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HandWiki. Proportional Cake-cutting with Different Entitlements. Encyclopedia. Available online: https://encyclopedia.pub/entry/30303 (accessed on 04 October 2026).
HandWiki. Proportional Cake-cutting with Different Entitlements. Encyclopedia. Available at: https://encyclopedia.pub/entry/30303. Accessed October 04, 2026.
HandWiki. "Proportional Cake-cutting with Different Entitlements" Encyclopedia, https://encyclopedia.pub/entry/30303 (accessed October 04, 2026).
HandWiki. (2022, October 20). Proportional Cake-cutting with Different Entitlements. In Encyclopedia. https://encyclopedia.pub/entry/30303
HandWiki. "Proportional Cake-cutting with Different Entitlements." Encyclopedia. Web. 20 October, 2022.
Proportional Cake-cutting with Different Entitlements
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The content is sourced from: https://handwiki.org/wiki/Social: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 [math]\displaystyle{ w_i }[/math] that sum up to 1, and every partner [math]\displaystyle{ i }[/math] should receive at least a fraction [math]\displaystyle{ w_i }[/math] of the resource by their own valuation. In contrast, in the simpler proportional cake-cutting setting, the weights are equal: [math]\displaystyle{ w_i=1/n }[/math] for all [math]\displaystyle{ i }[/math] Several algorithms can be used to find a WPR division.

valuation proportionality cake-cutting

References

  1. Template:Cite Robertson Webb 1998
  2. McAvaney, Kevin; Robertson, Jack; Webb, William (1992). "Ramsey partitions of integers and fair divisions". Combinatorica 12 (2): 193. doi:10.1007/bf01204722.  https://dx.doi.org/10.1007%2Fbf01204722
  3. Cseh, Ágnes; Fleiner, Tamás (2020-06-01). "The Complexity of Cake Cutting with Unequal Shares". ACM Transactions on Algorithms 16 (3): 29:1–29:21. doi:10.1145/3380742. ISSN 1549-6325. https://doi.org/10.1145/3380742. 
  4. Shishido, Harunor; Zeng, Dao-Zhi (1999). "Mark-Choose-Cut Algorithms For Fair And Strongly Fair Division" (in en). Group Decision and Negotiation 8 (2): 125–137. doi:10.1023/a:1008620404353. ISSN 0926-2644.  https://dx.doi.org/10.1023%2Fa%3A1008620404353
  5. Cseh, Ágnes; Fleiner, Tamás (2018), "The Complexity of Cake Cutting with Unequal Shares" (in en), Algorithmic Game Theory (Springer International Publishing): pp. 19–30, doi:10.1007/978-3-319-99660-8_3, ISBN 9783319996592  https://dx.doi.org/10.1007%2F978-3-319-99660-8_3
  6. Brams, S. J.; Jones, M. A.; Klamler, C. (2007). "Proportional pie-cutting". International Journal of Game Theory 36 (3–4): 353. doi:10.1007/s00182-007-0108-z.  https://dx.doi.org/10.1007%2Fs00182-007-0108-z
  7. Note that there exists a connected division in which the ratios between the values of the partners are 3:1 – give Alice the two leftmost slices and 8/11 of the third slice (value 4+16/11=60/11) and give George the remaining 3/11 and the rightmost slice (value 1+9/11=20/11). However, this partition is not WPR since no partner receives his due share.
  8. Segal-Halevi, Erel (2018-03-14). "Cake-Cutting with Different Entitlements: How Many Cuts are Needed?". Journal of Mathematical Analysis and Applications 480: 123382. doi:10.1016/j.jmaa.2019.123382.  https://dx.doi.org/10.1016%2Fj.jmaa.2019.123382
  9. Crew, Logan; Narayanan, Bhargav; Spirkl, Sophie (2019-09-16). "Disproportionate division". arXiv:1909.07141 [math.CO]. //arxiv.org/archive/math.CO
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