[EM] Trying to have CD, protect strong top-set, and protect middle candidates too (C.Benham)
Forest Simmons
fsimmons at pcc.edu
Thu Nov 17 12:21:30 PST 2016
I agree with all of your comments, but my new definition of Most Approved
Immune overcomes our common objection to the old definition (it sounds baad
to start from the bottom).
And I like your new Score based method of gradual collapse of pairwise
preferences in order of increasing magnitudes of score differences.
It reminds me of one of our dyadic approval variants where we removed rank
relations in order of increasing strength, i.e. first all single chevron
relations >, then all doubles >>, then all triples >>>, etc. until only the
strongest relation remained >>>...>>> (if necessary). The dyadic condition
was that these relations could be encoded with scores in binary so that the
successive collapses could be accomplished by erasing least significant
binary digits.
I wonder if there is any chance that it satisfies the FBC.
> Date: Fri, 18 Nov 2016 00:35:24 +1030
> From: "C.Benham" <cbenham at adam.com.au>
> To: Forest Simmons <fsimmons at pcc.edu>, Michael Ossipoff
> <email9648742 at gmail.com>
> Cc: EM <election-methods at lists.electorama.com>
> Subject: Re: [EM] Trying to have CD, protect strong top-set, and
> protect middle candidates too
> Message-ID: <09ddf69f-495a-5f7c-42ac-24063d2e570c at adam.com.au>
> Content-Type: text/plain; charset="utf-8"; Format="flowed"
>
> On 11/17/2016 9:00 AM, Forest Simmons 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.
>
> Forest,
>
> I like Smith//Approval and your usually equivalent Max Covered Approval
> method.
>
> But in this version, the stipulation that we "switch places of the two
> /lowest/ out of order adjacent members" could look a bit arbitrary and
> less smooth
> than Margins-Sorted Approval.
>
> BTW, it seems to me that both this and Smith//Approval can handle the
> Chicken Dilemma situation quite well if we use ranked ballots with
> approval cut-offs.
>
> (Or ratings ballots with many slots that register approval and as many
> (or maybe as few as only 2) that register unapproval.)
>
> http://wiki.electorama.com/wiki/Approval_Sorted_Margins
>
> http://wiki.electorama.com/wiki/Approval_Cutoff
>
> And here's another smooth Condorcet method that should do as well:
>
> *Voters score the candidates on some scale that allows large and varied
> gaps between the candidates: say 0-100.
> Elect the CW if there is one.
>
> Otherwise compress the 1-point gaps (if any) on all ballots into
> zero-point gaps (so that those ballots abandon their original pairwise
> preference for any
> X originally scored only one point more than any Y).
>
> Based on the thus modified ballot information, elect the CW if there is
> one.
>
> Otherwise compress the 2-point gaps (if any) on all ballots into
> zero-point gaps (so that those ballots abandon their original pairwise
> preference for any
> X originally scored two points more than any Y).
>
> Based on the thus modified ballot information, elect the CW if there is
> one.
>
> And so on, as gradually as possible compressing larger and larger gaps
> until we have a pairwise beats-all winner.*
>
> Chris Benham
>
>
> On 11/17/2016 9:00 AM, Forest Simmons 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 <mailto: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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