Do ‘relation’ (singular) and ‘relations’ (plural) both work in the following sentences?
1. Out of D.S. Chambers and Michael Baxandall and some Italian scholars Robinson measures up Pound's ideas about the right relation/relations between artist and patron against what we know of how patronage in fact worked in the ducal fiefs of Renaissance Italy.
2. The relation/relations between archbishop and prime minister became at times very uneasy.
3. Any relation/relations between members of the same sex which allowed their difference, did not assimilate both to one fantasy, would be heterosexual.
4. It leads either to problems about the relation/relations between God and the world (for example, to a denial that it is His creation) or….
1, 2, & 4. Artist and patron are singular, so are the archbishop and prime minister, and God and the world. Therefore, these pairs had a relation (or relationship). In sentence 3 the meaning of relation(s) is unclear as to number. Generally, in American English, if two people are having relations they are sexually involved with each other. If they have a relation it usaually means they are both related to the same person (like a cousin). In all of your examples I would have used the word relationship.