Comparison With Envy-free Division
Obviously, for two players proportional division is the same as envy-free division.
However, for three players and more, proportional division is weaker than envy-free division. It could happen that a player believes he received at least 1/n of the resource but also believes that there is a player that received more than he did. For instance, the Successive Pairs Algorithm for three persons could yield to a situation where the first person thinks that the third player received more than he did (if the portion of the second player part that the third player chose looks bigger - to the first player- than the other portions of the second player part).
Read more about this topic: Proportional (fair Division)
Famous quotes containing the words comparison with, comparison and/or division:
“What is man in nature? A nothing in comparison with the infinite, an all in comparison with the nothing—a mean between nothing and everything.”
—Blaise Pascal (1623–1662)
“But the best read naturalist who lends an entire and devout attention to truth, will see that there remains much to learn of his relation to the world, and that it is not to be learned by any addition or subtraction or other comparison of known quantities, but is arrived at by untaught sallies of the spirit, by a continual self-recovery, and by entire humility.”
—Ralph Waldo Emerson (1803–1882)
“Major [William] McKinley visited me. He is on a stumping tour.... I criticized the bloody-shirt course of the canvass. It seems to me to be bad “politics,” and of no use.... It is a stale issue. An increasing number of people are interested in good relations with the South.... Two ways are open to succeed in the South: 1. A division of the white voters. 2. Education of the ignorant. Bloody-shirt utterances prevent division.”
—Rutherford Birchard Hayes (1822–1893)