How the rents are worked out

Of all the ways to hand out the rooms, we pick the one that maximizes the total of everyone's bids for the room they end up in. If you value the balcony room at $1,400 and nobody else values it above $1,100, you are the one who should have it — putting it anywhere else wastes value the group could have had.

This is a classic problem called the assignment problem, solved exactly by the Hungarian algorithm. It is not a heuristic or an approximation: the result is provably the best possible pairing. This step also loses nothing, because any assignment that could be made envy-free is necessarily one of these maximum-total assignments.

Now the rents. The total is fixed, so this is purely about how to divide it. We require the result to be envy-free: for every person, the room they got at its rent must be at least as good for them as any other room at its rent. Written out, if you value your room at v and pay p, then v − p has to be at least as large as v′ − p′ for every other room.

Usually many different rent splits satisfy that, so we choose among them with the maximin rule: make the worst-off person as well-off as possible. This is the rule that Gal, Mash, Procaccia and Zick found people judged fairest when tested on real rent-division cases, and it has been running on Spliddit since 2015. Two properties make it a good choice: the outcome is unique, so there is no arbitrary tie-break to explain away, and it also happens to minimize the gap between the best-off and worst-off person.

Nobody envies anybody. You can look at every other room, at the rent it ended up with, and confirm you would still rather have your own. The results page shows the whole grid so you can check rather than take our word for it.

Nobody overpays for their own room. Because bids have to add up to exactly the total rent, envy-freeness forces everyone's rent to be at most what they said their room is worth. That is not a separate promise we bolted on; it follows from the two rules above.

No wasted value. There is no way to make one person better off without making someone else worse off.

In spirit, yes: bidding is sealed, there is a single round, and the rents are driven by how much competition there was for each room. In the strict sense, no — and the difference is worth understanding.

In a classic Vickrey auction the winner pays the second-highest bid, and the seller simply absorbs the difference between that and the winning bid. Rent division has no seller. The rents have to add up to exactly the rent your landlord charges, and second-price payments almost never do. So a literal Vickrey rule is not available here.

There is a deeper limitation too. No deterministic method for splitting rent can be fully strategyproof — there is always some situation where shading a bid would help someone. That is a proved impossibility, not a gap in this implementation, and any rent-splitting tool claiming otherwise is overselling. What we do offer is that honesty is a sound default: you cannot manipulate the outcome without knowing what everyone else will bid, and the surest way to end up in a room you wanted at a price you find acceptable is to report your actual preferences.

Occasionally, with four or more roommates, the only envy-free answer involves paying somebody to take a room. This is not a bug: there are bid patterns where envy-freeness and all-positive rents are provably impossible at the same time.

It happens when one room is so unwanted that no rent low enough to make someone content with it is still above zero. When we hit this, we show the envy-free answer along with the closest all-positive alternative, and we name exactly who would feel short-changed under it, so the group can decide with the trade-off in plain view.

Bid what each room is genuinely worth to you. A high bid on a room makes you more likely to get it and more likely to pay more for it; a low bid on a room you actually want risks losing it to someone else.

The absolute numbers matter less than the gaps. Since your bids are rescaled to the total rent anyway, what the calculation reads is how much more one room is worth to you than another. If two rooms feel interchangeable, give them the same number.