Consensus splitting

Consensus splitting, also called exact division, is a partition of a continuous resource ("cake") into some k pieces, such that each of n people with different tastes agree on the value of each of the pieces. For example, consider a cake which is half chocolate and half vanilla. Alice values only the chocolate and George values only the vanilla. The cake is divided into three pieces: one piece contains 20% of the chocolate and 20% of the vanilla, the second contains 50% of the chocolate and 50% of the vanilla, and the third contains the rest of the cake. This is an exact division (with k = 3 and n = 2), as both Alice and George value the three pieces as 20%, 50% and 30% respectively. Several common variants and special cases are known by different terms:Consensus halving – the cake should be partitioned into two pieces (k = 2), and all agents agree that the pieces have equal values. Consensus 1/k-division, for any constant k > 1 – the cake should be partitioned into k pieces, and all agents agree that the pieces have equal values. Another term is consensus splitting. Perfect division – the number of pieces equals the number of agents: the cake should be partitioned into n pieces, and all agents agrees that all pieces have equal values. -near-exact division, for any constant , the agents may disagree on the pieces values, but the difference between the values should be at most . Similarly, the approximate variants of the above-mentioned problems are called -consensus-halving, -consensus 1/k-division or -consensus-splitting, and -perfect-division. Problem of the Nile – there are infinitely many agents. Necklace splitting – the resource to divide is made of a finite number of indivisible objects ("beads").

This keyword could refer to multiple things. Here are some suggestions: