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+ - An Envy-Free Algorithm ->

Submitted by mikejuk
mikejuk (1801200) writes "If you want to find a way of dividing up some indivisible items between entities then here is a way to do it that eliminates envy as the outcome. The suggestion is that this could be a good way to divide up possessions during a divorce — algorithms get into everything. A new paper (http://www.ams.org/notices/201402/rnoti-p130.pdf) by New York University’s Steven Brams, Wilfrid Laurier University’s D. Marc Kilgour, and the University of Graz’s Christian Klamler and published this month in Notices of the American Mathematical Society, outlines how to do it so that both parties are happy in a maximal sort of way — i.e it assigns as many items in the pool of things to be divided and only holds back those that if allocated would cause envy.
As long as the players assign true rankings to the items then the more algorithm will find the maximal envy-free assignment and as the number of items increases, the probability of a complete envy-free assignment approaches one.
The bad news is that you can cheat.
If you lie about your ranking you can end up with an assignment that, when you true ranking is revealed, provokes envy. However, as the authors note the danger is that you won't work things out perfectly, because it depends on the ranking of the other player and you could end up worse off. The best strategy is to play fair and end up with an envy free allocation.
So the next time you file for divorce, remember to hire a programmer as well as a lawyer."

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Space

New Type of Star Can Emerge From Inside Black Holes, Say Cosmologists 193

Posted by Soulskill
from the cross-black-holes-off-your-list-of-good-hiding-places dept.
KentuckyFC writes "Black holes form when a large star runs out of fuel and collapses under its own weight. Since there is no known force that can stop this collapse, astrophysicists have always assumed that it forms a singularity, a region of space that is infinitely dense. Now cosmologists think quantum gravity might prevent this complete collapse after all. They say that the same force that stops an electron spiraling into a nucleus might also cause the collapsing star to 'bounce' at scales of around 10^-14cm. They're calling this new state a 'Planck star' and say its lifetime would match that of the black hole itself as it evaporates. That raises the possibility that the shrinking event horizon would eventually meet the expanding Planck star, which emerges with a sudden blast of gamma rays. That radiation would allow any information trapped in the black hole to escape, solving the infamous information paradox. If they're right, these gamma rays may already have been detected by space-based telescopes meaning that the evidence is already there for any enterprising astronomer to tease apart."

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