Envy-free

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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 scheme is envy free if each recipient believes that (according to their measure) no other recipient has received more than they have. A procedure for envy-free division was first published by Steven J. Brams and Alan D. Taylor in 1995.

The concept generalizes naturally to chore division: in this case, a division is envy free if each player believes her share is smaller than the other players'. The crucial issue is that no player would wish to swap her share with any other player.

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