Well, whether or not the election of the Pope is valid is not what matters now. What matters is that the one who leads the Church and the destiny of millions is Pope Alexander, formerly Cardinal Borgia. I can't say I fully agree with the idea of purchasing the papal throne, but I can't say I'm entirely against it either.
As the Pope recalled that day, the first task was the investigation of the Conclave. The second was appointing a vice-chancellor with a grand office and a salary to match, as a gift. I'm not sure if he was being ironic when he said this, but it probably just sounded ironic.
Of course, there were two clear candidates for that position: Cardinal Piccolomini and Cardinal Colonna. However, it seems he couldn't appoint either of them because they had questioned his election and appointment. Piccolomini started humbling himself, claiming it wasn't his intention, and Cardinal Colonna did the same.
