In 1785 the Marquis de Condorcet noticed something odd: every voter can have a perfectly consistent ranking, yet the majority prefers A over B, B over C and C over A. Quanta Magazine reports how researchers Ori Livson, Mikhail Prokopenko and Siddharth Pritam gave this paradox a shape. Building on a topological proof of Arrow's theorem, they found that circular preferences form the rims of a tube, and joining those rims requires a twist. The result is a Klein bottle, a surface with only one side. Each small patch looks consistent; the whole cannot be.

On US midterm day it is a reminder that 'the will of the people' is not a simple fact waiting to be counted. Choosing a voting system is a choice of values, not just arithmetic.

Source: Quanta Magazine (2026-10-26)

Summarised by the FTI newsdesk.