In mathematical sociology and especially game theory, envy-free is a property of certain fair division algorithms for a divisible heterogeneous good over which different players may have different preferences.
A division is envy-free if each recipient believes that according to his measure no other recipient has received more than he has. This requirement is stronger than proportional division.
There is a discrete procedure for three players and a moving-knife procedure for four players. Both have a bounded number of cuts. There is also a discrete procedure for any number of players, but this procedure has no fixed bound on the number of cuts required.
The concept generalizes naturally to chore division: in this case, a division is envy-free if each player believes their share is smaller than the other players'. The crucial issue is that no player would wish to swap their share with any other player.
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