On the homotopy type of choice spaces

TL;DR

This paper characterizes the topological conditions under which continuous, symmetric, and unanimous aggregation functions exist, showing they are only possible on contractible choice spaces.

Contribution

It establishes a topological criterion for the existence of certain aggregation functions, linking their existence to the contractibility of the choice space.

Findings

Aggregation functions exist iff the choice space is contractible.

Provides a topological characterization of aggregation functions.

Connects topological properties with social choice functions.

Abstract

We study continuous, symmetric and unanimous aggregation functions and continuous majority functions and prove that such functions exist on a choice space if and only if the choice space is contractible.