The Envy-Free Cake-Cutting Procedure

How to Ensure Fairness as a Mechanistic Outcome

In the context of economics and game theory, envy-freeness is a criterion of fair division where every person feels that in the division of some resource, their share is at least as good as the share of any other person — thus they feel no envy. For n=2 people, the protocol proceeds by the so-called divide and choose procedure:

The Envy-Free Cake-Cutting procedure states that if two people are to share a cake in way in which each person feels that their share is at least as good as any other person, one person ("the cutter") cuts the cake into two pieces; the other person ("the chooser") chooses one of the pieces; the cutter receives the remaining piece.

For cases where the number of people sharing is larger than two, n > 2, the complexity of the protocol grows considerably. The procedure has a variety of applications, including (quite obviously) in resource allocation, but also in conflict resolution and artificial intelligence, among other areas. Continue reading


This essay is part of a series of stories on math-related topics, published in Cantor’s Paradise, a weekly Medium publication. Thank you for reading!