The most obvious of the factors is income — but it is not the most important. Supporters of today’s affirmative action often point out that a strictly income-based version of the program would produce much less racial diversity, and they’re right. Fewer than one-third of households making $40,000 a year or less are black or Latino, according to census data.

Image Anthony P. Carnevale, one of the authors of “The Future of Affirmative Action.” Credit... Evelyn Hockstein for The New York Times

But income alone understates the challenges facing many minority children. Black and Latino students are more likely to live in poor neighborhoods than white and Asian students with similar incomes. Black and Latino families are also less wealthy than white and Asian families. And black children in particular are much more likely to be growing up without two parents in their home.

Proponents of a new kind of affirmative action prefer an approach that focuses on wealth, neighborhood and family structure, as well as parents’ income, education and other factors. Doing so steers clear of the legal restrictions on racial classifications — and, in the minds of most Americans, is fair. Is an affluent teenager with a 1,300 SAT score really more accomplished than the valedictorian of a troubled high school with a 1,250? No.

The second new book – “The Future of Affirmative Action,” which comes out Tuesday — includes a detailed analysis of class-based systems, from Anthony Carnevale, Stephen Rose and Jeff Strohl. The bottom line is that they would vastly increase economic diversity while leaving broadly similar racial diversity. Under some systems, particularly those that emphasize students’ high-school rank, racial diversity would increase. Using high-school rank — as Texas has done — is so powerful because of today’s high levels of economic and racial segregation.

“Universities have long said, ‘We can get racial diversity only if we use race,' ” said Richard Kahlenberg, the editor of the book, which The Century Foundation and Lumina Foundation are publishing. “There are a number of ways to produce racial diversity without using race.”

Of course, they would cost universities more than the current system. Today, students at top colleges (and, by extension, at elite employers) come from different races, religions, regions and even countries — but are overwhelmingly well-off. On the other hand, the colleges that are most aggressive about affirmative action are also the ones with the most money.