# Lowest Majority loser tie breaker

Steve Eppley seppley at alumni.caltech.edu
Sun Nov 3 22:33:26 PST 1996

```DEMOREP1 wrote:
>Yet another Condorcet circular tie breaker for single (or multiple)
>executive/judicial elections ----
>1. The voters vote yes or no on each candidate and rank number each
>candidate.

If you accept the following two reasonable "transitivity" assumptions

If a voter votes Yes on candidate X then the voter also votes
Yes on every candidate s/he prefers more than X.

If a voter votes No on candidate Y then the voter also votes
No on every candidate s/he prefers less than Y.

then the information contained in "YN+rankings" ballots is identical
to the information contained if the voters can insert the "None of
the Below" (NOTB) choice in their rankings:

The ballot
A>B>C > NOTB > D>E>F
implies
Yes:ABC No:DEF   1.A 2.B 3.C 4.D 5.E 6.F
and vice versa.

(See the definition of NOTB (a.k.a NOTR, None of the Rest) in the
report on the election-methods-list single-winner poll.)

I think a ballot which violates one or both transitivity assumptions
is inconsistent, and perhaps the ballot method shouldn't permit
inconsistency.  The NOTB approach doesn't permit inconsistency,
but the YN+rankings ballot does.  For example:
Yes:B No:A   1.A 2.B
What kind of tactics would be enabled by allowing inconsistencies?

>2. The simple Condorcet method is applied to those candidates who
>get a majority yes vote.
>3. If there is a Condorcet circular tie, then the candidate who has
>the lowest yes majority loses and the Condorcet method is redone.
>necessary until the winner remains (or winners remain).
>
>Item 3 is new. I repeat again the absolute necessity that the
>winner have majority "positive" support.

By "Condorcet method" I assume you mean "pairwise method", and are
crediting Monsieur Condorcet with its invention.  We need to be
careful to distinguish this from what we've been calling Condorcet's
method (i.e., use smallest largest loss if no one beats all others).

I'd like Demorep to provide an example where the result differs from
plain Condorcet, other than the obvious case where no candidate is
majority-approved.

-snip-
>A Condorcet tie breaker winner using the least votes against in
>his/her worst defeat will be absolutely blasted as being chosen by
>a minority (since such winner would be opposed by one or more
>majorities).

It's not necessarily true that the winner with the smallest largest
loss will be opposed by a majority.  In the 46/20/34 example where
the 46 truncate (creating a circular tie), the winner is opposed by
only a *minority* (34) in his worst loss.  In the 46/20/34 example
where the 46 order-reverse, the winner is opposed by only a minority
(46) in his worst loss.

The YN (or NOTB) option seems to really protect us only in cases
where *every* candidate is opposed by a majority.  (Other cases
are possible but are they plausible?  Example please...)  If you
stipulate that the improved voting method has already freed all
of the decent candidates to compete by taking away their spoiler
dilemma, then who's left to govern?  Is it really better to have
no winner than to elect the candidate who's least disapproved?

I advocate allowing the NOTB option when legislatures, councils,
and direct democracies rank rival proposals, since it normally
makes considerable sense to allow one or zero proposals to win.
But allowing disapproval of all candidates for office means risking
a vacuum of power.  So it's a double-edged option, and maybe we should
just use the KISS principle and avoid the YN and NOTB "enhancements"
in our election reform efforts.

>Could any of the 1996 U.S. President candidates on the Nov. 5, 1996
>ballot get a majority of yes votes? I doubt it.

So do I.  But with a better voting method we'd have more choices,
probably including people like Alexander, Forbes, Buchanan,
Robertson, Quayle, Cheney, Bennett, Bush, Jackson, J.Brown, Gephardt,
Gore, Lamm, etc., and if all of them are disapproved then we'd have
a serious crisis of a different sort: a vacuum of power.

I repeat my request: please provide an example where an approved
candidate loses to a disapproved candidate if the yn votes are
ignored and the rankings are tallied by plain Condorcet, so we can
study a Condorcet scenario which is disturbing and decide if it's