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In this article we study a cake cutting problem. More precisely, we studysymmetric fair division algorithms, that is to say we study algorithms wherethe order of the players do not influence the value obtained by each player. Inthe first part of the article, we give a symmetric and envy-free fair divisionalgorithm. More precisely, we show how to get a symmetric and envy-free fairdivision algorithm from an envy-free division algorithm. In the second part, wegive a proportional and symmetric fair division algorithm with a complexity inO(n 3) in the Robertson-Webb model of complexity. This algorithm is based onKuhn's algorithm. Furthermore, our study has led us to introduce a new notion:aristotelian fair division. This notion is an interpretation of Aristotle'sprinciple: give equal shares to equal people. We conclude this article with adiscussion and some questions about the Robertson-Webb model of computation.

Don't cry to be the first!Symmetric fair division exist