Proportional cake-cutting with different entitlements
In the fair cake-cutting problem, the partners often have different entitlements. For example, the resource may belong to two shareholders such that Alice holds 8/13 and George holds 5/13. This leads to the criterion of weighted proportionality (WPR): there are several weights that sum up to 1, and every partner should receive at least a fraction of the resource by their own valuation. In contrast, in the simpler proportional cake-cutting setting, the weights are equal: for all Several algorithms can be used to find a WPR division. Cloning Suppose all the weights are rational numbers, with common denominator . So the weights are , with . For each player , create clones with the same value-measure. The total number of clones is . Find a proportional cake allocation among them. Finally, give each partner the pieces of his clones. Robertson and Webb show a simpler procedure for two partners: Alice cuts the cake into pieces equal in her eyes; George selects the most valuable pieces in his eyes, and Alice takes the remaining pieces. This simple procedure requires cuts, which may be very large. For example, if Alice is entitled to 8/13 and George is entitled to 5/13, then 13-1=12