I know that even some Catholics think that certains Popes held personal heresies (were material heretics). For example Honorius I believed that Jesus had only one will, the heresy of monothelitism.

I understand that a Pope might be a heretic, but to preserve the believed infallibility of his office he can't impose those beliefs *ex cathedra*—i.e., using the full weight of his office—onto the Church.

Who has the authority to judge which statements issued by the Pope are infallible?

Note: This [question](https://christianity.stackexchange.com/questions/2133/when-does-the-pope-speak-ex-cathedra) seems to address what the "criteria" used are, but I am asking: Who uses these criteria to decide the matter?