At Penn, like many universities, R.A.s currently receive free housing and some meals but no pay for what the university describes as 15 to 20 hours per week of work.

Students involved in union drives at Penn and other schools have said that they want more benefits for undergraduate workers, including stipends, scheduling policies and protections against arbitrary firings and other kinds of discipline. The National Labor Relations Board had said that 218 undergraduate and graduate R.A.s would be covered by the new union at Penn.

“We as R.A.s are integral to campus life but are consistently undervalued and underpaid,” Penn union organizers wrote on Instagram in March, when they first filed a petition to be recognized. “We are organizing for fair compensation, better communication and a more democratic workplace — when R.A.s are supported, so is the entire Penn community.”

The demands challenge longstanding assumptions among administrators about the aims of undergraduate work gigs.

“What we thought of as training opportunities, they see as jobs,” Lori White, the president of DePauw University in Greencastle, Ind., said during a discussion with university presidents and journalists this month.

Until recently, labor organizing on college campuses usually involved faculty members, full-time employees or graduate students.

But this week’s vote in Penn’s Houston Hall extended efforts to bring undergraduates into labor’s fold. Since the start of 2022, some undergraduates have unionized at a range of universities, including Columbia, Barnard and Wesleyan. That has added up to an “extraordinary and historic” run of labor organizing on campuses, according to an analysis by the National Center for the Study of Collective Bargaining in Higher Education and the Professions at Hunter College.

Penn opposed the unionization effort on its Philadelphia campus, arguing that R.A.s were not covered by the federal law that governs collective bargaining. But in August, an N.L.R.B. official rejected Penn’s assertions and ordered this week’s secret-ballot election.

In a statement after the polls closed on Thursday night, Penn did not repeat its opposition. Instead, it thanked students “who participated in this important process.”

After the Penn election results are certified, the university and the newly recognized union will begin negotiating toward a contract, a process that could take months. Resident advisers at Tufts University, for example, voted in December to unionize and only this week ratified a three-year contract with the university, which agreed to pay the students $2,850 and cover 160 dining hall meals per academic year. The negotiations were sometimes tense: In August, the advisers staged a strike on move-in day.

Efforts to organize undergraduate students are also bubbling elsewhere. At the University of Oregon, student workers will vote in October on a unionization effort. Some Harvard undergraduates, including library and dining workers, will also vote next month.

And California State University students are waiting for a ruling from a state board about their quest for a unionization vote. Union officials have estimated that a successful campaign at Cal State, the largest four-year public university system in the country, would affect about 10,000 undergraduate workers.