The Supreme Court heard oral arguments today in a case regarding the constitutionality of affirmative action in college admissions. In the case, a white student claimed she was unfairly denied admission to the University of Texas due to its race-conscious admissions program.

Justice Elena Kagan, who was involved in the case as solicitor general, has recused herself. The court is apparently otherwise split, 4-3, along partisan lines with Justice Anthony Kennedy apparently the lone swing vote. In other words, once again Kennedy is the deciding vote in a major case. (A 4-4 vote would leave the existing precedent in place.)

How crucial is his vote? Well, consider this from the Wall Street Journal’s recap of the arguments:

Briefs filed by [attorneys for plaintiff Abigail] Fisher and UT each cite Justice Kennedy by name 20 times, with both sides asserting their arguments coincide with his prior opinions.