Most Massachusetts residents didn’t have a choice this November of who represented them at the State House. That didn’t stop them from sending legislative leaders a message.

The state’s voters on Tuesday overwhelmingly approved a pair of proposals that impose new scrutiny on the state Legislature and scrap the MCAS as a graduation requirement, bucking the state’s Democratic leaders who opposed, and in some cases outright campaigned against, two questions that will shake Beacon Hill in different ways.

The measures, listed as Question 1 and Question 2 on Tuesday’s ballot, accomplish two very different objectives. The first specifies that state Auditor Diana DiZoglio has the authority to audit the House and Senate; the second eliminates a decades-old mandate that makes earning a high school diploma contingent on students passing MCAS exams in English, math, and science.

Neither was popular among Beacon Hill’s top leaders. The Senate and House’s top Democrats opposed both questions and last month left open the possibility of changing them if they passed. Governor Maura Healey was a staunch opponent of the MCAS question and appeared on the campaign trail urging residents to vote against it. A legislative committee tasked with reviewing the measures before they reached voters said the Legislature shouldn’t pass them.

“This is one of those moments where there’s this incongruence between what our elected officials would like us to do as a state, and what our people would like us to do,” said Tatishe Nteta, the director of the UMass Amherst Poll. He said the passage of Question 1 particularly is a “warning sign” for the Legislature’s Democratic supermajority.

“Question 1 is the opportunity for citizens, symbolically or actually, to say they have some fundamental problems with the way the Legislature is working,” Nteta said. “In some ways, it’s a stunning rebuke of the lack of engagement and lack of activity in the Legislature.”

To what degree lawmakers view it that way remains to be seen. Almost immediately after the Associated Press projected Question 1 to pass late Tuesday, House Speaker Ron Mariano and Senate President Karen E. Spilka said they’d weigh “how to best respect the Question 1 election results” while potentially altering it. DiZoglio said separately she’d fight against any effort to “undercut” the initiative and would lobby Healey to veto any bill the Legislature passes seeking to alter it.

State Representative Paul Donato, a Medford Democrat, said Wednesday that the speaker had yet to gather his leadership team to discuss plans for the ballot questions.

“The Speaker’s got some ideas,” he said, without elaborating.

Legislative leaders regularly chafe at the idea of legislating by ballot, where advocates can write the laws as they see fit and lawmakers often fret about the potential for unintended consequences. Activists frustrated by legislative inertia are often the ones driving a measure to the ballot, either in hopes of forcing the Legislature’s hand to pass similar legislation or simply to circumvent it.

Indeed, voters approved another measure to give Uber and Lyft drivers the right to organize a union, the AP projected Wednesday.

Voters rejected two other statewide proposals, however, according to projections from the AP. About 57 percent of voters rejected a proposal to legalize the use and possession of psychedelics like psilocybin mushrooms. Question 5, which would have eventually raised the minimum wage for all tipped employees to $15 per hour, drew opposition from about 64 percent of voters, according to unofficial tallies.

It’s Question 1 and Question 2, however, that will reverberate loudest in the State House. Legislative leaders have argued that an audit of their chambers, particularly one that DiZoglio has sought to do, would violate the constitutional separation of powers. DiZoglio, a first-term Democrat, argued that the Legislature is among the most opaque legislative bodies in the country, and, on a recent podcast appearance, accused Democratic leaders of trying to “weaponize the Constitution to protect themselves.”

“Even folks who aren’t really sure about what exactly an audit would entail are across the board absolutely interested in more transparency,” DiZoglio said Tuesday, wearing a bright yellow jacket and shoes as symbols of her push to bring more “sunshine” to Beacon Hill.

Residents, she said, are “tired of not hearing about what’s happening with the bill until after the decision has already been made and it’s already been voted into law. And they want to be able to participate in what is called a democratic process, but is actually more like an authoritarian regime in the Senate and the House of Representatives right now.”

Voters who backed it Tuesday described the measure as a common-sense addition.

“That’s the point of the auditor,” said Matt Ramsey, a 46-year-old Arlington Democrat who backed the measure. Audits, he said, are meant to look back and identify problems in order to correct them. “It doesn’t have to be [about] penalization.”

That voters approved it by such yawning margins — 72 percent to 29 percent, according to unofficial results with 95 percent of votes in — doesn’t necessarily mean, however, that they believe in the abstract idea of an empowered state auditor, said Evan Horowitz, executive director of Tuft University’s Center for State Policy Analysis, which studies the impact of ballot questions.

“It’s a referendum on the Legislature,” he said. “That one is the clearest rebuke to current practice.”

For Question 2, he said, the message may be more muddled because voters likely have different reasons for getting rid of the graduation mandate. About 59 percent of voters supported removing the graduation requirement, compared with 41 percent who did not, according to unofficial vote tallies.

Indeed, voters on Tuesday cited a litany of reasons for supporting the measure in interviews with the Globe, from the strain they believe it puts on teachers to prepare students for the test to a general discomfort with the “one-size-fits-all” requirements the mandate creates.

“That’s not how students learn,” said Aimee Doherty, a 38-year-old Stoneham resident and elementary physical education teacher. “We already have state standards — and Massachusetts has really high standards.”

Horowitz, of Tufts University, said he read the Massachusetts Teachers Association victory another way.

“It’s some voters saying: ‘No, we don’t need a statewide system. We trust our districts more, we trust our teachers more,’” he said. “It should be a wakeup call to the education reform establishment on Beacon Hill, which I think has felt quite happy with the status of our education system and the effect of the last two decades.”

Ideally, voters who are unhappy with the direction the Legislature has taken on certain issues could make their voices heard with every biennial election, when every member of the House and Senate are on the ballot. But the Massachusetts Legislature is considered, by one measure, the least competitive in the country, meaning many voters don’t often have an opportunity to choose someone new to send to Beacon Hill even if they want.

Just three candidates seeking to unseat incumbent officeholders on Beacon Hill prevailed during the September primary. On Tuesday, roughly three out of every four seats in the Legislature listed a single name on the ballot. Only a handful of seats actually flipped parties, with Republicans netting a single seat in both chambers.

Nonetheless, polling has hinted at a growing frustration. The share of voters who said they approved of the Legislature has regularly dropped since the spring of 2023, when 57 percent of voters said in a UMass Amherst poll that they liked what lawmakers were doing. That sank to 46 percent by an October survey, at a time when lawmakers still had yet to pass major legislation addressing climate change or a sweeping economic development package, months after formal sessions had initially ended.

“There needs to be more transparency in the Legislature. It’s all Democratic. If you do elect some Republicans, you may have some balance,” said Lynn Wetzel, a 71-year-old North Andover resident who voted for the audit initiative Tuesday.

A registered independent, Wetzel said she had another reason to support it. “The fact that [lawmakers] are so strongly against being audited,” she said with a laugh.

Samantha J. Gross of the Globe staff contributed to this report.