Notes on dividing a house
Room Selector 5000 divides beds and cost among a group so that nobody prefers anyone else’s bed at its price. These are the notes behind it: what goes wrong with the obvious approaches, what the guarantee actually says, what it does not cover, and how to run the process for a real group.
Six people, one house, one bedroom everybody wants. You cannot give it to all of them, and giving it to whoever asked first is how a trip goes sour before it starts. These notes are about the alternative: put a price on the good room high enough that the people who did not get it would genuinely rather keep the money.
- Why splitting rent by room is harder than it looks Split evenly and the bunk subsidises the master. Rank the rooms and intensity is ignored. Auction them and the loser gets nothing. Each failure is predictable and the dilemma turns out to be false.
- What “envy-free” actually means The definition, why a solution always exists no matter what people want, why fairness costs nothing in efficiency here, and how the prices get chosen once you know the assignment.
- What the old algorithm got wrong Eighteen real ballots from a January 2026 trip, run through both versions. The old one charged six people more than they said their own bed was worth. The numbers, and how we checked them.
- What this does not fix Wealth still leaks in through bid spread. The mechanism is not strategyproof. And the price gap gets wider, not narrower. The boundaries of the guarantee, stated plainly.
- How to split a vacation rental without an argument The practical version. Agree the rule before anyone sees the rooms, describe the beds honestly, collect numbers privately, run it once — plus what to do when somebody drops out.
The tool itself is free. One person lists the beds, everyone else opens a link and ranks the ones they would accept.
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