[EM] Pairwise Strength Sorting

[Forest Simmons]

Suppose you have a list of candidates that you want to sort.pairwise.

We have several standard sorting methods available... Bubble, Sink, Merge,
Sorted Approval Margins (SAM), etc.

One that subsumes many of the rest is Pairwise Strength Sortimg:

While any candidate W is listed immediately below a candidate L that is
pairbeaten by it, swap positions of the two members of the strongest such
out of order pair:

The list order L>W is reversed to W>L in order to accurately reflect the
pairwise defeat order.

If defeat strength is gauged by the ratio of winner's approval to loser's
approval the strength sort, and we are pairwise strength a list of
candidates I'm descending order of approval, then the stromgest out of
order adjacent pai will be the one where the ratio of the respective
approvals is as close to unity as possible.

Similarly, if the gauge of defeat strength is difference of winning and
losing approval (W minus L, an out of order adjacent pair will have a
negative defeat strength,
A(W)minus A(L) < zero, and the less negative, i.e. the closer to zero to in
absolute value, the stronger the defeat of W over L.... which is the
identical rectificatiom priority that defines Sorted Approval Margins.

One way to make method based on Pairwise Strength Sorting, is yo
specify a nominal favorability criterion and a gauge of pairwise defeat
strength.

To get the finish order, Pairwise Stregth Sort the list of candidate given
in ?order of nominal favorability.

fws
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