[EM] Approval-Sorted Margins(Ranking) Elimination

[Forest W Simmons]

I would like to see how the  Yee/BOlsen  diagrams for this method 
compare with those of IRNR (Instant Runoff by Normalized Ratings), for 
example.
 

Chris Benham wrote:


>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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