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

[Joshua Boehme]

If I'm understanding this correctly, this method isn't always cloneproof. Consider the following pairwise matrix (entries are row candidate over column candidate)...

     A   B   C   D   E
A 500 525 485 485 485
B 475 500 510 510 510
C 515 490 500 550 350
D 515 490 450 500 600
E 515 490 650 400 500

The initial ordering is:

   A   B   D   E   C
485 475 450 400 350

which is pairwise correct so we don't switch any candidates.


If you drop D and E, which are clones of C, you get:

   C   A   B
490 485 475

which is also pairwise correct.



On 4/11/24 19:54, Ted Stern wrote:
> 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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