[EM] Trying to have CD, protect strong top-set, and protect middle candidates too

[Forest Simmons]

Yes, it is different. Standard Pairwise Sorted Approval starts sorting from
the top and works down.  This version starts at the bottom and works up.

Here's a simple recursive definition:

Elect the most approved candidate that is not beaten pairwise by the second
place candidate.

[The second place candidate is the one that would be elected by the method
if the first place candidate withdrew.]

Because of this characterization of the method we could call it MAI for
"Most Approved Immune."  Here "immune" refers to immunity from second place
complaints.

So the shortest (and most cryptic) definition of the method is

Elect the Most Approved Immune candidate X.

To unpack this definition you have to define immunity as meaning unbeaten
by the runnerup, and define runnerup as the (recursive) winner of the
ballot set with X disqualified.

On Wed, Nov 16, 2016 at 2:55 PM, Monkey Puzzle <araucaria.araucana at gmail.com
> wrote:

> Hi Forest,
>
> Is your suggestion different from Pairwise Sorted Approval?
>
> http://wiki.electorama.com/wiki/Pairwise_Sorted_Approval
>
> If not, the winner is not necessarily the most approved candidate in the
> Smith set.
>
>
>  Frango ut patefaciam -- I break so that I may reveal
>
> On Wed, Nov 16, 2016 at 2:30 PM, Forest Simmons <fsimmons at pcc.edu> wrote:
>
>> Here's a simple method that is essentially Smith//Approval without having
>> to mention the Smith set:
>>
>> List the candidates in order of approval, highest to lowest, top to
>> bottom.  While any candidate pairwise beats an adjacent candidate higher in
>> the list, switch places of the two lowest out of order adjacent members.
>>
>> When there remains no out of order adjacent pair, elect the candidate at
>> the top of the list.
>>
>> Note that the winner will automatically be a member of the top cycle, and
>> if it is a cycle of three, it will be the most approved member of the cycle.
>>
>> Also notice that it yields an unambiguous social order, and that there
>> can be no second place complaint.
>>
>> On Tue, Nov 15, 2016 at 5:19 PM, Michael Ossipoff <email9648742 at gmail.com
>> > wrote:
>>
>>> When I started my current EM participation, I was saying that 3-Slot ICT
>>> was my favorite method.
>>>
>>> That doesn't conflict with saying that I consider Approval the best,
>>> because I regard 3-Slot ICT, or unlimited-rankings ICT (when used
>>> approval-like) as an Approval version without chicken-dilemma.
>>>
>>> Later I realized that MDDTR is better than ICT, because it gives better
>>> protection to middle candidates.
>>>
>>> I measure that protection by how well they'd be protected if they were
>>> CWs.  ...what it would take to protect their win, and how well it's
>>> protected.
>>>
>>> I define "middle candidates" as candidates you rank or rate below top
>>> and above bottom.
>>>
>>> ICT gives no protection to middle candidates, against burial, or even
>>> against innocent, non-strategic truncation--the two things that threaten a
>>> CWs in pairwise-c0unt methods.
>>>
>>> MDDTR gives full truncation-proofness to middle candidates, but
>>> (contrary to what I earlier believed), its protection of middle candidates
>>> against burial can only be called "shabby".
>>>
>>> By the way, I no longer think that ICT or MDDTR needs to be 3-slot.
>>> 3-Slot would be fine with me, because I believe that ICT or MDDTR should be
>>> used as Approval, and that middle rating or ranking should only be used
>>> when seriously needed to deter chicken-dilemma defection. When middle is
>>> used in an unlimited-ranking MDDTR or ICT, it should probably consist of
>>> 2nd-place ranking, if you want to give the demoted candidates the best
>>> protection.   ...but maybe you'd rather rank them with respect to
>>> eachother, at different middle levels, as I probably sometimes would.
>>>
>>> But, as I've been saying, activists & organizations seem to like
>>> rankings, and some people--overcompromisers & rival parties--might very
>>> well need rankings to soften their voting errors.
>>>
>>> And it seems to me that there's no particular reason not to rank, in
>>> order of preference, your middle candidates, if some of them are better
>>> than others, or if the voters of some of them are less trustworthy than
>>> others.
>>>
>>> So, that's if you want CD, in addition to FBC, and good protection for
>>> middle candidates
>>>
>>> Even if you're using the method as Approval, you still want your demoted
>>> candidate(s) to be well protected. Just because you don't trust hir voters
>>> doesn't mean you want to throw her to the hounds and thereby lower Pt, the
>>> probability of electing from your strong top-set.
>>>
>>> Anyway, so far, this is all referring to CD methods.
>>>
>>> Of those, I like MDDTR best. As a rank method, it (as i said) gives only
>>> shabby burial-protection to a middle candidate. But evidently (please tell
>>> me it isn't so) you can't have FBC, CD, and good protection of middle
>>> candidates.
>>>
>>> I consider CD more important to how well protected middle candidates
>>> are. Yes, FBC + CD give poor protection to middle candidates, and that
>>> lessens the value of their CD. But non-CD methods don't have CD at all, and
>>> that's worse.
>>>
>>> So I prefer MDDTR to methods that give better protection to middle
>>> candidates, but don't have CD.
>>>
>>> So, where I used to say that my favorite method is 3-Slot ICT, now I say
>>> that my favorite method is MDDTR. Preferably with unlimited rankings.
>>> (Though one could use only the 1st, 2nd, & bottom positions if one chose
>>> to).   ...regardable as a chicken-dilemma-free version of Approval.
>>>
>>> ------------------------------------------------------------------
>>>
>>> Non-CD methods with better "middle-strategy" than CD methods:
>>>
>>> But, in an election, I'm just one voter, and so, how well-suited the
>>> method is to me is less important, and won't affect the outcome as much, in
>>> comparison to how well-suited the method is to lots of progressives.
>>>
>>> So, what if most progressives would rather have a method that's really
>>> good as a rank method, a method that has good "middle strategy" (strategy
>>> for protecting a middle candidate's win if s/he's CWs).
>>>
>>> That would be important if you knew that all or nearly all, or even most
>>> of them were going to use the method purely as a rank method.
>>>
>>> Bucklin is the traditional FBC rankings-method.
>>>
>>> I distinguish 2 kinds of middle strategy merit:
>>>
>>> 1. How well the method protects top-ranked candidates against
>>> middle-ranked candidates. I call that "Middle1"
>>>
>>> 2. How well the lmethod  protects a middle-ranked candidate against any
>>> candidate you rank lower than hir. I call that "Middle2".
>>>
>>> So, how to get the best middle strategy, with the main goal still being
>>> keeping a good probability, Pt, of electing from your strong top-set?
>>>
>>> MDDTR's middle1 seems better than that of Bucklin. In MDDTR, you're
>>> voting to contribute to a majority for your top against your middle. In
>>> Bucklin, you can protect top against middle by skipping some rating-levels
>>> above the middle candidates. In that way, you can give the top candidates
>>> time to receive the coalescing lower-choice votes that they'll get from the
>>> preferrers of other candidates, before giving anything to the middle
>>> candidates.
>>>
>>> That's a bit more work than just ranking in order of preference. It
>>> requires you to judge where, and how far down in rankings, your top
>>> candidates are going to receive lower-choice votes from.
>>>
>>> So I suggest that MDDTR does better at Middle1 than Bucklin does.
>>>
>>> But Bucklin does better at Middle2.
>>>
>>> In Bucklin, the CWs's win is protected by the people who pretty-much
>>> agree with you, the people of your wing, merely not ranking down too far.
>>>
>>> MDDTR needs that too, but it isn't enough to give MDDTR more than shabby
>>> protection.
>>>
>>> ...And Bucklin's Middle1, though not as convenient or easy as that of
>>> MDDTR, isn't as questionable as MDDTR's Middle2.
>>>
>>> So, overall, I'd say that Bucklin's Middle Strategy is better than that
>>> of MDDTR. So, for people who want to use the method purely as a
>>> rank-method, Bucklin is better than MDDTR.
>>>
>>> Bucklin also has the advantage of use-precedent.  MDDT has the advantage
>>> of precinct-summability,but I don't consider that essential.
>>>
>>> For voters using the method purely as a rank method, I'd prefer Bucklin
>>> to MDDTR.
>>>
>>> Chicken dilemma won't happen all the time, probably won't happen often.
>>> But middle-protection will always matter to people using it as a rank
>>> method.
>>>
>>> But it seems to me that, once we give up CD (for voters who need good
>>> middle strategly, because of their rank voting), then it might be possible
>>> to do better than Bucklin.
>>>
>>> It seems to me that methods that use both Approval and pairwise-count
>>> can do better than Bucklin, at middle protection.
>>>
>>> A lot of methods of that kind have been proposed, and I've ignored all
>>> of them because they don't meet CD. But, as mentioned above, for some
>>> electorates, middle strategy could be more important.
>>>
>>> It seems to me that MDDA (also evidently named MPOA) and Smith//Approval
>>> are two methods that might be better than Bucklin at middle protection..
>>>
>>> Using Approval as the cycle-solution is a very powerful idea (if you're
>>> willing to give up CD, for an electorate's needs). But most of you already
>>> knew that, before I paid attention to it (...because I was only looking at
>>> CD methods)..
>>>
>>> MDDA's & Smith//Approval's burial vulnerability doesn't matter much,
>>> when the Approval winner wins the cycle. In fact, Smith//Approval's
>>> truncation-vulnerability could even be regarded as an advantage, for when
>>> your strong top-set doesn't include the CWs.
>>>
>>> MDDA & Smith//Approval look better to me than Bucklin.
>>>
>>> Simpler Middle1.
>>>
>>> Precinct-Summability is an added bonus.
>>>
>>> MDDA seems to have a briefer definition than either Bucklin or
>>> Smith//Approval, and brief definition can be decisive.
>>>
>>> I know of Bucklin being rejected when MDDTR was accepted. MDDA would
>>> almost surely have been accepted too.
>>>
>>> I don't  think Smith//Approval would go over well, with its need to
>>> define the Smith set, which greatly lengthens the definition.
>>>
>>> For an electorate that need good Middle1 & Middle2 more than CD, MDDA
>>> seems the winner so far.
>>>
>>> Smith//Approvsl of course meets Smith.  ...which of course means that it
>>> fails FBC. But does it need FBC?
>>>
>>> It could be argued (but I don't know if it's true) that Smith//Approval
>>> doesn't need FBC, because, though you don't have an efffective Approval
>>> vote at the top, you still can vote Approval, with the approval-cutoff, or
>>> by only ranking your strong top-set.
>>>
>>> So, though Compromise could become pair-beaten by Favorite because you
>>> raise Favorite to top with Compromise, resulting in a cycle instead of a
>>> CWv win for Favorite, the cycle will be judged by approvals, and you're
>>> approved only your strong top-set.
>>>
>>> Of course, just because Favorite was almost the CWv doesn't necessarily
>>> mean that s/he'll win the Approval count. But are you any worse off than
>>> you'd have been with MDDA?
>>>
>>> Forest (but maybe others too) has proposed a number of methods that
>>> combine pairwise-count and Approval. Do any of those beat MDDA &
>>> Smith//Approval by the standards of protecting one's strong top-set, and
>>> Middle1 & Middle2?
>>>
>>> in particular, do any of them do better than MDDA by those standards? Do
>>> any do as well as MDDA by those standards and have as brief a defintion, or
>>> nearly as brief a definition?
>>>
>>> In other words, are there methods that achieve those things better than
>>> MDDA & Smith//Approval, or achieve them better than MDDA and have as brief
>>> a definition?
>>>
>>> In fact, is there a method that meets FBC (or doesn't need it), meets
>>> CD, and does as well by Middle1 & Middle2 as MDDA, Smith//Approval or
>>> Bucklin?
>>>
>>> Michael Ossipoff
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>
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