[EM] Simple Acceptable Ranked Choice Voting

[Forest Simmons]

It seems the way through is to make every step a covering step ... then
when the winner W gets a stronger step ... cutting in front of a bunch of
Y's that it followed before its strength increase ... it still covers all
of those Y's so no Z can be added just because it beats W and the previous
members of the chain.

I think we can get away with the very first step A>B  not being a covering:

Make it the single strongest defeat possible so that the first chain head A
is the "Gross Defeat Strength Champ."

Then until the current chain head is uncovered ... at each stage the new
head is the candidate with the strongest possible defeat of the old head by
any candidate covering it (the old head).

Example:

35 A>B>C
25 B>C>A
40 C>A>B

The strongest defeat is A>B (75 to 25).

And since the head A is uncovered, the chain cannot be continued, since by
our new rule all defeats after the first must be coverings.

So A wins.

Now is this monotone?

Shall we call it Max Gradient Ascent MGA?

-Forest


On Mon, Jan 9, 2023, 10:51 AM Forest Simmons <forest.simmons21 at gmail.com>
wrote:

> 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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