Justice Antonin Scalia’s black leather Supreme Court chair could be empty for months as the Senate argues about whether to replace him. His death on Saturday leaves behind a divided court and will have profound implications for this year’s docket of cases and possibly next year’s as well.

As the scholars Andrew Martin and Kevin Quinn wrote for FiveThirtyEight this morning, “It is very likely that many cases during the current term will end in 4-4 ties; when that happens, the decision of the lower court is affirmed without creating a precedent.”

We can’t know for sure which lower-court decisions would have been reversed on 5-to-4 votes at the Supreme Court this term. But we can guess, using two sources of Supreme Court prediction: the {Marshall}+ algorithm and the wisdom of the crowd competing in everyone’s favorite Supreme Court/fantasy sports mashup, FantasySCOTUS. Seven cases currently before the court were predicted by one or both of those sources to result in 5-to-4 reversal votes in which Scalia would’ve been in the majority. In other words, there are seven cases in which Scalia was predicted to be a pivotal voter but are now seen as likely to result in a tie. They include the following:

Contraception: Priests for Life v. Burwell

In yet another challenge to the Affordable Care Act, this case, which has been consolidated with a number of other similar cases, is focused on the law’s mandate that insurance provided by employers include contraception coverage. The petitioners want to see the religious exception to this mandate expanded — churches, for example, are already exempt from it — to include religiously affiliated schools, hospitals, nonprofits, charities and so on. FantasySCOTUS had seen this as a 5-to-4 strike against an already battle-weary Obamacare. But without Scalia’s predicted vote, a ruling further limiting the health care law now seems unlikely.

Voting rights: Wittman v. Personhuballah

This case originated from a redistricting ruling in Virginia. A lower court held that race played too strong a role when the state legislature redrew the boundaries of a Virginia congressional district. The court said the district, Virginia’s Third, was gerrymandered because the legislature packed black voters into its boundaries in a way that diluted their vote in other districts. Republicans appealed that ruling to the high court. Scalia was seen by FantasySCOTUS as very likely to vote to overturn the lower court’s ruling.

Unions: Friedrichs v. California Teachers Association

This is a case involving the ability of public-sector unions to collect the equivalent of dues from workers who choose not to join the union. The unions say that if they lose that ability, they will not be able to effectively bargain with government employers, but the justices — and particularly Scalia — seemed unsympathetic to that position during oral arguments in January. Scalia’s death may allow these unions, with a combined membership of more than 9 million public workers, to avoid a loss, at least for the time being.

The four other cases are less sexy but are also seen as likely to end up tied: Bernard v. Minnesota concerns whether it’s a crime for someone to refuse to take an alcohol test when stopped under suspicion of driving while intoxicated; Spokeo v. Robins concerns who has a right to sue in civil cases; Franchise Tax Board of California v. Hyatt concerns whether state agencies are immune from being sued in other state courts; and Bank Markazi v. Peterson concerns whether certain federal statutes violate the separation of powers. All were seen as 5-4 reversals, with Scalia in the majority.

There are also some big cases not on the list above. One is Fisher v. University of Texas, a major affirmative action case involving the admissions policies of a large state university. Justice Elena Kagan recused herself from the case because she worked on a related brief when she was solicitor general, so now only seven justices are left to decide it. If the predictions are correct, that case will see an unusual 4-3 reversal, resulting in a major defeat for supporters of affirmative action. A 4-3 reversal hasn’t happened since 1984, according to the Supreme Court Database.

Other major cases not making this list are Whole Woman’s Health v. Hellerstedt, a challenge to Texas’s restrictions on abortion providers, and Evenwel v. Abbott, about whether states violate the “one person, one vote” principle if they count nonvoters (such as undocumented immigrants or prisoners) when drawing legislative districts. The predictors don’t see these cases as particularly close at the moment — the crowd foresees a 9-0 affirmation in Evenwel, allowing states to continue counting nonvoters. But Whole Woman’s Health won’t be argued until March, and the wisdom of the crowd can improve dramatically after the court hears oral arguments. In any case, it’s a safe bet that Scalia would’ve voted against a challenge to abortion restrictions. (So far this term, the crowd has been 84 percent accurate in predicting the justices’ votes, and the algorithm 71 percent. One member of the team behind these predictors put together his own list of cases likely to be affected by Scalia’s death.)

And what, precisely, happens to the cases that result in 4-4 ties? It’s true that, as Martin and Quinn wrote, a tie means the lower-court decision is upheld without creating a national precedent. But in previous terms with a missing member, the court has sometimes chosen to reconsider cases with tie votes after a vacancy is filled. It could be a long time before there is clarity on these cases, and on the court’s future direction.