Quantum Democracy Is Possible

TL;DR

This paper explores the limitations of extending Arrow's Impossibility Theorem to quantum logic, demonstrating that certain ultrafilters in quantum structures are non-principal, which affects the theorem's applicability.

Contribution

It shows that Arrow's Impossibility Theorem does not hold in quantum logic due to the existence of non-principal ultrafilters in quantum structures.

Findings

Ultrafilters over finite quantum logics are not necessarily principal.

Arrow's Impossibility Theorem does not extend to quantum logic.

Quantum structures exhibit properties that differ from classical logic in social choice contexts.

Abstract

It is shown that, since an ultrafilter over an operator-algebraically finite (i.e. isomorphic to the lattice of projectors of a finite Von Neumann algebra) quantum logic is not necessarily principal, Arrow's Impossibility Theorem doesn't extend to the quantum case.