[EM] Ultimate SPE Agenda Processing: Sink Swap Bubble

[Forest Simmons]

I think we can make this practical by restricting the runoff ballot to the
Smith set from the first ballot set: Just as a ballot CW is very likely a
sincere CW, so also Ballot Smith is likely to contain Sincere Smith.

The received wisdom seems to be that 90 percent of the time Smith is a
singleton (in public elections).

If so, probably 99.9 percent of public Smith sets are triples (cycles of
three).  Much more rare a cycle where one member of the cycle was cloned to
yield a Smith set of 5.  The twisted prism has six ... we'll never see more
than seven in a public Smith set ... and that is a perfectly practical
number for this kind of ballot.

To make the method ISDA compliant ...

If there is no ballot CW,

 (1) eliminate all the non Smith candidates and

(2) list the remaining candidates in order of minPairwiseSupport.

(3) Sink Sort this list and then ...

(4) reverse it to be used as the runoff ballot in the second round after
the instructions have been attached to it.

Publish the ballot so voters will have time to grok it ... and pundits time
to chew it over publicly.

To make the instructions as clear as possible ... "Put a check mark next to
the first candidate on the list, unless you like one of the other two
better. Also put a check mark next to your preferred of the last two
candidates.

If that is too complicated, just go back to step (4) above and replace it
with
(4') now sunk sort it again with a fresh set of preference ballots
(restricted to the Smith set from step (1)) determining the defeat matrix
for pairwise sorting purposes.

Assuming rational voters ... the head of this refried sorted list will be
the same candidate as the winner determined from the new fangled ballot.

So the two methods are the same ... which means that neither gives more
incentive than the other for insincere voting ... which was my main purpose
for creating the new tangled method.

In other words, the new method is DMC restricted to Smith ... with the
final sink sort done according to the pairwise preferences from a fresh set
of ballots!

Or you could simply say ... start with an "approval-like order" ... and
elect the lowest approval candidate that defeats every more approved
candidate ... just make sure the approval order was not determined from the
same ballots that determined the pairwise defeat relation.

-Forest



On Wed, Apr 12, 2023, 2:44 PM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> On 4/12/23 14:11, Forest Simmons wrote:
> > OK ... lacking an ndefeated candidate to elect ...
> >
> > 1. Use the RCV ballot informatioren to construct an elimination agenda
> > ... a list of the candidates with the less favorable near the top of the
> > list, and the more favorable near the bottom.
> >
> > 2.This list is to be published a week or ten days before the runoff.
> >
> > 3. The runoff ballot is an official copy of this agenda with the
> > following accompanying instructions:
> >
> > 4. Put a check mark next to the name of every candidate you like better
> > than any of the candidates listed below it. The check mark is an
> > abbreviation for BTAOTB "Better Than Any of the Below"
> >
> > 5. Elect the highest candidate on the list that has a BTAOTB check mark
> > on more than 50% of the submitted ballots.
> >
> > 6. The candidate listed last (bottom) is the default winner (when no
> > other candidate is preferred over "The Below" by a full majority of the
> > participating voters).
> >
> > All registered voters should be able to  participate in this runoff,
> > even if they did not participate in the first round (the check for a
> > candidate undefeated pairwise).
> >
> > It seems to me that the simplicity and importance of the runoff would
> > attract excellent participation.
> >
> > Thoughts and suggestions?
>
> It seems a bit complicated and if we suppose that voters have
> preferences among clones (i.e. don't consider them all equally good), it
> would fail clone independence.
>
> I would think that in a multi-way election, there would be a very low
> probability that a majority would consider a single candidate to be
> BTAOTB. Majority runoffs work because there are only two candidates, so
> in the absence of ties, there's always a winner, but I don't think that
> would generalize easily to multiple candidates. (In a way, this is the
> same problem as the clone dependence one; or rather, both are effects of
> the same root cause.)
>
> I really ought to make a variation on my strategy calculator for finding
> optimal methods with a honest runoff stage, but I have so many projects
> already...
>
> -km
>
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