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 ${\displaystyle w_{i}}$ that sum up to 1, and every partner ${\displaystyle i}$ should receive at least a fraction ${\displaystyle w_{i}}$ of the resource by their own valuation.

In contrast, in the simpler proportional cake-cutting setting, the weights are equal: ${\displaystyle w_{i}=1/n}$ for all ${\displaystyle i}$

Several algorithms can be used to find a WPR division.