[EM] Web interfaces and Condorcet scores

[Rob Lanphier]

Hi Rob,

Comments inline.

Rob Brown wrote:

> So I'm thinking, what I need to concentrate on is finding the "delta 
> score" between a candidate and the one above him.  This value should 
> always be positive, of course, and should represent the number of 
> votes necessary to tie that candidate, but that is *not* necessarily 
> the pairwise margin between those two candidates (since as you 
> mention, that could be negative, which would confuse people). 


This works to express the delta between two adjacent candidates, but 
using the sum of the delta scores for the top candidate implies that an 
overstated delta between the top candidate and the bottom candidate.

Using your example:

>
> As an example:
>
>         A       B       C       D
> A       X       81      30      64
> B       19      X       29      22
> C       70      71      X       69
> D       36      78      31      X
>
> Pairwise victories:
> A -> C  (70 30)
> B -> A  (81 19)
> B -> C  (71 29)
> B -> D  (78 22)
> D -> A  (64 36)
> D -> C  (69 31)
>
> Ranking:
>
> B:      number of wins: 3
> D:      number of wins: 2
> A:      number of wins: 1
> C:      number of wins: 0
>
> So:
>
> For D to tie B in the final ranking, D would simply need to tie B in a 
> pairwise ranking (which would need 56 votes). So we'll say that B 
> beats D by 56 votes.
>
> For A to tie D in the final ranking, A would either have to tie D in a 
> pairwise ranking (which would need 38 votes) or tie B pairwise (which 
> would take 62 votes).  The smaller of these is 38, so we'll say that 
> that D beats A by 38 votes.
>
> For C to tie A in the final ranking, C would either have to tie A in a 
> pairwise ranking (which would need 40 votes) tie B (which would take 
> 42 votes), or tie D (which would take 38 votes).  The smallest of 
> these is 38, so we'll say that that A beats C by 38 votes (even though 
> the 38 represents NOT the pairwise margin for C vs. A, but for C vs. D).
>
> So now our scoring looks like this:
>
> B: x + 38 + 38 + 56
> D: x + 38 + 38
> A: x + 38
> C: x


This implies that the delta between B and C is 38+38+56=132.   However, 
the delta is actually only 42 votes.

Rob