[EM] "Margin Sorted Minimum Losing Votes (equal rated whole)" candidate in poll

[Ted Stern]

Chris, what I nominated for the poll was essentially the same as what you
proposed in October of 2016, but simplified to require no elimination step
iteration. Just one margin sort on MinLV(erw).

http://lists.electorama.com/pipermail/election-methods-electorama.com/2016-October/000599.html

ERW means that if A and B have equal rank above bottom, we fill in the
pairwise array as if it were one whole vote of A>B and one whole vote of
B>A.

The reason I proposed it is that seeding the margin sort with MinLV score
in descending order is analogous to minimum pairwise opposition in
ascending order. MinMaxPO is burial resistant, the property we're looking
for, and for margin sort, we want a metric that is analogous to approval,
with descending scores.

If we wanted the *exact* complement, we would do margin sort on *min votes*,
to get the closest approximation to MinMaxPO(wv) possible while still being
Smith compliant. However, minmax (or rather maxmin) is not clone proof, as
can be seen by applying margin sort min votes to the example you posted
last week:

http://lists.electorama.com/pipermail/election-methods-electorama.com/2024-April/005616.html

By using minLV instead of min votes, C's minimum score of 18 (with clone)
is ignored and so the seed ranking before margin sort is unchanged by the
addition of the clone.

My motivation for the nomination: while margin sorted approval is an
excellent method, the approval cutoff (what I prefer to think of as a
preference cutoff, since all ranked candidates are approved) is an
additional step, requiring either an additional count for implicit
approval, or an extra mental judgment by the voter.

Margin Sorted MinLV(erw) is automatic, and from my limited testing, tends
to find a candidate with strong top ratings.

On Thu, Apr 11, 2024, 01:17 Chris Benham <cbenhamau at yahoo.com.au> wrote:

> Ted,
>
> I'm not completely clear on what the "equal rated whole" part means, and
> likely there are some other possible
> voters who have no idea what any of it means.
>
> This is what I think it all means.
>
> Voters rank the candidates from the top, equal ranking an truncation
> allowed.  Then we construct a pairwise matrix.
>
> A ballot voting A over B gives one vote in the A-B comparison to A and
> nothing to B.   A ballot that truncates (or votes
> equal-bottom) both A and B gives nothing to both in the A-B comparison.
>
> But in the case a ballot explicitly votes A=B above bottom, do you propose
> that the ballot give a whole vote each to
> A and B in the A-B comparison? (Until I hear otherwise from you, I'll
> assume this is  what you mean.)
>
> An alternative reasonable idea would be for this to be only the case where
> the ballot votes A and B below no other
> candidates, and if they are voted A=B above bottom but below top then the
> ballot gives half a vote to each of A and
> B in the A-B comparison.
>
> In any case I understand that we  score each candidate according to the
> minimum number of votes they got in a pairwise
> loss, and order them from highest to lowest.
>
> Then candidates are listed in  score order and if any adjacent pairs are
> pairwise out of order then this is corrected by
> flipping the out-of-order pair with the smallest margin. If there is a tie
> for this we flip the lowest scored tied pair. Repeat until
> there are no adjacent pairs of candidates that are pairwise out of order,
> then elect the highest-ordered candidate.
>
> I am favourably disposed to this, but I'd like some clarification (and
> hopefully some de-confusing justification) on the issue
> of how we treat equal ranking (or "rating").
>
> Chris Benham
>
>
>
> *Ted Stern* dodecatheon at gmail.com
> <election-methods%40lists.electorama.com?Subject=Re%3A%20%5BEM%5D%20Poll%20on%20voting-systems%2C%0A%20to%20inform%20voters%20in%20upcoming%20enactment-elections&In-Reply-To=%3CCAHGFzOTaPTdMnVw7TELxExvM4ZjbAEtaxJWZ-%2Bpcttf4ATXhPw%40mail.gmail.com%3E>
> *Sat Apr 6 12:33:35 PDT 2024*
>
>
> ------------------------------
>
> I'd like to nominate
>
> Margin Sorted Minimum Losing Votes (equal rated whole)
>
>
>
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