[EM] Approval-Sorted Margins(Ranking) Elimination

[Chris Benham]

Hello,
My current favourite plain ranked-ballot method is  "Approval-Sorted 
Margins(Ranking) Elimination":

1. Voters rank candidates, truncation and equal-ranking allowed.

2. Interpreting ranking above bottom or equal-bottom as 'approval', 
initially order the candidates
according to their approval scores from the most approved (highest 
ordered) to the least approved
(lowest ordered).

3. If any candidate Y pairwise beats the candidate next highest in the 
order (X) , then modify the order
by switching  the order of the X>Y  pair  (to Y>X) that are closest in 
approval score.
Repeat until all the candidates not ordered top are pairwise beaten by 
the next highest-ordered candidate.

4. Eliminate and drop from the ballots the (now) lowest ordered candidate.

5. Repeat steps 2-4 until one candidate (the winner) remains.


Simply electing the highest ordered candidate after step3 is ASM(Ranking):

http://wiki.electorama.com/wiki/Approval_Sorted_Margins

> First "seed" the list in approval order. Then while any alternative X 
> pairwise defeats the alternative Y
>  immediately above it in the list, find the X and Y of this type that 
> have the least difference D in approval,
> and modify the list by swapping X and Y.

It is equivalent to ASM(R) in the situation where there are three 
candidates in the top cycle with no voter
ranking all three above bottom  (and in any election with just three 
candidates).

The advantage of this over ASM(R) is that there is less truncation 
incentive and voters who rank all the
viable candidates plus one or more others will normally face little or 
no disadvantage compared to informed
strategists. At some point in the process all except the candidates in 
the top-cycle will be eliminated, and
assuming three remain then from that point it will proceed like an 
ASM(R) election as though the "over-rankers"
'approve'  their two most preferred candidates (of the 3 in the top cycle).

An advantage it has over  Winning Votes (BP, RP,River) is that it 
doesn't have a 0-info. random-fill incentive.
Also unlike both WV and Margins it meets the  Possible Approval Winner 
(PAW) criterion.

35: A
10: A=B
30: B>C
25: C

C>A 55-45,   A>B 35-30,   B>C 40-25.

In this Kevin Venzke example, if we assume that voters rank all approved 
candidates strictly above all others
then it isn't possible for B to be approved on more ballots than A.  WV 
and Margins elect B.

ASM(R)E, like ASM(R) and DMC(R), elects C.

It seems obvious that ASM(R)E meets Minimal Defense.
http://nodesiege.tripod.com/elections/#critmd
//
If more than half of the voters rank candidate A above candidate B, and 
don't rank candidate B above
anyone, then candidate B must be elected with 0% probability.//

Referring to this definition, while A and B remain uneliminated A will 
always be considered to be more 'approved'
than B and of course A pairwise beats B, so B will always be ordered 
below A and so must at some point be
eliminated.

Chris  Benham

//



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