# Mixed Condorcet-Plurality

Buddha Buck bmbuck at 14850.com
Tue Apr 10 21:28:43 PDT 2001

```"Tom Ruen" <tomruen at itascacg.com> writes:

> This is an example that Condorcet handles reasonably because there are no
> cycles. B and C have a united coalition - one of them is guaranteed to win
> by any good method.
>
> The question here in judging between using Runoffs or Condorcet is whether
> you want A supporter's second rank preference to decide a winner between B
> and C. Since B and C have a mutually united coalition we might imagine they
> were in the same party and a primary could have chosen between them which
> should run against A. Well, I mean this shows why IRV can replace primaries
> while Condorcet can not.

Actually, this is a simplification of a standard example I use to show
one of the problems with IRV.  It is not clear that B and C have a
mutually united coalition.  Try this varient instead:

41 ABC
39 CBA
12 BCA
08 BAC

Again, you have Plurality selects A, IRV selects C, Condorcet selects
B.

Personally, I don't care about primaries.  Primaries are tools
political parties use to directly decide who is going to be on the
ballot.  I have a philosophical objection to parties having a direct
say in who is going to be on a ballot.

> My original email said use Condorcet if there is a candidate that beats all
> others in pairwise elections and otherwise use plurality among the top set
> of mutually pair-defeatable candidates.

That may be a reasonable method, but I'd like to see it compared to
other Condorcet-based methods.

> Tom
>
> From: "Buddha Buck" <bmbuck at 14850.com>
> To: <election-methods-list at eskimo.com>
> Sent: Tuesday, April 10, 2001 3:30 PM
> Subject: Re: Mixed Condorcet-Plurality
>
> [snipped]
> ...
> > Here's an example where Plurality, Condorcet, and IRV all yield different
> > results!
> >
> > 45 ABC
> > 35 CBA
> > 20 BCA
> >
> > Plurality: A wins
> > IRV: B is eliminated, and 20 votes transfer to C, C wins
> > Condorcet: B defeats A 55:45, B defeats C 65:35, B wins

```

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