[EM] Margins Sorted Top-Ratings

[Chris Benham]

Ted,

You asked me a while back to explain how Margins Sorted Top Ratings 
"fails Independence from Clones".

The answer is that wearing that badge I think it technically doesn't, 
because if Ratings ballots are used
I think a (say) pair of candidates have to be given the same rating on 
every ballot to qualify "clones".

But if we instead call it  "Margins Sorted FPP(Whole)" using ranking 
ballots, then it can fail Clone-Winner
as in this example:

34 C
33 A>B
32 B

The FPP order is C>A>B and C pairwise beats A and A pairwise beats B 
(and that is all we need to know)
so C  wins.

Now say we add a clone of C, X.

18 C>X
16 X>C
33 A>B
32 B

Now the FPP order is A>B>C>X and as before no adjacent pair is pairwise 
out of order, i.e A (still) pairwise
beats B and B pairwise C and C pairwise beats X, so cloning C changes 
the winner from C to A.

I find this the more natural and useful way of looking at it.

Chris Benham




> On Mon, Jan 29, 2024 at 10:55 AM C.Benham <cbenham at adam.com.au  <http://lists.electorama.com/listinfo.cgi/election-methods-electorama.com>> wrote:
>
> >/(This is a re-send with an error corrected) />//>/I think Margins Sorted Top Ratings would be a good relatively burial />/resistant public proposal. />//>/* Voters rank from the top however many candidates they wish. />/Equal-ranking allowed. />//>/Give each candidate a score according to the number of ballots on which />/they are ranked below />/no others. />//>/Line them up in that order, highest to lowest. />//>/Check to see if all the candidates above bottom in this order pairwise />/beat the candidate immediately />/below them. />//>/If they do then elect the candidate highest in the order. />//>/If not begin with the pair that is pairwise out of order by the lowest />/margin and swap them. />/(if there is an exact tie in the size of the margin then swap the />/tied-margin pair lowest in the order). />//>/Repeat until no pair of adjacent candidates are pairwise out of order />/and then elect the highest-ordered />/candidate. * />//>/This could also use ratings ballots. />//>/This meets Condorcet, but can be at least be explained (if not sold) />/without reference to Condorcet or Smith. />//>/It would be as monotonic as it is possible for a Condorcet method to be. />//>/For the sake of simplicity (and elegance) it has some short-comings. />/When there is a top cycle, voters who />/didn't top-rate (rank below no other candidates) any of the candidates />/in the Smith set are disadvantaged by comparison />/those that did. It would also fail Clone-Independence. />//
> Could you explain how Top-rated Sorted Margins fails Independence from
> Clones? I'm not seeing how that would happen, unless you have unusual
> restrictions on top-rating

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