What is fair in this scenario?

[Slippa]

A and B want to live together. A owns a house and B doesn’t.

For various reasons B can’t move in with A and has suggested renting their own house. A and B will then split their time across both properties. New property is beneficial location-wise for both parties (nearer to work and friends, good amenities).

The rent on B’s property will be twice the amount of A’s mortgage. However A would prefer B to live with them.

How should expenses be split, if at all?

A pays for their house. B pays for their house. If B can't afford it, then B either needs to stay where they are, rent somewhere cheaper or move in with A.

Just have separate finances. It's not up th either A or B to subsidise mortgage or rent.

A pays for their house, B pays for their house. There's no splitting of anything needed imo. B can't move in with A and has suggested renting - B should go ahead and do that. Rent being double the mortgage isn't really a point I don't think.

The new property is hardly "beneficial" to both parties if B suggested it and A would prefer them to live in As house. Just because it has a good location 🤷🏻‍♀️