.

Officers are limited, but may still use Tasers in special circumstances.

Evan Sernoffsky is a San Francisco Chronicle staff writer. Email: esernoffsky@sfchronicle.com Twitter: @EvanSernoffsky