The opinions poured in, 280 characters at a time, as to whether it was good or bad that Elon Musk had offered to buy Twitter for more than $40 billion and take it private.

A person’s politics typically dictated how they felt: Conservatives cheered it as victory for free speech. Liberals fretted that misinformation would spread rampantly if Musk followed through with his plan to dismantle how the social network monitors content.

But what no one seemed to be able to say with any certainty was what kind of political philosophy the enigmatic billionaire believes himself.