The Ivy League, especially Harvard, Yale and Princeton, have long looked for leadership.
That’s (arguably) much rarer than high test scores.
In my opinion–which you need not ascribe to-- the institutions don’t educate leaders. They admit leaders, at least those whose test scores are high enough. (High enough, not perfect.) Attending HYP will not transform a follower into a leader.
For all the talk about “leadership” which stretches it beyond its bounds, such as being a good person, “leadership” in this sense means having the capacity to be elected to national office.
If Ted Cruz wins the election, I’m sure Princeton and Harvard will be quick to reach out to him. The other Ivy-affiliated candidates are:
Hillary Clinton (Yale Law)
Donald Trump (Wharton)
Dr. Ben Carson (Yale undergrad)
Interesting to note that George W. Bush attended Yale, but Jeb Bush attended the University of Texas.
We’ll see if the pattern holds. However, it’s not that HYP accept high test scores, and end up by accident with leaders. With the exception of Carson and Cruz, I’d be surprised if the other candidates’ test scores were outstanding.