It’s not the top 10%. “No more than 10 percent of the candidates for degrees in liberal arts and sciences are elected.” That’s from the PBK web site. Emphasis mine.
Also from the PBK site, “To be eligible for election, students must have pursued a broad program of study in the liberal arts and sciences and met other academic criteria as required by the electing chapter.”
I point this out because I was a graduate of the College of Creative Arts of my university, and I was not eligible for Phi Beta Kappa. It kinda pissed me off at the time (only because my older sister, with whom I was extremely competitive, was elected to be in PBK at the same university).
Since I diddled around for two years before declaring a fine arts major, I had a pretty broad general education – two years of Latin, history and philosophy classes out the wazoo. OK, no more than the minimum science and math to satisfy gen ed requirements – but I can guarantee my sister took no more than I did.
Nonetheless, since my degree was not from the College of Arts and Sciences, it didn’t matter. In contrast, when I worked for a liberal arts college, every graduate was eligible for PBK – even the ones in fine arts majors. But every graduate earned a B.A.