[EM] Hay guys, look at this...

[Forest Simmons]

Let me rephrase the question ... suppose that there were only three
candidates and you already knew that they were in a rock paper scissors
pairwise preference cycle.

How would you decide which one to vote for if you could only vote for one?

That's the one you should make your first choice on an RCV ballot if the
cycle breaker is FPTP as you have been suggesting.

That decision is at least as difficult as the approval decision would be,
because under approval strategy you should approve that candidate X (the
one you would vote for if you had only one vote) AND also approve your
favorite if X was not already your favorite.

These are the same candidates that you would naturally rank on an RCV
ballot ... leaving the 3rd choice unranked ... the one that is neither your
favorite nor your compromise.

If you mis-triangulate the compromise in an FPTP election ... too bad: you
wasted your vote. But the approval ballot also counts towards everybody you
like better than your compromise, including your favorite.

That's why Approval is often proposed as a Condorcet completion method in
the absence of a runoff.

Implicit approval takes advantage of the natural strategy of truncating the
candidates you don't like, while ranking your preferred of the two front
runners AND anybody you liked better ... including your favorite ...
whether or not it was a frontrunner.

Yes, the cycle is already there ... but it cannot split the votes unless
the method allows vote splitting by not having any contingent backup vote.
Approval has the simplest backup vote capability ... any other method
requires some kind of runoff/elimination step to ameliorate the potential
vote split.

Example ballot profile:

40 A>B (Sincere is A>C)
35 B>C
25 C>A

Under Plurality A wins.

The Implicit Approval (fewest truncations) winner is B with only 25
truncations, compared with 35 A truncations and 40 C truncations.

This is a typical kind of ballot profile resulting from the burial by the
largest faction ... of the sincere Condorcet Winner (C in this example).

If the C supporters wanted to protect C, they could have truncated A:

25 C instead of 25 C>A.

This would not change the Plurality winner, but reinforces the Implicit
Approval winner, which gives the sincere CW a defense against burial by
punishing the burying faction ... electing their sincere last choice
instead of their sincere second choice.

With this defensive truncation B still has the fewest truncations 25, but
now the burial perpetrator A has way more truncations (60) than either of
the others ... no chance of success in their burial gambit.

Electing the Plurality choice (lacking a ballot CW) rewards the burial
perpetrator in this example .... so it encourages candidates with large
first place support to bury the sincere CW.

This example is typical in this respect ... the insincere  burial (of
sincere CW) gambit is most tempting to the faction with the greatest first
place support.

On the other hand it is not tempting to bury the CW when lacking a CW the
implicit approval candidate is elected ... because this burial gambit will
almost certainly fail if not outright backfire.

It seems to me that anybody who understands why Approval is superior to
FPTP Plurality as an election method ... such a person should be able to
see how Approval is a better fall back alternative than Plurality (absent a
CW) .... an appreciable positive difference at no extra cost.

The little Dutch boy was right to put his finger in the dike ... a stitch
in time is in deed worth nine.







On Fri, Feb 17, 2023, 7:07 PM robert bristow-johnson <
rbj at audioimagination.com> wrote:

>
>
> > On 02/17/2023 9:44 PM EST Forest Simmons <forest.simmons21 at gmail.com>
> wrote:
> >
> >
> > Suppose the whole election was to choose one of the three candidates ...
> no noncycle members were in the election at all.
> >
> > Would you recommend FPTP Plurality over Approval?
> >
> >
>
> I dunno.  I would recommend Condorcet RCV and, only in the super-rare case
> of a cycle, I would recommend plurality of first-choice votes because it's
> no worse than we already have now with FPTP and it's simple to explain to
> voters why that one candidate (the one with more first-choice votes than
> anyone else) is, in some sense, uniquely more preferred by the electorate
> over any other candidate.
>
> In a competitive 3-way race, I dunno if Approval would be better than
> FPTP.  I *do* know, if it were Approval, that I would have a tactical
> decision to make regarding my second-favorite candidate.
>
> But with RCV, I would have no tactical decision to make.  I would know
> immediately what I would do with my second-fav.
>
> --
>
> r b-j . _ . _ . _ . _ rbj at audioimagination.com
>
> "Imagination is more important than knowledge."
>
> .
> .
> .
>
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