Within days, the U.S. Supreme Court is expected to issue a series of decisions that could transform three fundamental social institutions: marriage, education and voting.

The extraordinary run of blockbuster rulings due in the space of a single week will also reshape the meaning of legal equality and help define for decades to come one of the Constitution’s grandest commands: “the equal protection of the laws”.

If those words require only equal treatment from the government, the rulings are likely to be a mixed bag that will delight and disappoint liberals and conservatives in equal measure. Under that approach, same-sex couples who want to marry will be better off at the end of the term, while blacks and Hispanics may find it harder to get into college and to vote.

But a tension runs through the cases, one based on different conceptions of equality. Some justices are committed to formal equality. Others say the Constitution requires a more dynamic kind of equality, one that takes account of the weight of history and of modern disparities.

The four major cases yet to be decided concern same-sex marriage; affirmative action in higher education; and the fate of the Voting Rights Act of 1965, which places special burdens on States with a history of racial discrimination.

Formal equality would require that gay couples be treated just like straight couples when it comes to marriage, white students just like black students when it comes to admissions decisions and southern states just like northern ones when it comes to federal oversight of voting. The effect would be to help gay couples, and hurt blacks and Latinos.

But such rulings — “liberal” when it comes to gay rights; “conservative” when it comes to race — are hard to reconcile with the historical meaning of the 14th Amendment’s equal protection clause, adopted in the wake of the Civil War and meant to protect the newly freed black slaves. It would be odd, said David A. Strauss, a law professor at the University of Chicago, for that amendment to help gays but not blacks.

“What’s weird about it would be the retreat on race, which is the paradigm example of what the 14th Amendment is meant to deal with”, he said, “coupled with fairly aggressive action on sexual orientation”.

But actual as opposed to formal racial equality has fallen out of favour in some circles, Mr. Strauss said. “One thing that seems to be going on with these historically excluded groups,” he said, “is that they come to be thought of as just another interest group. Blacks seem to have crossed that line.”

Justice Antonin Scalia appeared to express that view during the argument in February in the voting rights case, Shelby County v. Holder, No. 12-96. “Whenever a society adopts racial entitlements”, he said, “it is very difficult to get out of them through the normal political processes”.

Gay men and lesbians have yet to achieve formal legal equality. They are not protected against job discrimination in much of the nation, may not marry their same-sex partners in most of it and do not have their marriages recognised by the federal government in any of it. The fact that they are asking for equal treatment may help their cause in the cases challenging the federal Defence of Marriage Act, or DOMA, which for purposes of federal benefits defines marriage as the union of a man and a woman; and Proposition 8, the California voter initiative that banned same-sex marriage there.

But Chief Justice John G. Roberts Jr. suggested in March that ordinary politics would sort things out. “As far as I can tell,” he told a lawyer challenging the federal marriage law in United States v. Windsor, No. 12-307, “political figures are falling over themselves to endorse your side of the case”.

In the three months since that argument, three more states have adopted same-sex marriage, raising the total to 12, along with the District of Columbia.

Kenji Yoshino, a law professor at New York University, said the two different conceptions of equal protection are animated by different concerns. One is sceptical of government classifications based on race and similar characteristics, whatever their goals. The other tries to make sure that historically disfavoured groups are not subordinated.

Consider the case of Abigail Fisher, a white woman who was denied admission to the University of Texas. She says the university, an arm of the State government, should not classify people on the basis of race because that violates a colour blind conception of the Constitution’s equal protection clause.

— New York Times News Service

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