[EM] calculating margins in condorcet
Curt Siffert
siffert at museworld.com
Mon Apr 19 19:20:27 PDT 2004
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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