[EM] A pairwise elimination satisfying SFC,SDSC

Forest Simmons fsimmons at pcc.edu
Fri Apr 6 15:39:52 PDT 2001

Blake Cretney patiently pointed out that I had a misconception about SFC,
and that the method described below doesn't really satisfy SFC.

I thought that SFC just meant that the method yields the sincere CW when
voters vote sincerely (which any form of Single Pairwise elimination would
satisfy). But Blake explained that it has to yield the sincere CW even
when truncations are allowed (if I understood him correctly). 

He pointed out some other faults as well including lack of independence
from clones.

I plead ignorance on the fine points of Condorcet completion.

The method was not intended to be in the same league as SSD, Ranked Pairs,
etc... but merely to be infinitely better than IRV.

What we need is a method that will appeal to IRV psychology and still not
haphazardly eliminate excellent candidates in the early stages of the
simulated runoff.

Here's my general description of a runoff that would be infinitely
better than ordinary plurality runoff:

At each stage of the runoff one of the two strongest contenders for last
place is eliminated by majority vote. 

Alternate wording:

In each round of the runoff one of the two candidates with weakest support
is eliminated by majority vote.

[end of method description]

It doesn't matter too much how "strongest contender for last place" or
"candidate with weakest support" is interpreted, except of course that it
must be spelled out in any version of this method that is adopted.

The reasons that I believe it may appeal to IRV psychology are ...  (1) 
IRV supporters like majority decisions. A decision as important as
elimination from a political contest should be made by majority vote.  (2) 
The method can be simulated with IRV style ballots which allow the kind of
expressivity that they believe in.  (3) The method is essentially IRV with
an extra majority check to make sure the best of the two apparently worst
candidates is not eliminated out of order. This precaution costs nothing
in the simulation.

In the first version I proposed below, I had a reason for specifying that
we interpret the candidates with weakest support or strongest contenders
for elimination as the ones with the most last place choices.

The purpose for this was to allow voters to use truncations as additional
tools to cope with the inexorable, myopic, unidirectional march of an
elimination method.

By truncating, voters rate several candidates as last place choices. In
other words, truncation allows a show of disapproval for several of the
bottom choices if necessary. Voters can vote down to Gore and leave Bush
unranked. That ballot counts as a last place vote for Bush and whomever
else is left unranked.  Don't tell anybody, but that's just Disapproval in

So that method would tend to eliminate the candidates at the bottom of the
Approval list before eliminating anybody else.

With these interpretations the method can be considered a version of
Approval Seeded SP, which isn't the best method, but sure beats IRV by a
long shot. And it does satisfy WDSC.


On Mon, 2 Apr 2001, Forest Simmons wrote:

> Mike O. recently reminded us that it seems impossible to get IRV
> supporters to budge on anything. I think it is a sign of insecurity.
> Before Mike reminded me of that, I was thinking of a method based on
> preference ballots that might have some of the same psychological
> attraction as IRV and still satisfy the SFC and SDSC.
> Here it is:
> In each round of the runoff either the candidate with the greatest number
> of last place votes or the one with the next to greatest number of last
> place votes is eliminated, whichever loses in the pairwise comparison of
> the two.
> This method satisfies SFC because a CW will never lose a pairwise
> comparison, and therefore never be eliminated.
> This method satisfies SDSC because if a majority prefers A over B, then
> truncation at the level of B will insure that B loses as follows:
> Candidate B will come up for elimination before A does since B will have
> more last place votes than A. If B is not already eliminated before
> the time that A is considered for elimination, then B
> will lose to A, and thereby be eliminated, QED. 
> As far as I know this is the only method based on preference ballots that
> meets SFC and SDSC while totally avoiding the issue of cycles.
> Do you think this method has a better chance among IRV supporters than 
> Approval or CR ?
> If so, then shouldn't we offer it to them as an alternative?
> Forest

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