Abel and Galois cannot share a cake in a simple and equitable way

Guillaume Chèze (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

In this note we study a fair division problem. We show that there exist explicit couples of measures for which no algorithm outputs an equitable fair division with connected parts. In order to state this result we have defined a new model of computation: the algebraic Robertson-Webb model. In this model the mediator can ask the same queries as in the usual model but he or she can only perform algebraic operations. All existing algorithms described in the classical Robertson-Webb model can be described in this new model. The main tool of our approach is Galois theory.

Domaines: Système multi-agents [cs.MA]; Théorie des nombres [math.NT]

Guillaume Chèze. Abel and Galois cannot share a cake in a simple and equitable way. 2018. ⟨hal-01953971v1⟩