This is a topic I no longer spend much time on. There are two Papal encyclicals which are without question accepted by all Catholics (who care to think about this question) as being ex cathedra -- Ineffabilis Deus and Munificentissmus Deus. In both cases, before issuing the document, the Pope polled the Bishops of the Church and got near unanimous agreement on the doctrine. Now, under Catholic theory on the infallibility of the church, whenever the Bishops (as successors of the office of bishop originally held by the Apostles) all speak in unison on a matter of faith and morals, that point is ipso facto an infallible dogma. So the formal Papal pronouncement in these cases, IMO, didn't really add anything. It's a bit of two paths to the same dogma.
There is some debate among Catholic theologians as to whether some other encyclicals meet the Vatican I definition. But it's not a question that keeps Catholics up at night wondering about.
*Near unanimous*? So it’s not the pope himself who decides it but he gets to make the pronouncement?
If the Holy Spirit is leading them, it had better be unanimous.
So how does this happen?
Does the pope get up there and proclaim (something to the effect of) Thus saith the Lord?
Does he get a *feeling*? Sit in a certain chair? Have someone else tell him? Make the decision on his own that it ought to be ex cathedra? Or is he just a figurehead who gets the privilege of making the pronouncement that others decided?
And how do they decide? VOTE on it?
Which ones are the poorly catechized ones?