[EM] Variable Inferred Approval Sorted Margins Elimination

C.Benham cbenham at adam.com.au
Wed Jun 19 10:59:43 PDT 2019

This is my favourite Condorcet method that uses high-intensity Score 
ballots (say 0-100):

*Voters fill out high-intensity Score ballots (say 0-100) with many more 
available distinct scores
(or rating slots) than there are candidates. Default score is zero.

1. Inferring ranking from scores, if there is a pairwise beats-all 
candidate that candidate wins.

2. Otherwise infer approval from score by interpreting each ballot as 
showing approval for the
candidates it scores above the average (mean) of the scores it gives.
Then use Approval Sorted Margins to order the candidates and eliminate 
the lowest-ordered

3. Among remaining candidates, ignoring eliminated candidates, repeat 
steps 1 and 2 until
there is a winner.*

To save time we can start by eliminating all the non-members of the 
Smith set and stop when
we have ordered the last 3 candidates and then elect the highest-ordered 


In simple 3-candidate case this is the same as Approval Sorted Margins 
where the voters signal
their approval cut-offs  just by having a large gap in the scores they give.

That method fulfils Forest's recent 3-candidate, 3-groups of voters 
scenarios requirements, resists Burial
relatively well and meets mono-raise. The motivation behind this version 
is to minimise any disadvantage
held by naive (and/or uninformed) sincere voters.

Chris Benham

*Forest Simmons* fsimmons at pcc.edu 
/Thu May 30 /

> In the example profiles below 100 = P+Q+R, and  50>P>Q>R>0.
> I am interested in simple methods that always ...
> (1) elect candidate A given the following profile:
> P: A
> Q: B>>C
> R: C,
> and
> (2) elect candidate C given
> P: A
> Q: B>C>>
> R: C,
> and
> (3) elect candidate B given
> P: A
> Q: B>>C  (or B>C)
> R: C>>B. (or C>B)

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