The same notation can apply for two different hypothetical orderings of the same voter.

Arrow proposed to examine mapping different sets of individual orderings to possibly different social orderings.

They often arise when different orderings on certain finite sets are considered, possibly only because one wants to ignore such orderings and needs to know how many configurations are thus identified.

For example, structural Marxists have attempted to use comparative methods to discover the general processes that underlie apparently different social orderings in different societies.

The product depends on the order in which they are taken, but different orderings produce conjugate elements, which have the same order.

But the monoid structure of the sphere sequence is not commutative due to different orderings of the coordinates.

They reflect the fact that observers moving at different velocities may measure different distances, elapsed times, and even different orderings of events.

Multivariate division requires a monomial ordering, the basis depends on the monomial ordering chosen, and different orderings can give rise to radically different Gröbner bases.

In fact I always find it fun to see how Data::Dumper shows different orderings of hash arrays, even when just looping through some code over and over.

Faceted classification is used in faceted search systems that enable a user to navigate information along multiple paths corresponding to different orderings of the facets.