Timeline for Fair cake-cutting between groups
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Apr 26, 2015 at 15:30 | history | edited | Manfred Weis | CC BY-SA 3.0 |
added a sketch for a way to equitably split the land to each individuals cost measure
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| Apr 26, 2015 at 15:14 | history | edited | Manfred Weis | CC BY-SA 3.0 |
added a sketch for a way to equitably split the land to each individuals cost measure
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| Apr 26, 2015 at 10:26 | comment | added | Erel Segal-Halevi | What makes the median interesting is that, if you define the state-value of each land-plot as the median of the value of her citizens over that plot, you don't get a value measure (it is not additive)! So, the standard cake-cutting algorithms that deal with measures, are not directly applicable here. | |
| Apr 26, 2015 at 10:23 | comment | added | Manfred Weis | But no matter, how state utility is derived from individual utility, one ends up with two functions, one for each state, of which the center of mass is calculated and, the land is partitioned by lines through those centers of mass (here also the centers of mass or the partitioning lines may coincide). | |
| Apr 26, 2015 at 9:59 | comment | added | Erel Segal-Halevi | The problem with this model is that it may satisfy only a minority in each state (e.g. 2/3 the citizens in each country feel that their country got only 25%, while the remaining 1/3 feel that their country got 100%; the total is 50%). I think it makes more sense to define the "state utility" as the median of utilities of its citizens. In this model, a division for 2 states always exists, but not for 3 or more states. | |
| Apr 26, 2015 at 9:40 | comment | added | Manfred Weis | @Erel yes, that is what my solution is about and it also leads to further questions that I didn't mention. | |
| Apr 26, 2015 at 8:57 | comment | added | Erel Segal-Halevi | If I understand correctly, your solution works in two phases: a. For each state, create the value measure of the state by summing the value measures of all citizens. b. Divide the land fairly based only on the two "state measures". Is this what you meant? | |
| Apr 25, 2015 at 15:29 | history | answered | Manfred Weis | CC BY-SA 3.0 |