WASHINGTON — The Supreme Court on Wednesday takes up a “faithless elector” challenge to the Electoral College, a sleeper case with potentially big ramifications for how the country chooses a president and one that could allow just a few people to decide the outcome of a close election.

Opponents of the existing system hope that the legal battle will spur the states to adopt changes that they say would make elections more responsive to the public.

The issue is a simple one: Are the 538 presidential electors free agents, or must they vote in accordance with the election results in their states? If they are free to vote as they wish, a small group of them, or even a single one in a tight contest, could decide who wins the White House.

When voters go to the polls in November, they do not vote directly for a presidential candidate. Instead, they choose a slate of electors appointed in their states by the political parties of the presidential candidates. Those electors meet in December to cast their ballots, which are counted during a joint session of Congress in January.

In more than half the country, electors are required to obey the results of their state’s popular vote and cast their ballots accordingly. The problem of “faithless electors” who disregard the popular vote outcome has not been much of an issue in American history, because when an elector refuses to follow the results of a state’s popular vote, the states usually throw the ballot away. But can the states do that?

The cases before the Supreme Court involve faithless electors during the 2016 presidential election. Instead of voting for Hillary Clinton, the Democratic nominee, who won the popular vote in Colorado, Micheal Baca cast his vote for John Kasich, a Republican and then the governor of Ohio. And in Washington state, where Clinton also won the popular vote, three of the state’s 12 electors voted for Colin Powell, the former secretary of state.

Baca told NBC News that after Donald Trump was declared the apparent winner in November: “I thought we would need electors who would choose a moderate compromise candidate. We wanted to put our country before party and maybe throw the election (into) the House of Representatives.”

Colorado tossed Baca’s vote out and found another elector who voted for Clinton. So he sued, and the 10th Circuit Court of Appeals in Denver ruled that electors can vote for any legitimate candidate.

States are free to choose their electors however they want, the court said, and can even require electors to pledge their loyalty to their political parties. But once the electors are appointed and report in December to cast their votes, they are fulfilling a federal function, and the state’s authority has ended.

In Washington, the state accepted the votes of its rebel electors but fined them for violating state law. The electors challenged the fines, but the state Supreme Court upheld the law requiring them to conform to the popular vote.

The U.S. Supreme Court took both cases to decide which outcome is the correct one. The court ruled in 1952 that states do not violate the Constitution when they require electors to pledge that they will abide by the popular vote. But the justices have never said whether it is constitutional to enforce those pledges.

The states argue that the while Constitution gives them broad powers to decide how electors are appointed, it also authorizes them to attach conditions.

If the electors are right that they are free agents, “a state could not remove or sanction an elector after appointment even if it learned that he was offering his vote to the highest bidder, was being blackmailed by a foreign power, or had lied about his eligibility to serve,” Washington state said in its court brief.

The lawyers for the electors, however, said the states have no power to compel an elector’s choice.

“The structure of the Constitution, as interpreted by this court over our 230-year history, prohibits the states from interfering with the exercise of this plainly federal function,” said Lawrence Lessig, a Harvard law professor involved in both cases.

Lessig has said he hopes the cases will eventually lead to a change in the Electoral College, either through a constitutional amendment or by encouraging more states to adopt a system in which they would assign all of their electors to whoever wins the nationwide popular vote for president. Fourteen states have already agreed to do so. An interstate agreement to make the change would take effect once the participating states represent at least 270 votes, the minimum number needed to be elected president.

Rick Hasen, a professor and an election law expert at the University of California at Irvine, called the decision to bring the cases to the Supreme Court “a well-intentioned, audacious gambit. And it could backfire spectacularly.” Lessig, he said, “is playing with fire.”

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Hasen said there’s a chance the Supreme Court could declare electors to be free agents. He and others supporting the challengers note that Alexander Hamilton, writing in the Federalist papers, said presidential electors would be “persons, selected by their fellow-citizens from the general mass … most likely to possess the information and discernment requisite to such complicated investigations” as determining who was qualified to serve as president.

But Hasen says there’s little chance that in the current polarized atmosphere, the country would come together and agree on how to change the system.

Paul Smith, of the Campaign Legal Center, a nonprofit watchdog group, agrees, saying: “It is one thing to upend the election-regulation landscape. It is quite another to do so just months before a hotly contested presidential election.”

The court will likely issue its decision by late June.