Not quite what you asked, but approaching it from the other side, how righteousness effects the whole world.
This is from Elder Sophronys' book 'Saint Silouan the Athonite'.
The ontological unity of humanity is such that every separate individual overcoming evil in himself inflicts such a defeat on cosmic evil that its consequences have a beneficial effect on the destinies of the whole world. On the other hand, the nature of cosmic evil is such that, vanquished in certain human hypostases [persons] it suffers a defeat the significance and extent of which are quite disproportionate to the number of individuals concerned.
A single saint is an extraordinarily precious phenomenon for all mankind. By the mere fact of their existence – unknown, maybe, to the world but known to God – the saints draw down on the world, on all humanity, a great benediction from God. The Staretz [St. Silouan] writes:
‘Because of these people, I believe the Lord preserves the world, for they are precious in His sight, and God always listens to His humble servants and we are all of us all right because of their prayers.’
‘Prayer keeps the world alive and when prayer fails, the world will perish…”Nowadays,” perhaps you will say, “there are no more monks like that to pray for the whole world.” But I tell you that when there are no more men of prayer on earth, the world will come to an end and great disasters will befall. They have already started.’