The U.S. Supreme Court on Wednesday will revisit the vexed question of affirmative action in college admissions, with the case of Fisher v. University of Texas.

Abigail Fisher, a white student, claims the university denied her admission because of her race.

In 2003, a narrowly divided Supreme Court issued a pair of rulings on affirmative action in public higher education.

One came in a case challenging the race-conscious admissions program used in undergraduate admissions at the University of Michigan. The other was a challenge to the program used at Michigan Law School.

Four justices would have rejected both plans, and four would have embraced both. Justice Sandra Day O’Connor split the difference: with her support, a 5-4 majority rejected the undergraduate plan, and a different 5-4 majority endorsed the law school approach.

In both decisions, the Court began with the idea that the Fourteenth Amendment’s guarantee of “equal protection” means that the laws should generally treat whites and blacks, and people of other races and of mixed ancestry, exactly the same — unless the government has some especially good reason for treating them differently.

The justices ask two questions. First, they look to see whether the challenged policy is designed to accomplish an especially important goal, or whether the aim is more modest, such as to achieve administrative efficiency or cost savings.

Then they look to see whether the goal could have been achieved in some other way, less offensive to the value of treating all individuals as equals. Unless the challenged policy is truly necessary to the accomplishment of a very important goal, it will be rejected.

In both of the 2003 decisions, the court accepted the university’s argument that the educational benefits that come from having a diverse student body constituted a sufficiently “compelling” interest. The court — or O’Connor — ruled that the mechanical and quantitative approach used in Michigan’s undergraduate admissions program did not treat applicants as individuals.

Because the law school did not use a quantitative system but examined applicants individually and insisted that race was considered as only one element in a holistic review of applicants’ potential contribution to a diverse educational environment, O’Connor endorsed the law school’s admissions program.

At issue on Wednesday are the admissions policies used now at the flagship campus of the University of Texas.

Here’s how they work: all Texas high school graduates who finish in the top 10 percent of their high school’s graduating class are awarded admission automatically. Between 70 percent and 80 percent of an entering class are admitted through this 10 percent program. For the remaining 20 percent to 30 percent of places at the campus, however, UT uses a form of affirmative action modeled on the Michigan Law School plan.

Attorneys for the University of Texas argue that, by employing the Michigan Law model, UT is doing exactly what the Supreme Court approved back in 2003.

Fisher’s lawyers insist, however, that because the 10 percent plan already yields a diverse student body, without requiring any applicant to be judged on the basis of his or her race, UT cannot persuasively argue that the Michigan Law School-type affirmative action program it uses when selecting the remainder of the class is truly necessary.

Though the lower courts sided with UT, the university is not likely to prevail in the Supreme Court, if only because it is difficult to see why the Supreme Court would have taken the case simply to reaffirm a recent decision.

Moreover, in a 2007 case, the Supreme Court invalidated a race-conscious school assignment plan on the grounds that it was not necessary, because a race-neutral method achieved the diversity sought by the district. By the same logic, the Court should find that the 10 percent plan, which achieves diversity without judging anyone on the basis of race, renders any consideration of race unnecessary and therefore unconstitutional.

It is possible that a majority of court will go further and ask colleges and universities to provide hard evidence about the benefits they claim to flow from having a racially diverse student body, which up until now they have not been required to do.

If the court were to reject the idea that achieving these claimed educational benefits does not amount to a “compelling” goal, it would effectively doom all race-conscious admissions programs everywhere in public higher education.

Wednesday’s oral argument may give us a hint about which way the court aims to go. We can expect to hear its decision sometime this winter. Whichever way it comes out, expect the result to create controversy.

Joseph R. Reisert is associate professor of American constitutional law and chairman of the department of government at Colby College in Waterville.