[EM] Re: Condorcet package

[Ted Stern]

On 24 Feb 2005 at 12:24 PST, Paul Kislanko wrote:
>  
>
>> -----Original Message-----
>> From: election-methods-electorama.com-bounces at electorama.com 
>> [mailto:election-methods-electorama.com-bounces at electorama.com
>> ] On Behalf Of Ted Stern
>> Sent: Thursday, February 24, 2005 1:05 PM
>> To: election-methods at electorama.com
>> Subject: [EM] Re: Condorcet package
>> I used 'relative margins' when what I meant to say was 'margins'.
>
> Well, thanks for clearing THAT up. Neither is well-defined.

Context: We're discussing how to use the pairwise matrix, "A", to determine
the winner in a Condorcet completion scheme when there is no Condorcet winner
(CW).

In the pairwise matrix, the location A_{i,j} indicates the number of votes for
the i-th candidate [C_i] against the j-th candidate [C_j].

In terms of the pairwise matrix, a candidate C_k is the Condorcet Winner when
A_{k,j} is greater than A_{j,k} for each j not equal to k.

Since there is no such k, most robust completion schemes under discussion rank
the defeats C_i > C_j.  Here's how winning votes and margins rank them:

    Winning votes:      A_{i,j}

    Margins:            A_{i,j} - A_{j,i}

I'm not entirely sure what Relative Margins are relative to, but this is my
current understanding:

    Relative Margins:   (A_{i,j} - A_{j,i}) / (A_{i,j} + A_{j,i})

If you're still unclear on these concepts, please search the list archives or
start delving (and contributing) on the Election Methods Wiki:

      http://wiki.electorama.com/wiki/Main_Page

I notice that the Ranked Pairs page on this site (copied from Wikipedia) is
Tideman's original version, which uses Margins.  Steve Eppley's MAM version
uses winning votes.  And no, there is no definition of winning votes or
margins there.

Ted
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