Faulty Sorts

  Consider a faulty sort mechanism intended to separate good from bad. If the decision depends on the perception of what's good and what's bad the sort can end up getting more mixed up instead of improving the sort. Using counts instead of probabilities one can show that the "sort" has an equilibrium distribution.

If A is the matrix containing the components a, b, c, d in the last blog then the limit after repeatedly multiplying an initial distribution by A can be determined with N₁=N_∞ and N₂=N₀-N_∞.

So if A represents a faulty processing mechanism used to sort successive distributions then the limit of the distributions will be (90, 10)^T. One can treat the column vectors of A as "distributions" with their limits being A^∞ above. One could use the equilibrium distribution to characterize the sort mechanism.

One can view a decision mechanism as a kind of sort. From this perspective it might be better to do an objective test of each item rather than rely some preconceived notions.

Note that the final result of the repeated sort is dependent on the process itself and not on whether or not a particular item is good or bad. It can degrade better sorts and improve poorer sorts.