[EM] Score Cover Sort

[Forest Simmons]

It's not obvious that it is monotone, but in a real sense, it is simpler
than the Score Landau method whose monotonicity we have carefully verified:

Initialize variable X with the name of the candidate with the greatest
score. Then ...
While any candidate covers X,  store in variable X the name of the highest
score candidate that covers the most recent previous value of X.

The reason I have such hope for the new (card deck) version is that it is
simply Ranked Pairs where the defeat strength of (X defeats Y) is measured
(primarily) by whether or not X covers Y, and secondarily by the score of
the pairwise winner of the pair.

To complete this card deck version of Ranked Pairs ... after all of the
out-of-order coverings have been rectified the deck should be bubble sorted
to rectify any (remaining) out-of-order adjacent pairs with priority to the
pair whose winner has the highest score (among adjacent pairs still in need
of rectification).

The Landau efficient version of Ranked Pairs nearest to SPE (in our gradual
process of generalizing SPE to other agenda based methods) is to measure
defeat strength primarily by whether or not the pairwise winner covers the
pairwise Loser, and secondarily by how close the loser is to the
unfavorable end of the agenda.

This is most easily done by two consecutive sorts... the first to rectify
the covering defeats, and then the second sort ... a bubble sort to rectify
the out of order adjacent pairs giving priority to pairs whose losers are
closest to the unfavorable end of the agenda.Since this second sort will
not contradict any of the order reversals of the first sort, the final
winner is still uncovered.

Also in the first (strong) sort of this version, each (strong)rectification
is accomplished by moving the loser of the pair (i.e. the covered member)
next to the winner of the pair (the one that covers the loser) on the side
towards the unfavorable end of the agenda.

I'm hopeful that the monotonicity of ordinary RP will carry over to to this
new Landau generalization of SPE. Praying won't help, but let's try
crossing our fingers :-)

So far the only Banks efficient agenda method proven to be monotone is
Agenda Based Chain Climbing.  I still have hope for Adanced Placement Chain
Climbing but it is maddenly elusive as are various other Banks efficient
agenda methods.

El mar., 26 de jul. de 2022 2:48 a. m., Kristofer Munsterhjelm <
km_elmet at t-online.de> escribió:

> On 7/18/22 2:37 AM, Forest Simmons wrote:
> > Remember that candidate X "defeats" candidate Y iff X is ranked or rated
> > ahead of Y on more ballots than Y is ranked or rated ahead of X.
> >
> > Additionally candidate X "covers" candidate Y iff candidate X not only
> > defeats Y, but also any candidate that does defeat X also defeats Y.
> >
> > For each candidate, make a 3"×5" card with its name, score, list of
> > candidates it covers, and a list of any other candidates defeated by it.
> >
> > First sort the cards by score.
> >
> > Then while any candidate X covers some candidate Y above it (in the card
> > deck) reinsert the highest such X card immediately above the highest
> > candidate Y that it covers.
> >
> > Elect the candidate that finishes at the top of the deck.
> >
> > This is the simplest monotone, clone free finish order that I know of
> > that always elects an uncovered candidate.
> >
> > Since it respects the score as far as possible while monotonically
> > electing an uncovered candidate, it is probably the highest Voter
> > Satisfaction Efficiency, monotone method that always elects an uncovered
> > candidate.
>
> I see no reason why it shouldn't work :-) But it's a complex method (in
> terms of dynamics) and there may be something I'm missing!
>
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