Divide and choose

[1] Since ancient times some have used the procedure to divide land, food and other resources between two parties.

Currently, there is an entire field of research, called fair cake-cutting, devoted to various extensions and generalizations of cut-and-choose.

The United Nations Convention on the Law of the Sea applies a procedure similar to divide-and-choose for allocating areas in the ocean among countries.

A developed state applying for a permit to mine minerals from the ocean must prepare two areas of approximately similar value, let the UN authority choose one of them for reservation to developing states, and get the other area for mining:[4][5] Each application... shall cover a total area... sufficiently large and of sufficient estimated commercial value to allow two mining operations... of equal estimated commercial value...

Divide and choose assumes that the parties have equal entitlements and wish to decide the division themselves or use mediation rather than arbitration.

The divide and choose method does not guarantee that each person gets exactly half the cake by their own valuations -- the cutter may perceive the advantage of parts of the cake differently from the chooser and anyways the chooser chooses what he thinks is the better half.

Martin Gardner popularized the problem of designing a similarly fair procedure for larger groups in his May 1959 "Mathematical Games column" in Scientific American.

If Bob is the cutter and he is unaware of Carol's preference, his safe strategy is to divide the cake so that each half contains an equal amount of chocolate.

It is entirely possible that Bob, in his ignorance, would put all the vanilla (and some amount of chocolate) in one larger portion, so Carol gets everything she wants while he would receive less than what he could have gotten by negotiating.