How to split the cost of furnishing a shared flat
The problem with shared furniture is not buying it, it is that it cannot be split when somebody goes. So the question to answer up front is not who pays what, it is who owns it afterwards β and households that decide ownership first find the payment obvious.
One person buys it and owns it
The simplest arrangement by a distance. Whoever wants the sofa buys the sofa, everybody uses it, and it leaves when they do. Nothing to divide, nothing to value, nothing to argue about in eighteen months.
The cost is real: one person has spent money everybody enjoys. Households often even that out somewhere else β they cover a smaller share of something recurring β which is easier than co-owning a physical object.
Everybody chips in, and it stays with the flat
The second version treats shared furniture as part of the flat rather than as anybody's property. Everybody pays a share, nothing is owed to anybody who leaves, and whoever replaces them inherits the use of it without buying in.
It works, and it only works if it is stated. Somebody who paid a third of a television twelve months ago and hears they are owed nothing will not consider that obvious.
Buy it together and buy each other out
The third is the most fair and the most work: joint ownership, and whoever stays pays the leaver a share of what it is now worth. It needs somebody to put a number on a two-year-old sofa, which is exactly the conversation the other two arrangements exist to avoid.
Whichever you pick, keep one list of what was bought together and who paid. It takes a minute per item and it is the only thing that helps at the end.
For a house rather than a couple
Everyone sees the same number.
Invite the people you live with by code. Nobody hands over a bank login, nobody has to trust one person's spreadsheet, and settling up is the fewest transfers rather than a group chat.