It is unclear when the justices will decide whether to hear arguments in those cases. Arguments themselves would not take place until next year.
Yet there still is a chance that the court could become enmeshed in election disputes, even before the ballots are counted. Suits in Ohio over early voting and provisional ballots appear the most likely to find their way to the justices before the Nov. 6 election, said Richard Hasen, an election law expert at the University of California at Irvine law school.
Among other important cases already on the court’s docket:
— A high-stakes dispute, to be argued first thing Monday, between the business community and human rights advocates over the reach of a 1789 law. The issue is whether businesses can be sued in U.S. courts for human rights violations that take place on foreign soil and have foreign victims.
— A challenge to the use of drug-sniffing dogs in two situations. Florida police used a marijuana-sniffing dog’s alert at the door of a private home to obtain a search warrant to look inside the house. The question is whether the dog’s sniff itself was a search. A separate case looks at the reliability of animals trained to pick up the scent of illegal drugs.
— A challenge to the detention of a man who police picked up a mile away from an apartment they had a warrant to search. Occupants of a home may be detained during the search for the safety of officers, but this case tests how far that authority extends away from the place to be searched.
— Environmental disputes involving runoff from logging roads in Oregon and water pollution in Los Angeles.
Paul Clement, the Republican lawyer who lost the health care case and could be before the justices on gay marriage and voting rights, said last term punctured the notion that in close cases, the court goes where Kennedy wants.
‘‘We've all been reminded that’s not always the case,’’ he said.
The idea that could be tested this term is whether Roberts’ concern for the court as an institution that is apart from politics will influence his votes, or at least his reasoning, in the year’s biggest cases.
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