By reading some basic texts (in English translation) (like Hungrvaka) I came to know that the bishops were elected on Iceland, and then had to make a journey to mainland Europe to be consecrated (Audience with the pope, then consecration by some north European archbishop) It is also hinted that the 'chieftains' had much influence on the election.
Where the clergy to decide? Or the gođar who had a say in the Allthing? Or some more general circle of landowners? And after there were more than one Episcopal sees established, were only those to decide, who lived in the now vaccant bishopric?
And where there a majority vote, or they simply talked over the question and came to an agreement?