Take a set {A, B, C, D, E}, and assume each of the set elements has a random real value attached to it between 0 and 1. For example, this gives us: {A, B, C, D, E} = {0.1, 0.9, 0.4, 0.6, 0.5}. Assume that the set has a preferred order, {A > B > C > D > E}.

Repeatedly taking random pairs of this set, and assigning an increment to the element of the pair that 'beats' the other element according to the preferred order, results in the real values having a ranking.

For example:

A v's B: A <- 0.1 + increment, B <- 0.9 - increment

C v's D: C <- 0.4 + increment, D <- 0.5 - increment

and so on for many pairings.

So the result after many pairings in a simulation is, for example:

{A, B, C, D, E} = {0.9, 0.7, 0.3, 0.3, 0.1}

Is there a proof that can be created that states that a ranking will always emerge in such a scenario?