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)
“It is very important not to become hard. The artist must always have one skin too few in comparison to other people, so you feel the slightest wind.”
—Shusha Guppy (b. 1938)
“Don’t order any black things. Rejoice in his memory; and be radiant: leave grief to the children. Wear violet and purple.... Be patient with the poor people who will snivel: they don’t know; and they think they will live for ever, which makes death a division instead of a bond.”
—George Bernard Shaw (1856–1950)