Similarly, pairwise comparison does not respect rotational symmetry, so it can lead to paradoxes too.

ECONOMIST: The mathematics of voting

This is a form of rotational symmetry, since the three votes form a rotating cycle.

ECONOMIST: The mathematics of voting

Geometry dictates that only two-, three-, four- and sixfold rotational symmetry can exist.

ECONOMIST: The 2011 Nobel prizes

Rotational symmetry means that if you turn something through a fixed angle, it looks the same (as a starfish would if you turned it through a fifth of a circle).

ECONOMIST: Particle physics makes sense, but it assumes too much