Proportional (fair Division) - Comparison With Envy-free Division

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:

    I have travelled a good deal in Concord; and everywhere, in shops, and offices, and fields, the inhabitants have appeared to me to be doing penance in a thousand remarkable ways.... The twelve labors of Hercules were trifling in comparison with those which my neighbors have undertaken; for they were only twelve, and had an end; but I could never see that these men slew or captured any monster or finished any labor.
    Henry David Thoreau (1817–1862)

    Away with the cant of “Measures, not men!”Mthe idle supposition that it is the harness and not the horses that draw the chariot along. No, Sir, if the comparison must be made, if the distinction must be taken, men are everything, measures comparatively nothing.
    George Canning (1770–1827)

    Imperialism is capitalism at that stage of development at which the dominance of monopolies and finance capitalism is established; in which the export of capital has acquired pronounced importance; in which the division of the world among the international trusts has begun, in which the division of all territories of the globe among the biggest capitalist powers has been completed.
    Vladimir Ilyich Lenin (1870–1924)