The US Supreme Court begins its 2012-13 term on Monday with a blunt question: Which version of Chief Justice John Roberts will show up at the high court this year?

Will it be the hard-charging conservative who struck down election-season speech restrictions on corporations in the 2010 Citizens United decision, and who invalidated racial preferences in public schools in Seattle and Louisville, Ky., in 2007?

Or will it be the circumspect judicial minimalist who guided the high court away from overturning a major provision of the Voting Rights Act in a 2009 Texas case, and who last June voted with the court’s liberal wing to prevent the election-year invalidation of President Obama’s health-care reform law?

The chief justice is expected to have ample opportunity in the new term to become reacquainted with his conservative colleagues in potential blockbuster cases involving affirmative action, voting rights, and gay marriage.

The question is, will he?

How much do you know about the US Constitution? A quiz.

Legal analysts suggest Chief Justice Roberts has earned a degree of goodwill from would-be liberal critics in the wake of his surprising vote to uphold the health-care law. Some scholars praised the chief justice’s acrobatic decision as a modern-day version of Marbury v. Madison.

Conservatives scoff at such suggestions. They say Roberts appears to have caved in to bullying and threats from President Obama and others who launched what they say was a sustained campaign of intimidation once it looked as if the court was poised to overturn the health-care mandate.

“Whatever explanation [exists] is not legitimate, because we all agree that it is not a good thing for justices – chief justices – or judges to act politically, to try to split the differences, to try to balance competing imperatives,” Washington lawyer David Rivkin said during a recent panel discussion at the libertarian Cato Institute.

Mr. Rivkin, who served as a lawyer challenging the health-care law, said a similar “campaign of intimidation” would likely arise in future high-stakes cases.

The court’s docket suggests it may not be a long wait.

On Oct. 10, the Supreme Court is set to examine the constitutionality of racial preferences in college admissions at the University of Texas.

In addition, the high court is expected to soon consider whether to take up appeals involving California’s Proposition 8 ban on same-sex marriages and whether the Defense of Marriage Act's prohibition on same-sex spouses collecting federal benefits violates the Constitution’s guarantee of equal treatment.

If the high court agrees to hear one or both of these issues, the new term would become a major test of the scope of gay rights in the United States and the Supreme Court would once again become a flash point in the ongoing culture war.

The justices are also likely to take up at least one of more than five pending appeals raising the same issue the court confronted and dodged in 2009 – whether Section 5 of the Voting Rights Act is an unconstitutional extension of congressional power.

Section 5 requires certain designated states and counties with a past history of discrimination (in the 1960s and '70s) to obtain preapproval in Washington before making any changes to voting procedures that might undercut minority political clout.

Many of the covered jurisdictions complain that they have run discrimination-free elections for decades and should no longer be punished for violations a generation ago.

The internal dynamics on the nine-member court are well known. In general terms, there are four conservative justices, four liberal justices, and conservative-centrist Anthony Kennedy, who often casts a deciding swing vote in close cases.

The conservative-liberal breakdown rarely comes into play in routine cases, but the lineup does emerge in disputes presenting high-stakes, hot-button issues like affirmative action, voting rights, and abortion.

The potential new wrinkle in this equation is whether the chief justice will again attempt to head off a controversial conservative decision that might trigger political attacks on the legitimacy of the Supreme Court or on the justices themselves.

Although analysts will be watching closely, most do not expect such a move. They predict that Justice Kennedy will retain his status as the high court’s most significant swing vote in big cases.

“The chief [justice] is obviously important, but on things like gay rights – on abortion, race, and gays, Kennedy matters,” Washington lawyer and Supreme Court advocate Lisa Blatt told a recent gathering of the American Constitution Society.

The first big test for Kennedy as a potential swing vote this term may come when the high court takes up the Texas affirmative action case.

At issue is whether the University of Texas’ use of race to foster a greater degree of student diversity violates the Constitution’s equal protection clause. Analysts say the dispute could become the most important affirmative action case ever.

“This is an issue the chief justice cares deeply about,” Georgetown Law Professor Pam Harris said in a Supreme Court preview. “I don’t think anyone thinks affirmative action is long for this world.”

Roberts has made clear his distaste for using racial classifications to distribute government benefits. “It is a sordid business, this divvying up by race,” he wrote in an often-quoted passage from a dissent in a 2006 redistricting case.

Among other cases on the court’s docket, the justices have agreed to decide whether foreign corporations doing business in foreign countries can be sued in US courts by foreign citizens alleging human rights abuses overseas.

The case pits international human rights advocates against multinational corporations. It is set for oral argument on Monday.

The dispute involves a law written by the first Congress in 1789. The Alien Tort Statute (ATS) allows noncitizens to sue in US courts for violations of international law.

For the past thirty years, human rights lawyers have used the ATS to file lawsuits in American courts on behalf of oppressed foreign citizens. At first, the suits sought damages from torturers and foreign government officials involved in alleged human rights abuses. Eventually, resourceful lawyers discovered that they could also sue multinational corporations conducting business in troubled areas of the world and seek to hold them financially responsible for allegedly aiding and abetting human rights abuses of foreign governments. At least 150 such suits have been filed and more than a dozen are still pending.

Lawyers for the companies argue that foreign corporations should not be held liable in a US courtroom for acts that allegedly took place overseas with little or no connection to the US.

The appeal stems from a lawsuit filed on behalf of former residents of an oil-rich region of Nigeria. The residents claim they were subject to a government crackdown after they began complaining about pollution and other effects of oil exploration near their villages. They say the Netherlands company Royal Dutch Petroleum, part of Shell, aided and abetted the government in its human rights violations and should pay damages.

Human rights lawyers are urging the high court to embrace a broad interpretation of the ATS to include a wide variety of defendants and plaintiffs around the globe. Lawyers for targeted corporations are asking the court to restrict the scope of the statute.

“It has really become the bane of the existence of corporations who do business in other countries that they will be sued under the Alien Tort Statute for some sort of a human rights violation for working somehow with the government in a bad area,” Washington lawyer and former State Department legal adviser John Bellinger said during a recent Supreme Court preview at the Washington Legal Foundation.

“The Alien Tort Statute and all these lawsuits cause enormous diplomatic friction because it requires our judges to be judging the acts of not only foreign corporations but often of foreign governments,” he said.

Human rights lawyers say that if Shell wins at the Supreme Court, victims of torture and other abuses overseas will lose one of the only avenues available to hold their abusers accountable in a fair court system.

How much do you know about the US Constitution? A quiz.