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Adjusted winner procedure
A fair-division procedure introduced by Steven Brams and Alan Taylor in 1993; It works only for two players, and begins by having each player independently spread 100 points over the items to be divided so as to reflect the relative worth of each object to that player; The allocation resulting from this procedure is equitable, envy-free, and Pareto-optimal; It requires no cash from either player, but one of the objects may have to be divided or shared by the two players.
Bottom-up strategy
A bottom-up strategy is a strategy under an alternating procedure in which sophisticated choices are determined by working backwards.
Cake-division scheme
A fair-division procedure that uses a cake as a metaphor; Such procedures involve finding allocations of a single object that is finely divisible, as opposed to the situation encountered with either the adjusted winner procedure or KnasterŐs procedure; In a cake-division scheme, each player has a strategy that will guarantee her a piece with which she is "satisfied," even in the face of collusion by the others.
Convention of the Law of the Sea
An agreement based on divide-and-choose that protects the interests of developing countries in mining operations under the sea.
Divide-and-choose
A fair-division procedure (or cake-division scheme) for dividing an object or several objects between two players; This method produces an allocation that is both proportional and envy-free (the two being equivalent when there are only two players).
Envy-free
A fair-division procedure is said to be envy-free if each player has a strategy that can guarantee him or her a share of whatever is being divided that is at least as large (or at least as desirable) as that received by any other player, no matter what the other players do.
Equitable
An allocation (resulting from a fair-division procedure like adjusted winner) is said to be equitable if each player believes he or she received the same fractional part of the total value.
Fair-division problem
A problem that involves the dividing up of an object or set of objects among several individuals (players) so that each individual considers the part he or she receives to be a fair portion.
Fair-division procedure
A method for solving a fair-division problem; Each participant in the procedure must have a way of realizing a share that he or she views as fair in his or her own value system.
First-choice strategy
A strategy for an alternating procedure that indicates only what a player's first choice should be.
Knaster inheritance procedure
A fair-division procedure for any number of parties that begins by having each player (independently) assign a dollar value (a "bid") to the item or items to be divided so as to reflect the absolute worth of each object to that player; The allocation resulting from this procedure leaves each party feeling that he or she received a dollar value at least equal to his or her fair share (and often more so); It never requires the dividing or sharing of an object, but it may require that the players have a large amount of cash on hand.
Last-diminisher method
A cake-division scheme introduced by Stefan Banach and Bronislaw Knaster in the 1940s; It works for any number of players and produces an allocation that is proportional but not, in general, envy-free.
Lone-divider method
A cake-division scheme introduced by Hugo Steinhaus in the 1940s; It works only for three players and produces an allocation that is proportional but not, in general, envy-free.
Pareto-optimal
When no other allocation, achieved by any means whatsoever, can make any one player better off without making some other player worse off.
Player
A participant in a fair-division scheme.
Preference lists
Rankings of the items to be allocated, from best to worst, by each of the participants.
Proportional
A fair-division procedure is said to be proportional if each of n players has a strategy that can guarantee him or her a share of whatever is being divided that he or she considers to be at least 1/n of the whole in size or value.
Selfridge-Conway procedure
A cake-division scheme introduced independently by John Selfridge and John Conway around 1960; It works only for three players but produces an allocation that is envy-free (as well as proportional).
Taking turns
A fair-division procedure in which two or more parties alternate selecting objects.
Trimming procedure
A cake-division scheme introduced by Steven Brams and Alan Taylor in 1992; It works for any number of players, requires only finitely many steps, and produces an allocation that is envy-free (as well as proportional).