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arXiv · 1508.04741

Arrow type impossibility theorems over median algebras

Miguel Couceiro·Stephan Foldes·Gerasimos C. Meletiou
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Abstract

We characterize trees as median algebras and semilattices by relaxing conservativeness. Moreover, we describe median homomorphisms between products of median algebras and show that Arrow type impossibility theorems for mappings from a product $\mathbf{A}_1\times \cdots \times \mathbf{A}_n$ of median algebras to a median algebra $\mathbf{B}$ are possible if and only if $\mathbf{B}$ is a tree, when thought of as an ordered structure.

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Miguel Couceiro, Stephan Foldes, Gerasimos C. Meletiou. 2015-08-19. Arrow type impossibility theorems over median algebras. https://arxiv.org/abs/1508.04741

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