I tend to be skeptical of such criteria - the accolades list, for instance, includes members of the National Academy of Sciences - a group that includes about 1,900 scientists - as well as Rhodes Scholars (about 30 a year in the US), Fields Medal winners (less than 1 a year on average), and Nobel laureates. It’s hard to say where we should draw the line.
If Bernie Sanders counts (and I’d agree with you on that point), would Martin O’Malley (assuming he was a UChicago alumnus)? Looking at the Republican field, which offers a real spectrum, where do you draw the line between “political leader” and the rest of the pack?
Marco Rubio, Ted Cruz, and even Ben Carson or Donald Trump (shudder) would probably count. Jeb Bush is a former governor and a Bush, so I suppose we’d have to include him.
What about Chris Christie? Mike Huckabee?
Moving down the field, does Lindsey Graham count? George Pataki? Rick Santorum?
Do you rank Lawrence Lessig ahead of some of these others in terms of his influence, even if he’s dropped out of the race?
The Wikipedia article includes the likes of John Paul Stevens or Nate Silver, but also those like Rebecca Jarvis - a former Celebrity Apprentice contestant and journalist. Interesting person? Maybe. Great scholar? Business/political leader? I’m not so sure.
I think any attempt to quantify the prominence of a university’s alumni is futile, because it’s impossible to find an point where all will agree that you can draw the line between “great leader/thinker” and “ordinary alumnus.” I just don’t believe this is something quantifiable - it’s like trying to put a number on a school’s kindness or the number of “true friends” someone has.