Check the rent split you already have

How to check this yourself

1. Add every room price. The exact result must equal the stated total rent.
2. Confirm each room appears once in the assignment.
3. For each person, subtract every room's price from that person's reported value for the room. Their assigned room must tie or beat every alternative. A tie is not envy.
4. For assignment optimality, add each printed person potential to each printed room potential. Every sum must be at least the corresponding reported value, with equality on assigned pairs. When the total of the potentials equals the chosen assignment's total reported value, no assignment can do better.
5. Repeat the first and third steps on the prices rounded to cents. Independent rounding can spoil the rent total or create envy, so it has its own verdict.

The optimality witness is a certificate, not a claim about how this page searched. It takes a square table of additions and comparisons to verify. If the proposed assignment is not optimal, the certificate instead carries a better one-to-one comparison assignment.

The two results are not independent, and that is the useful part

An envy-free split's assignment always maximises the total of what each person said their own room was worth. This is the first welfare theorem, arriving here because envy-free rent division is a Walrasian equilibrium with unit demand; it appears as Svensson (1983) and is derived that way by Gal, Mash, Procaccia and Zick (2017, Theorem 3.2). So the combination "no envy, but the rooms went to the wrong people" cannot occur. If this page ever prints it, that is not a discovery about your split, it is proof of a bug here, and research/rent-check/verify.mjs tests exactly that invariant against brute force over random valuations.

Which means the optimality witness earns its place only when the envy check has failed, where it answers the question a household actually has next. If the assignment already maximises total reported value, the split can be repaired by moving prices alone and nobody has to move rooms. If it does not, no prices whatsoever will make this assignment envy-free, and the comparison assignment printed beside it names the swap that could.

Zero and negative room prices

A zero price is allowed. A negative price means the household pays someone to take that room while the other room prices cover the rent. That can be required for envy-freeness when a room is sufficiently undesirable. The page flags it without treating it as an arithmetic error. Whether such a subsidy is practical is a household decision outside this model.

Privacy, with a precise limit

All calculation happens in this browser. Nothing is uploaded, and the page makes no third-party requests. The certificate menu can make a one-person copy containing only that person's valuation row. That lets each housemate check and share their own arithmetic without circulating everybody else's bids. Anyone who can see the original input on this browser can still see the full household data.

What the published example is

The one-click control reproduces Table 1 of Dominik Peters, Ariel D. Procaccia, and David Zhu, “Robust Rent Division,” Advances in Neural Information Processing Systems 35 (2022), pages 13864 to 13876. It uses rent 1000, three complete valuation rows, the identity assignment, and Spliddit's published prices 100, 500, and 400. Bob is exactly indifferent between Rooms 1 and 2, which is a useful check that equality is accepted rather than called envy.