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)
“We teach boys to be such men as we are. We do not teach them to aspire to be all they can. We do not give them a training as if we believed in their noble nature. We scarce educate their bodies. We do not train the eye and the hand. We exercise their understandings to the apprehension and comparison of some facts, to a skill in numbers, in words; we aim to make accountants, attorneys, engineers; but not to make able, earnest, great- hearted men.”
—Ralph Waldo Emerson (1803–1882)
“That crazed girl improvising her music,
Her poetry, dancing upon the shore,
Her soul in division from itself
Climbing, falling she knew not where,
Hiding amid the cargo of a steamship
Her knee-cap broken.”
—William Butler Yeats (1865–1939)