[EM] ranked pair method that resolves beat path ties.

[robert bristow-johnson]

so this is interesting.  it seems to be an extension of Tideman 
ranked-pairs that considers first the margins and then the opposing 
votes (or winning votes for the opponent) to break ties.  is that 
essentially it?

On 11/27/11 10:21 PM, Ross Hyman wrote:
>
> When beat path produces a tie, this method can produce a single winner 
> unless the tie is genuine.  It is the same method I presented earlier 
> except for the addition of the Removing step, which resolves the ties.
>
>
> Candidates are classed in two categories: Winners and Losers.  
> Initially, all candidates are Winners.  Every candidate has an 
> associated Set of candidates that includes itself and those candidates 
> that have defeated it.  Every candidate initially has a set composed 
> of itself and no other candidates.  Winners are those candidates who 
> have no Winners in their set aside from themselves.
>
> The pairs are ranked in order.All pairs are ranked in the form A>B 
> indicating more voters rank A above B than rank B above A.
>
now this is ranked pairs w.r.t. margins.

> Pairs with equal votes for A above B and B above A are not ranked.
>
not immediately, but is this not what the procedure below is about?

> For winning votes ranking, A>B is ranked higher than C>D if more 
> voters ranked A above B than ranked C above
>
> If the same number of voters ranked A above B as ranked C above D then 
> A>B is ranked higher than C>D if more voters ranked D above C than 
> ranked B above A.
>

so maybe i got it wrong, first it's Winning Votes that determines the 
order of ranking and then Margins is used to break the tie?

> If the same number of voters ranked A above B as ranked C above D and 
> the same number ranked D above C as ranked B above A then these pairs 
> are equally ranked.
>

because *both* the winning votes is tied and the margins is tied.  what 
else is there?

i wonder if it would be better to first rank each pair according to 
Margins and then, in the case of tie of Margins, Winning Votes are used 
to break the tie to determine which pair result has priority over the other.

for some reason, i like Margins because it is the product of the percent 
spread (which indicates how decisive a defeat is) times the number of 
voters participating (which indicates how important the pair election 
is).  that product is a natural measure for how important and decisive a 
pairwise defeat is.  Winning Votes, all by itself, should not be the 
sole (or primary in the present case) decider.  what if there is a lot 
of voters, but the pair-election is close (say a defeat by 1 vote)?  
it's not a decisive defeat, but Winning Votes would say it is.  i think 
Margins is more salient than Winning Votes.

-- 

r b-j                  rbj at audioimagination.com

"Imagination is more important than knowledge."