Put aside for a moment the lengthy debate in the opinions about “political restructuring” doctrine. Here is the nub of the problem the plaintiffs faced (excerpted from my article on Schuette in the NYU Journal of Law and Liberty, footnotes omitted):

Under Supreme Court precedent, affirmative action preferences as pursued by state universities are unconstitutional if they are used for any purpose other than to promote diversity, or perhaps to pursue the “compelling interest of remedying the effects of [a university’s own] past intentional discrimination.” They are unconstitutional if used to promote racial balancing, if used to promote “compensatory justice” for past societal wrongs to African Americans or other groups, if used to redress current societal discrimination and statistical inequalities, if used to provide role models for minority youths, if used as a proactive means of avoiding discrimination lawsuits by members of minority groups, and, a fortiori, if used to satisfy the desires of constituents who lobby for them out of self-interest.
Because affirmative action preferences are constitutional only when a court finds that university officials have determined that such preferences are “essential to [a university’s] educational mission,” from a legal perspective their underlying purpose cannot be to benefit black students or other minority students who receive admissions preferences. Rather, they must benefit all students at the university due to “the educational benefits that flow from a diverse student body.” The Supreme Court’s diversity rationale suggests that the main benefit of achieving a critical mass of minority students through affirmative action preferences is that it improves the education of the non-minority students. If white students benefit from “diversity” -based preferences at least as much as minority students, there is no particular group being disadvantaged by Proposition 2’s ban on such preferences.
In other words, Proposition 2 can’t be unconstitutional because it makes it more difficult for minority students (and other members of minority groups) to lobby for benefits for themselves, given that it would be unconstitutional for the state government to respond to such lobbying by enacting racial preferences. Rather, Proposal 2 represents a public determination that whatever the benefits of student diversity to all students, the majority of the population thinks those benefits are outweighed by harms accrued from allowing the government to discriminate based on race. The hypothetical black or Hispanic student has no more standing to object to that determination than the white student who thinks he would benefit from having more “diverse” classmates, nor can the elimination of preferences be said, as a constitutional matter, to be harmful especially to minority students and not to the white students who benefit from diversity.

Justice Sotomayor tried to get around this problem by claiming that though diversity is the underlying rationale for the constitutionality of preferences, preferences nevertheless disproportionately benefit “racial minorities” (a category that oddly in her estimation seems to include a non-racial group, Hispanics, and excludes a racial group, Asians). Making it more difficult for them to get this benefit is unconstitutional, even in the absence of discriminatory intent. But as Justice Scalia points out in rebuttal, plenty of people, including a significant number of members of the minority groups in question, don’t believe that preferences do in fact benefit those who receive the preferences, and indeed, one might add, at least some of the objections to preferences arise from just that skepticism.

Meanwhile, it’s telling, as Ilya notes, that Sotomayor never mentions Asian Americans.  It’s well-established that affirmative action preferences  in higher education make it more difficult for Asian-American applicants to win admission.  By the dissent’s own reasoning, therefore, overturning the ban on preferences would be unconstitutional for harming a racial minority, i.e., Asians, to wit:   “Everyone else can try to get a constitutional amendment passed via referendum in Michigan to ban certain factors that are harmful to them from being considered by admissions committee, such as legacy preferences or sports preferences. Only Asian Americans are prohibited from trying to get a constitutional amendment that will benefit them, i.e., one that bans consideration of race.”  Had the dissent been the majority, the Supreme Court would have restructured Michigan’s political process to the disadvantage of Asian Americans, and thus, even in the absence of discriminatory intent, been unconstitutional decision under the (hypothetical) majority’s own theory! [Sotomayor: “The problem with §26 is that §26 reconfigured the political process in Michigan such that it is now more difficult for racial minorities, and racial minorities alone, to achieve legislation in their interest."]