Objection 1. It would seem that suffrages offered by the living for the dead do not profit those who offer them. For according to human justice a man is not absolved from his own debt if he pay a debt for another man. Therefore a man is not absolved from his own debt for the reason that by offering suffrages he has paid the debt of the one for whom he offered them.
Objection 2. Further, whatever a man does, he should do it as best he can. Now it is better to assist two than one. Therefore if one who by suffrages has paid the debt of a dead person is freed from his own debt, it would seem that one ought never to satisfy for oneself, but always for another.
Objection 3. Further, if the satisfaction of one who satisfies for another profits him equally with the one for whom he satisfies, it will likewise equally profit a third person if he satisfy for him at the same time, and likewise a fourth and so on. Therefore he might satisfy for all by one work of satisfaction; which is absurd.
On the contrary, It is written (Psalm 34:13): "My prayer shall be turned into my bosom." Therefore, in like manner, suffrages that are offered for others profit those who satisfy.
Further, the Damascene says in the sermon "On those who fell asleep in the faith: Just as when about to anoint a sick man with the ointment or other holy oil, first of all he, " namely the anointer, "shares in the anointing and thus proceeds to anoint the patient, so whoever strives for his neighbor's salvation first of all profits himself and afterwards his neighbor." And thus the question at issue is answered.
I answer that, The work of suffrage that is done for another may be considered in two ways. First, as expiating punishment by way of compensation which is a condition of satisfaction: and in this way the work of suffrage that is counted as belonging to the person for whom it is done, while absolving him from the debt of punishment, does not absolve the performer from his own debt of punishment, because in this compensation we have to consider the equality of justice: and this work of satisfaction can be equal to the one debt without being equal to the other, for the debts of two sinners require a greater satisfaction than the debt of one. Secondly, it may be considered as meriting eternal life, and this it has as proceeding from its root, which is charity: and in this way it profits not only the person for whom it is done, but also and still more the doer.
This suffices for the Replies to the Objections: for the first considered the work of suffrage as a work of satisfaction, while the others consider it as meritorious.
Source: Summa Theologica (New Advent)