[EM] Simple Acceptable Ranked Choice Voting

Forest Simmons forest.simmons21 at gmail.com
Mon Jan 9 10:51:27 PST 2023


Let's see where my proof goes wrong .... my mistaken proof of monotonicity
for the one sided chain where every addition to the chain becomes the new
head:

Suppose the final head (the winner) H increases pairwise relative to some
candidate X while all of the other pairwise relations are undisturbed.

Then before H is added the sequence of additions proceeds exactly as before
... H has no influence.

If X is among those added before H, then the increase in H>X strength has
no relevance unless it allows H to immediately follow X instead of waiting
for Y1,Y2, etc ... where the Y1>X defeat was stronger than the H>X defeat
(but no longer is).

But now none of these Y's can be added because they are still defeated by H.

How about some Z that defeats H but was kept out by one of those Y's? Now
that those Y's are gone, that Z gets admitted.

So H is no longer the final head of the chain.

Back to the drawing board!

On Mon, Jan 9, 2023, 12:17 AM Forest Simmons <forest.simmons21 at gmail.com>
wrote:

> The candidate added to the tail would be the one defeated most strongly by
> the current tail. Whether to lengthen the chain forward or backwards at a
> given stage would depend on which new direct defeat was stronger.
>
> On Sat, Jan 7, 2023, 5:05 PM Kevin Venzke <stepjak at yahoo.fr> wrote:
>
>> Hi Forest, I may give it a look, but a couple of issues.
>>
>> One thing, I feel a little unsure it will be monotone to pick a new
>> candidate to add to the
>> chain based on who the current head is. Normally these methods don't
>> actually depend on the
>> ordering of candidates already in the chain.
>>
>> > It is well known that not all nice properties are compatible with each
>> other in a common
>> > single winner voting method. However, we shall see by example that the
>> following nice
>> > features are mutually compatible in a simple RCV voting method (MGCB
>> defined below).
>> > Therefore, excluding any of them can only be justified by trading in
>> the excluded ones for
>> > equally important ones in an equally simple method.
>> >
>> > 1. The method should be clone independent like IRV ... therefore not
>> plagued by the spoiler
>> > problem like First Past The Post Plurality or by "teaming" like the
>> Borda Count.
>>
>> Generous of you to imply that IRV is not plagued by a spoiler problem.
>>
>> > It was a comment of Kristofer that inspired this method. He mentioned
>> that according to his
>> > recent simulations electing the winner of the over-all strongest defeat
>> A>B is a
>> > surprisingly burial resistant stand-alone method.  It seems to me that
>> the burial resistance
>> > should carry over to this MGCB completion of his discovery.
>>
>> Well. That kind of method is a stone's throw away from just being
>> approval.
>>
>> > Furthermore, it appears that if defeat strength is gauged by margins,
>> then the method is
>> > Chicken resistant.
>>
>> If you mean "more" chicken-resistant then OK, but if you mean satisfying
>> the CD criterion,
>> there's no reason for that to be true. If you want to guarantee CD you
>> need to deliberately
>> reject some majorities (which is completely in its spirit), not simply be
>> indifferent to
>> them.
>>
>> More importantly, I would point out that from a CD criterion standpoint,
>> the Alaska RCV
>> outcome was probably completely correct.
>>
>> It seems to me the Alaska race demonstrates that the CD criterion can't
>> deliver on its
>> promise even under IRV, its most advantageous setting. It's not going to
>> be better under a
>> method that poses actual incentives to withhold lower preferences.
>>
>> > A fairly simple modification ... where the chain is built up from both
>> ends ... always
>> > giving priority to the end where the new defeat is stronger ....
>> preserves all six of the
>> > nice features in our list while adding a Strong Reverse Symmetry
>> feature ... reversing all
>> > of the ballot rankings precisely reverses the output chain ....
>> swapping the head and tail
>> > of the completed chain.
>>
>> I don't follow. Are you just saying there's a choice of whether you beat
>> the head or the
>> tail, but in either case the newly added candidate becomes the new head?
>>
>> Kevin
>> votingmethods.net
>>
>
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