# [EM] Re: Pairwise winner of the 2 least-beaten

Mike Ossipoff dfb at bbs.cruzio.com
Sun Mar 3 18:09:33 PST 1996

```Steve Eppley writes:
>
> Mike O. wrote:
> >You suggested that circular ties be solved by determining which 2
> >candidates are the 2 least-beaten ones, and choosing, as the winner,
> >the one of those two who beats the other in a pairwise comparison. It's
> >to that proposal that that letter is a reply.
>
> No, I suggested:
> If the least beat also pairwise-beat the 2nd least beat,
> then the least beat wins.
> Else a runoff between the two.
>
> Mike's example:
> >40%: Buchanan, Nader, Clinton  (order-reversal cheating attempt)
> >25%: Clinton   (defensive truncation to thwart order-reversal)
> >35%: Nader, Clinton  (the side needing the compromise votes for him)
>
> Tie-break summary:
> Buchanan -60%
> Clinton  -75%
>
> Since Nader (the winner in plain Condorcet) is least beat but
> Buchanan beat him, we get a runoff between Nader and Buchanan.  This
> gives the Clinton voters a chance to vote for Nader, so Nader wins
> runoff.
>
> The runoff costs time and money, but it squelches the claims of the
> Buchanan crowd that they were robbed by a weird voting system.  This
> was the point of my proposal.
>
> Thanks for the example numbers.  They make it so much easier for me
> to understand.  I hope we make this a universal practice.
> .-
>
There's no guarantee that all the Clinton voters will vote for Nader
over Buchanan. Even if most of them do, Buchanan can still win, since
he has so much more 1st choice support. If that happens, then the
Nader voters who thought they were safe voting Clinton in 2nd place,
because this would count toward Clinton winning instead of Buchanan,
if Nader can't win will wish that they'd abandoned their favorite &
voted for the un-liked "lesser-evil" Clinton in 1st place. That's what
we want to avoid.

Never only inlcude 2 candidates in a 2nd balloting. Whether, as in
Runoff, we hold a 2nd balloting whenever no one gets a 1st choice
majority, or whether we use a 2nd balloting to solve a circular tie,
the 2nd balloting has got to include all of the candidates (or at
least all of the candidates in the circular tie).

I have nothing against saying "If the least beaten candidate doesn't
beat the 2nd least beaten candidate, then hold a 2nd balloting between
all the candidates (or all the candidates in the circular tie). As
far as results are concerned, that's ok. But I warn that it's an added
rule that complicates the definition, and that if people accept the
importance of those 2 least beaten candidates, they'd just as well
be willing to just elect the least beaten one, and not do a 2nd
balloting.

***

Though Condorcet's method is my actual public proposal, I
non-publicly propose 2 other very good methods which sometimes
require a 2nd balloting:

Runoff-Pairwise (or BeatsAll-Approval):

In the event of a circular tie, hold a 2nd balloting between all the
candidates (or all the candidates in the circular tie), by Approval.

Condorcet-Approval:

Use Condorcet's method, but if every candidate (or every candidate
in the circular tie) is beaten with a full majority against him,
then hold a 2nd balloting between all the candidates (or all the
candidates in the circular tie).

My main purpose with these two 2-balloting methods would be for
devious electorates. Though order-reversal can create a circular
tie, it can't get you anywhere in that 2nd balloting. I'm not saying
these 2-balloting methods are _necessary_ for devious electorates, only
that they'd be a convenient simple way to eliminate even what small
amount of strategy dilemma Condorcet's method could have.

Of those two 2-balloting methods, Condorcet-Approval is the more
deluxe one, since it doesn't require a 2nd balloting nearly as often.
If order-reversal causes a circular tie that could otherwise make
the cheaters' candidate win, then Condorcet-Approval automatically
detects it & calls for a 2nd balloting, since such a circular tie will
be one in which everyone is beaten with a full majority against them.
Otherwise, rarely will everyone be that beaten, and so, with
Condorcet-Approval, Condorcet's count rule will ordinarily solve
circular ties without there being need for a 2nd balloting.

As I said, BeatsAll-Approval (Runoff-Pairwise) is good for groups
that agree on Pairwise-Count, but don't agree on how to solve
circular ties.

***

Mike

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