[EM] calculating margins in condorcet

[Stephane Rouillon]

If you ask voters to add an approval cut-off, you could use residual approval
weights
to obtain a bijection mapping between voters and candidates, thus your 100%
distribution.
The idea is the following:
1) Solve your Condorcet method to obtain a ranking;
2) Process like with IRV but eliminate the last of the Condorcet ranking;
3) Attribute to the eliminated candidate the support of voters for which the
eliminated candidate is the last approved;
4) result is proportional in the sense every voter has an equal weight in the
final result.
The only problem is the initial order may not be respected because some
preferences
may get transferred to a higher acceptable clone, but the winner will still
win.

Steph

Curt Siffert a écrit :

> Hi, I'm trying to figure out a way to calculate margins for multiple
> candidates in a Condorcet-counted election, normalized to 100%.
>
> Assume there's a Condorcet Winner for first place.  He beats everyone
> else head-to-head.  Remove him from the ballots, recount, and then
> assume there's another Condorcet Winner for second place, beating
> everyone else head-to-head (except, of course, the first place winner).
>   Etc down the line.  So assume there is very clear ordering of who came
> in first, second, third, etc.
>
> How do you communicate how much everyone is leading everyone else?
> Like, normalized to 100% total.
>
> I can honestly not think of a way to mathematically convert or
> normalize the results into a familiar percentage ordering.
>
> For instance,
> A->B  67->33
> A->C  54->46
> B->C  51->49
>
> It's clear the ordering is A, B, C, but how do you convert this into a
> percentage normalized to 100% total?  Like:
> A: 40%
> B: 31%
> C: 29%
>
> Given that some of us like to theorize about a redesigned electoral
> system, a normalized system like that is important for schemes that do
> things like award proportional delegates or electoral votes (such as in
> the democratic primary, which awards proportional delegates for
> everyone over 15% support).
>
> It's possible in plurality by counting first-place votes, but there's
> still vote-splitting concerns there.  It's possible with Borda by
> comparing points to total points, but Borda has strategic problems and
> doesn't work as well for incomplete ballots.  It's possible for IRV
> even, by again only counting first-place votes.  But it doesn't seem
> possible with Condorcet.
>
> I've played with systems like figuring the margin between candidates,
> but it doesn't work well, because in examples like the above, B is
> definitely in second place, but C requires less of a voter shift to win
> than B does.
>
> It seems like there *should* be a way to calculate something like
> "total Condorcet support" expressed by a population, and then
> communicate what share of that support each candidate got, but I can't
> think of it.  Borda is tempting, but then you can end up with a
> different ordering of candidates.
>
> If it's not Condorcet, what's the best vote-counting system for a
> multi-candidate, single-winner election where it is nonetheless
> important to know the relative performance in percentage terms of each
> candidate?
>
> Perhaps the solution is not to calculate condorcet winners for every
> placement, but instead to count the fewest number of votes that would
> need to shift for each candidate to be the Condorcet winner, and then
> compare these votes to the total number of participating voters?  This
> doesn't seem to work either because maybe these B->C voters prefer 200
> other candidates to C as well.
>
> Any ideas?
>
> Thanks,
> Curt
>
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