[EM] Fwd: Tideman & Green-Armytage Paper on Selecting Two Finalists

[Forest Simmons]

Four years ago James Green-Armytage and Nicolaus Tideman published a paper (
https://jamesgreenarmytage.com/runoff.pdf) that explored different ways of
selecting the finalists for a two candidate runoff.

They point out that, although RCV ballots can enable instant versions where
no second trip to the polls is necessary,  (among other things) some voters
might prefer to wait until they know who the finalists are before investing
the time and energy that goes into that final decision.

The immediate relevance of this point is borne out by Richard The VoteFair
Guy's recent message reminding us of the difficulty of getting Ranked
Choice ballots on  which the candidates can be fully ranked ... even where
Ranked Choice Voting has already been approved.

For example, after several elimination steps and vote transfers the
remaining RCV ballot profile might be something like

4900 C
2600 A>B
2500 B

The incomplete ballots might be because of lack of awareness that C and B
had a chance of being finalists ... or because forced equal rankings at
previous stages from lack of room on the ballot ... or from deliberate
strategic truncations by manipulators.

If B or C gets eliminated, there is no way of knowing where to transfer
their votes.

For example, both IRV and BFD (Best Friend Deference) would eliminate B
leaving 4900 C, 2600 A. The 2500 B voters' votes had no way of being
transferred.

Do we just say, "tough luck, you should have voted B>A or B>C ..."?

Or would it be better to have a real two candidate runoff between A and C
as suggested by Tideman and Green-Armytage?

Some of us have suggested allowing voters the option of including a
separate sincere ballot that would cover the runoff between the two
finalists, but that wouldn't address the lack of ballot space concern ...
nor would it allow the additional focus on the finalists.

Finally it would exclude voters that would like to be part of the final
decision without all of the hassle of filling out a long ballot.

We might say, "Just vote your too two preference."

But that would not help if their top two included neither of the finalists.

Is the voting system supposed to serve the people ... or are the people
supposed to be cogs in a bureaucracy?

Back to our example:
4900 C
2600 A>B
2500 B

As already noted, If B is eliminated as in IRV or BFD, the finalists are A
and C.

But it has been pointed out that no decent method based on this ballot
profile aline can elect A, because A is ranked on fewer ballots than C's
first place ballots.

So perhaps A should be eliminated instead of B. That judgment agrees with
Classical Condorcet which eliminates the A>B defeat because it is the
weakest link in the beat cycle ABCA  N. Leaving the defeats B>C and C>A ...
making B the winner.

But this choice rewards the manipulators that truncated the sincere 2500
B>A preferences, if indeed that was the cause of the cycle.

The manual final runoff between A and C cuts through all of the fog.  The
true preferences are revealed!


fws


---------- Forwarded message ---------
From: C.Benham <cbenham at adam.com.au>
Date: Sat, Jun 24, 2023, 11:31 PM
Subject: Re: Elimination by MinPO to the MMPO candidate.
To: Forest Simmons <forest.simmons21 at gmail.com>


Forest,

Something I just stumbled on that you might find interesting:

https://jamesgreenarmytage.com/runoff.pdf

Chris
On 24/06/2023 6:34 am, Forest Simmons wrote:

It looks like the simplest procedure is to start by eliminating all
candidates outside of Smith.

Then elect the sincere winner between the Smith MMPO candidate K and the
Smth candidate X with the MaxPO against K.

I should have listened to Chris in the first place!

To make this method Landau compliant, if K is covered, repeatedly update
the candidate  variablenK as the candidate that covers K with the least
pairwise opposition from the previous value of K.

Then initialize variable X as the candidate with the greatest PO against
this final value of K, and repeatedly update it as the candidate that
covers its previous value with the greatest pairwise opposition to K.

The sincere runoff is between these two Landau candidates.

None of this changes the results of our examples, because all candidates
were members of the Landau set ... which is the case whenever Smith has
fewer than four candidates.

fws
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