Topological aggregation, the twin paradox and the no show paradox

TL;DR

This paper demonstrates that within the topological aggregation framework, fundamental paradoxes like the Twin Paradox and the No Show Paradox are unavoidable, regardless of anonymity or unanimity assumptions.

Contribution

It proves the inherent presence of these paradoxes in topological aggregation, highlighting limitations of the framework.

Findings

Twin Paradox cannot be avoided in topological aggregation

No Show Paradox cannot be avoided in topological aggregation

Results hold without requiring anonymity or unanimity

Abstract

Consider the framework of topological aggregation introduced by Chichilnisky (1980). We prove that in this framework the Twin Paradox and the No Show Paradox cannot be avoided. Anonymity and unanimity are not needed to obtain these results.