Bid for rooms

Everyone writes down what each room is worth to them, as if they were paying the whole rent. The calculator gives each room to the person who makes the total value highest, then sets prices so nobody would rather swap.

This works best when people disagree about which room is best. If you only care about floor area, the room size calculator is simpler.

Result

How it works

First it tries every way of giving one room to each person and keeps the one where the values add up highest. With the example bids that means the person who cares most about the front bedroom gets it, even though another person also ranked it first.

Then it looks for prices. A set of prices is envy-free if everyone's "better off by" number (what they said their room is worth, minus what they pay) is at least as high as it would be in any other room at those prices. For the assignment above, such prices always exist. There's usually a whole range of them. This page takes the middle of that range.

The idea comes from the fair division research behind Spliddit, built at Carnegie Mellon. Spliddit goes one step further and picks the envy-free prices that do best by whoever is worst off. The midpoint used here is simpler and runs entirely in your browser, but it can differ from Spliddit by a few dollars.

Questions