Despite the billions the campaigns will spend this year to take the presidency, most voters have already chosen their candidate, according to new research cited in The New York Times.

That means that the deciding votes now rest in a handful of swing states. But in some of these states, it’s not yet clear who will get to cast a ballot come November.

Since last year, 16 states have passed some kind of restrictive voter laws, an “unprecedented” number, according to voting rights advocates.

Many of the new laws require voters to present some form of government-issued identification. But these requirements raise new barriers for minorities and people who can’t afford or otherwise obtain the proper documentation, according to a recent study [pdf] by the Brennan Center for Justice, a nonpartisan civil rights watchdog.

Proponents of the laws say the goal is to prevent fraud. While instances of ineligible voters casting a ballot are extremely rare, according to civil rights advocates and a recent study by News21, a Carnegie-Knight investigative reporting project, those focused on fraud argue that even a few people voting illegally could skew the vote.

But the Brennan Center says such laws amount to voter suppression, which has a much greater impact on the final tally. It said that the laws could make it “significantly harder” for as many as 5 million people to vote.And at least two Republican officials have suggested that’s the intent of recent efforts in their states.

Given the tight race, there are three swing states that are likely to be most affected by new voting policies this election: Florida, Ohio and Pennsylvania. Ohio and Pennsylvania are waging battles in court right now over who will — or won’t — be counted in November. Decisions are expected in both cases this week.

Here’s what you need to know:

FLORIDA

This swing state has a history of problems with its voter rolls, and this year is no exception.

In May, state officials announced a purge to remove non-citizens from its voter rolls. But the list it sent to county officials included names of eligible citizens. County election supervisors suspended the purge, and the Justice Department sued the state to officially ban it.

The Justice Department and civil rights groups argued the purge was discriminatory, a charge the state denies. But Jim Greer, the former state GOP chairman, said in a May court deposition that party officials and staff had held meetings to talk about “keeping blacks from voting.” (Current GOP state officials deny these discussions and say Greer is trying to taint the party. Greer was forced to resign his position in 2010 amid allegations he had mishandled party money, and now faces six charges of money laundering and fraud.)

In June, a federaljudge upheld Florida’s purge, clearing the way for the Department of Homeland Security to give the state access to a database it maintains to verify citizenship of some individuals. The two parties are working on a memorandum of agreement that specifies how the process will work.

“We’re still very optimistic that can be done very soon, and once we get that signed we’ll then begin to verify the names of potential non-citizens we’ve identified,” said Chris Cate, the spokesman for Florida’s Secretary of State, Ken Detzner.

Florida’s primary election will be held Aug. 14. State officials hope to start drawing up a new list to purge before the general election in November.

Local officials, meanwhile, have threatened to rebel again if the list is flawed.

PENNSYLVANIA

The swing state passed a law in March requiring voters to produce a government-issued photo ID card to vote.

The American Civil Liberties Union has challenged the Pennsylvania law on the grounds that people without a valid birth certificate or driver’s license can’t procure an ID that would allow them to vote.

OHIO

In this swing state, the fight is over provisional ballots.

Provisional ballots are those handed out to voters whose names aren’t on the list or have other complications on voting day. These ballots aren’t counted in the initial tally, but can be included later if the voter proves his eligibility.

Congress mandated the nationwide use of provisional ballots after the controversial 2000 election as a fail-safe way to ensure that every eligible voter can cast a ballot, even if there’s a question about their status on Election Day.

But Ohio state law discounts any provisional ballots cast in the wrong precinct — and the state has a lot of multi-precinct polling locations, where that voters from different precincts all report to a single building, then need to find their own precinct’s designated room or table. If a voter turns up at the wrong precinct, his name won’t be on the election officials’ list. Instead of checking to see if a voter should go to a different table, a poll worker can hand them a provisional ballot.

But under Ohio law, that ballot wouldn’t be counted.

The Advancement Project, a civil rights group, has joined with the Service Employees International Union to sue the state to abandon that provision in the law. “It feels like voters are being entrapped into voting ballots that don’t count,” said Penda Hair, a voting rights expert at the Advancement Project.

The Washington, D.C.-based group examined public records after the 2008 election and found that 40,000 of Ohio’s provisional ballots had been tossed — of those, 14,000 were rejected because they were cast in the wrong polling station.

The state’s attorney, Aaron Epstein, argued in court that the number of provisional ballots that might be discarded is too small to worry about in court.

A decision is expected this week. Either way, both sides are likely to appeal. Still, Hair said: “What happens will impact the election one way or another this fall.”

Read more: Background on the “unprecedented” number of restrictive voting laws that were introduced last year, Florida election officials’ resistance to the voter-roll purge in Florida, and the state’s next steps.

Update: Aug. 15: A Pennsylvania judge declined on Wednesday to grant an injunction against the state’s voter ID law — that is, he allowed it to go forward, saying the state was working to address problems with the requirements. The ACLU plans to appeal.

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