Solve fair division problems using cut-and-choose, adjusted winner, and Knaster methods. Visualize allocations and envy-freeness.
Fair division means every party values their own share at least as much as anyone else's. This calculator applies three classic procedures: cut-and-choose for two parties splitting one continuous asset, adjusted winner for two parties dividing items by point valuations, and Knaster's sealed-bid method for several parties with cash settlement. It visualizes the allocation, any fractional split, and whether the result is envy-free, all in the browser with nothing uploaded. The surprise: the result is only as fair as the numbers you enter. Methods trust stated valuations, and envy-freeness is judged on each party's own scale, not an outsider's.
A concrete input and expected output from the current implementation.
Input
Two parties, Ann and Bob, divide an apartment, a piano, and a car by points (each party's total is 100). Apartment: Ann 40, Bob 30. Piano: Ann 35, Bob 45. Car: Ann 25, Bob 25.
Expected output
Ann receives the apartment and 60% of the car: 40 + 15 = 55 points. Bob receives the piano and 40% of the car: 45 + 10 = 55 points. The parties tie at 55 of 100, each values the other's bundle at 45, so the allocation is equitable and envy-free.
Each item goes to the party valuing it more; the tied car goes to Ann, who was behind on points. Ann leads 65 to 45, but transferring the whole car would overshoot, so the calculator splits the car at the point where both parties reach exactly 55 points - the envy-free, equitable outcome.
The calculator takes each party's valuations as points. Two parties dividing discrete items enter valuations totaling 100 each, and adjusted winner allocates and equalizes them. Two parties splitting one continuous asset use cut-and-choose: one party divides, the other chooses. Any number of parties use Knaster's sealed-bid method, where each item goes to the highest bidder and cash transfers balance every party's net value. Everything runs in the browser.
Adjusted winner awards each item to the party valuing it more; equal valuations go to the party behind in points. The party ahead surrenders items in order of smallest valuation ratio - the item they disagree about least goes first - and the final item is split fractionally if a whole transfer would overshoot, until both parties hold equal points. Hence results often end with a percentage share of one item.
Adjusted winner needs every party's valuations on one additive scale, and 100-point totals are the convention. Only the ratios between a party's own item values matter, so any consistent scale would work; the calculator just normalizes your entries. The sum must stay 100, which means valuing each item independently - bundles, dependencies, or double-counting will distort the allocation.
Then the result is fair only against the stated numbers. Cut-and-choose protects both players whatever they do: the divider can always secure a half, and the chooser can always take a preferred piece. Adjusted winner is not strategy-proof - a party who knows the other's valuations can sometimes gain by misstating - and Knaster's method has no way to detect a dishonest bid, so input honesty is part of the method.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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