Lyft echoed the sentiment, saying it “provides consumers with an alternative to vehicle ownership and drivers with the ability to make money in their free time.”

On-demand workers elsewhere have also explored organizing, including workers on the Amazon service Mechanical Turk, who perform piecework assignments that range in complexity from tagging photos to rewriting blog content. In 2014, a group of Uber drivers in Southern California associated themselves with a local Teamsters union in hopes of organizing. Neither effort seems to have borne much fruit.

ABDA is working with Seattle Teamsters Local 117. Dawn Gearhart, a representative for Local 117, said working for on-demand companies provided flexibility but had downsides. “It’s a really attractive model for employers, but that doesn’t mean that all the rights that workers have fought for over the past century should go out the window,” she said.

Unionization could give drivers leverage to negotiate on issues many of them feel powerless to do anything about now. For instance, drivers could gain a voice on minimum per mile charges for riders and establishing processes for deactivating drivers that seem less arbitrary than the ones currently in place at Uber, said Mike O’Brien, a Seattle City Council member who introduced the unionization legislation.

“It’s clear the nature of work has shifted in part because of technology and in part because there are corporations that don’t like labor protections,” he said. “What is that reality going to look like? I believe there should be some solutions.”

Uber has clashed with the city of Seattle before. Last year, the City Council voted to place caps on the number of cars allowed on the road for Uber and other smartphone ride services. Uber mobilized its customers against the proposal, making it simple for supporters to call their local political representatives with a tap in the app. The city eventually killed the cap.

This time, the process in this tech-loving city — home to many Amazon and Microsoft employees — is playing out differently. On Wednesday, the phones in Mr. O’Brien’s office were quiet. He said he had received few complaints from Uber customers about the right-to-unionize vote and, to his knowledge, Uber had not sought to mobilize its users the way it did before.