[EM] Criterias - weighted margins

[Stephane Rouillon]

Relative margins were an attempt to obtain a behaviour
between margins and winning votes ( relative margins are thus
relative to the number of expressed ballots).

As the result was not the one expected, maybe weighted
margins would lead to some truncation resistance using
a margin-based criteria. Although I would fid it harder to
justify such a criteria. At least relative margins corresponded
to the case "unexpressed preferences are interpreted like
disinterested voters trusting other voters who took the time
to express a preference". Margin is equivalent to a 50/50
split of unexpressed preference, and winning votes simply discards
unexpressed preferences as if the elector did not vote.
I have no idea how to interpret weighted margins...

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

Steph

Ted Stern a écrit :

> 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
> --
> Send real replies to
>         ted stern at u dot washington dot edu
>
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>
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