Here is the Collect for today’s Mass on 22 December. The Roman Station today is the Basilica of the Twelve Apostles.
Deus, qui, hominem delapsum in mortem conspiciens,
Unigeniti tui adventu redimere voluisti,
ut, qui humili eius incarnationem devotione fatentur,
ipsius etiam Redemptoris consortia mereantur.
Consortium is a compound of the preposition cvm and sors, which has to do with "lot", as in casting "lots" for determining something by chance. Thus it comes to mean "community of goods" and therefore "fellowship, participation, society", according to the mighty Lewis & Short. If we look in Blaise/Dumas we find plural consortia having a meaning of "union" almost as if it were conjugal union.
O God, who, gazing upon him fallen into death,
desired to redeem man in the advent of Your Only Begotten,
grant, we beseech You,
that, those who profess His incarnation in humble devotion,
may merit participation in Him also as Redeemer.
Once again we are seeing the "janus"-like backward-forward perspectives, looking back to the First Coming even as we look forward to the Second. There is a development of thought from the fall, to death, to the Nativity, to humility, to ultimate redemption.