[EM] Condorcet-Kemeny clarifications
Richard, the VoteFair guy
electionmethods at votefair.org
Fri Oct 29 11:09:03 PDT 2021
On 10/27/2021 11:27 PM, Forest Simmons wrote:
> People are always oohing and awing about Kemeny-Young as a supposedly
> ideal Condorcet method ...
> ... (3) it does not take voter preference
> strengths into account (because the K-Y ballots do not register that
> kind of information)... not even as much as Ranked Pairs, because K-Y
> requires complete rankings ... no equal ranks ... no truncations, etc.
The Condorcet-Kemeny method does not require complete rankings. A voter
can mark multiple candidates at the same preference order, and the voter
can leave candidates unmarked. These conventions have been running on
the VoteFair survey service for a decade.
> (1) it is computationally intractable,
Actually it's easy, and fair in real elections (as opposed to software
test simulations), to quickly eliminate all but the top 12 candidates
and quickly do the calculations for the top 12. Or the top 6 if a
minute or two is too long to wait. The VoteFair service sets a limit of
6 choices as the default, but I increase the limit to 12 when that's needed.
> (2) it fails clone independence,
It has a nice balance between clone independence and independence of
irrelevant alternatives. "Fails" just means the failure rates are not zero.
Richard Fobes
The VoteFair guy
On 10/27/2021 11:27 PM, Forest Simmons wrote:
> Also ...
>
> The Approval Order is essential for finding the order of finish beyond
> first place ... first to last with the important Reverse Symmetry
> property that is lacking in most other methods.
>
> Approval gives voters the opportunity to get the candidates in roughly
> the right order by emphasizing the most important distinctions between
> acceptable and unacceptable ... then the pairwise adjustments applied to
> the adjacent pairs where the approval order is not as definite (where
> the approval margins are statistically less signicant) is a refinement,
> and insurance that the Burlington Vermont embarrassment of IRV is
> impossible under ASM. It would be technically possible to miss the CW
> without the pairwise sorting, but only barely ... quite unlikely ...
> even with a total lack of sophistication among voters.
>
> Therefore, as you say, the sorting is a redundant backup ... a safety
> net for the sincere Condorcet Candidate. It is redundant, but at no
> extra cost ... it's free like the symmetry compliant order of finish.
>
> People are always oohing and awing about Kemeny-Young as a supposedly
> ideal Condorcet method with Reverse Symmetry, but it cannot hold a
> candle to ASM because (1) it is computationally intractable, (2) it
> fails clone independence, and (3) it does not take voter preference
> strengths into account (because the K-Y ballots do not register that
> kind of information)... not even as much as Ranked Pairs, because K-Y
> requires complete rankings ... no equal ranks ... no truncations, etc.
> .... that allow other Condorcet methods to show a little bit of relative
> strength of preference ... though not as simply and directly as ASM.
>
> Supposedly KY is hard to manipulate because it is hard to compute, but
> that is a superstitution ... it does nothing to prevent crowding,
> burial, etc. The basic defenses against burial are not even available,
> as can be seen in the three candidate case ... are we supposed to
> believe that as the number of candidates increases that new burial
> defenses magically appear out of nowhere?
>
> FWS
>
>
>
>
> El mié., 27 de oct. de 2021 9:57 p. m., Forest Simmons
> <forest.simmons21 at gmail.com <mailto:forest.simmons21 at gmail.com>> escribió:
>
>
>
> El mié., 27 de oct. de 2021 9:19 p. m., Ted Stern
> <dodecatheon at gmail.com <mailto:dodecatheon at gmail.com>> escribió:
>
> Hi Forest,
>
> I've been thinking about the modified version of ASM. I think it
> should be called
> *P*referred-*A*cceptable-*I*nsufficient-*R*eject Sorted Margins,
> or PAIR-SM. I don't like movable demarcations, and I think more
> than 3 levels within each category would be excessive, so I
> would go with 10 total levels (score 0 to 9, rank inferred from
> rating): scores 9, 8, 7 are Preferred, scores 6, 5, 4 are
> Acceptable, scores 3, 2, 1 are Insufficient (formerly
> "compromise": the voter finds candidates at this level
> distasteful, but better than the alternative) and score 0 is reject.
>
>
> And blank is counted as zero, too.
>
>
> Preferred ratings get 10 points, Acceptable ratings get 5
> points, Insufficient candidates get 0 points but have pairwise
> votes over lower rated Insufficient candidates and all Rejected
> candidates. Then Sorted margins is run using those points.
>
> PAIR-SM could also be run with only 2 levels within each of the
> approved categories, for a total of 7 levels, if you want to
> retain an odd number of ratings.
>
>
> Small scale elections could get by with seven levels, but rigid
> demarcations work better with ten imho.
>
>
> The one problem I've had on the EndFPTP subreddit is explaining
> how the ranking is more important than approval. While the
> Approval level is in fact what sets up the seed ordering, it is
> practically irrelevant unless there is a Condorcet cycle. It's a
> little hard to explain that the Approval rating is more of an
> insurance that it won't be needed.
>
> On Wed, Oct 27, 2021 at 6:31 PM Forest Simmons
> <forest.simmons21 at gmail.com <mailto:forest.simmons21 at gmail.com>>
> wrote:
>
> I prefer Ted Stern's version of Approval Sorted Margins over
> any other single-winner public proposal I've seen lately,
> other than simple asset voting as proposed by Charles
> Dodgson in the 19th century, and more recently a symmetrical
> version of Majority Judgment currently in the works if it
> can be simplified adequately w/o sacrificing its integrity.
>
> Ted's version of ASM uses a version of what we used to call
> "3-slot approval" to seed the finish order which is then
> sorted pairwise with pairs that show the least discrepancy
> in their 3-slot scores getting priority for pairwise
> rectification. It is important to note that the ordinal
> information is inferred from six slots, twice as many as
> those used for the cardinal seeding.
>
> This is valuable for several (including psychological)
> reasons. One is that 3-slots are not enough for the ordinal
> information to fully distinguish the pairwise preferences
> important to the voters. But increasing the score slots (as
> in STAR) is not the answer, for several reasons ... STAR
> voters aware of optimal approval strategy (vote only at the
> extremes) would feel too much tension between the need to
> make use of the intermediate score levels for ordinal
> information and the need to avoid those levels for optimal
> cardinal strategy.
>
> But for non-perfect information elections, even
> sophisticated approval voters might welcome a middle slot.
>
> I like three slots because, personally I would reserve the
> top and bottom slots for definite approvals and disapproval,
> respectively. [Bottom also takes care of blank or no
> opinion to obviate darkhorse candidates].
>
> How do you know if you "definitely" approve or disapprove of
> a candidate?
>
> Easy ... if you don't know that you do, then you don't. If
> you are not sure, or if you have to ask, then your approval
> or disapproval is definitely not definite.
>
> So it's easy to know how to vote honestly under that rule,
> which should be part of the instructions to the voters.
>
> People who think they can out wit the devil may be tempted
> to vote dishonestly, but at least they have the option of
> voting honestly if those "definite instructions" are the
> official instructions.
>
> So Ted Stern's version of ASM is one of the best possible
> public proposals IMHO.
>
> However personally, I would rather have it implemented in
> the format of a Ranked Ranking ballot, so that the voter has
> more freedom in defining the cutoffs demarcating the three
> slots, and making more ordinal distinctions within the three
> approval levels if needed to distinguish among clones in a
> large election:
>
> A>B1>B2>C>>U>V>W1>W2>W3>>X>Y>Z...
>
> BORDA is quoted as saying that his method was only intended
> for "honest men." But honestly would not fix the greater
> design flaw ... clone dependence ... in particular, clone
> loser. Cardinal Ratings is a partial solution ... with all
> of the caveats expressed in Kristofer's reservations.
>
> A solution nearer to the spirit of Borda would be a point
> system based on Ranked Rankings.
>
> Borda can be thought of as a way of converting rankings into
> a score/point system ... sacrificing clone dependence.
>
> A minimal tweak of Borda (to restore clone independence)
> would be to base a point system on Ranked Rankings ... with
> weaker rankings reflected in smaller point/score gaps.
>
> This idea is not my favorite way of using Ranked Rankings
> ... but it may help some people to see the value of a
> different kind of ordinal ballot ... more expressive than
> ordinary rankings without the strategic and psychological
> burden (including cognitive dissonance) of the (obviously
> exaggerated) implied numerical precision of ratings.
>
> El mar., 26 de oct. de 2021 8:26 a. m., Kristofer
> Munsterhjelm <km_elmet at t-online.de
> <mailto:km_elmet at t-online.de>> escribió:
>
> On 10/25/21 2:35 AM, fdpk69p6uq at snkmail.com
> <mailto:fdpk69p6uq at snkmail.com> wrote:
> > Why does their identity matter? Discuss the facts,
> not ad hominems.
> >
> > Also, I'm surprised and a bit saddened that you
> haven't come around to
> > cardinal systems yet. :/
> >
> > The goal of democracy is to elect the candidate who
> best represents the
> > will of the voters. My near-indifference between two
> candidates
> > shouldn't arbitrarily be given the same weight as your
> strong preference
> > between them.
>
> Let me make a ranked voting advocate (ordinalist?)
> argument here. I'll
> be referring to "simple cardinal methods", by which I
> mean things like
> Range, and not so much things that I'm fumbling towards
> in my utility posts.
>
> Cardinal supporters tend to use two arguments to argue
> for the
> superiority of cardinal methods over ordinal ones.
>
> The first is that cardinal methods support strength of
> preference; and
> the second is that, because they pass FBC (and IIA),
> they inherently are
> more robust to strategy.
>
> My response to these are, much abbreviated, that first,
> the "strength of
> preference" that these methods gather is probably
> ambiguous, and if it
> weren't, it would come with significant disadvantages.
>
> And second, that the methods' IIA and FBC compliance
> take a form that
> shoves what used to be tactical voting into a mush
> that's kind of
> honest, kind of not; and that once that's made clear,
> it's obvious that
> the methods no longer achieve the impossible. But
> because it doesn't
> look like ranked voting strategy, cardinal advocates can
> shift between a
> position that the methods permit everybody to vote
> "honestly" (an easy
> position) and that the methods are strategy-proof (a
> hard, incorrect
> position).
>
> -
>
> So for the first point, let's use Range as the standard
> cardinal method.
> Range asks for a set of ratings that are intended to
> represent utility,
> so that your rating is proportional to the utility you
> achieve from
> seeing this candidate elected. That's what's being
> demonstrated in
> examples like the pizza election: that the meat eaters
> show that their
> utility from getting mushroom pizza is not that far off
> from the utility
> of getting pepperoni, so that the method elects the
> pizza that satisfies
> all.
>
> But here's a problem. I can't know that my scale is
> calibrated the same
> way as yours. In philosophy, this is known as the
> problem of
> incommensurability. Suppose I happen to feel more
> pleasure (and pain)
> than you, but due to growing up in the same society as
> you, I mistakenly
> appear to use the same scale as you. It's then quite
> hard to know that
> when I say 6/10 I mean what you would consider twice as
> good as that.
>
> At first it would seem, though, that Range has dodged a
> bullet. Because
> if utility were directly comparable on an absolute
> scale, then there
> might exist "pleasure wizards"[1] who obtain so much
> utility from a
> choice that they effectively become dictators. By
> insisting on a 0-1
> scale (in its continuous version), Range limits the
> power any one voter
> has and so enforces a weak type of one man, one vote. It
> is what I
> called a type three method - voters might voluntarily
> decide to forego
> some of their power to make the outcome better for
> others (again, as in
> the pizza election).
>
> But the problem with this is that Range supposes that
> there's a common
> scale where there isn't. As a consequence, the concept
> of just what is a
> honest vote becomes blurred. E.g. suppose that I
> consider the sure
> election of Y to be equally good as a 50-50 shot of
> either X or Z
> winning. Do I rate X 1, Y 0.5, and Z 0? Or do I rate X
> 0.5, Y 0.25, and
> Z 0? Because there's no way to answer that question
> (unless it somehow
> becomes possible to get at utility information), there's
> more than one
> honest vote, and a honest voter is faced with the burden
> of having to
> decide *which one*. (It is assumed that voters will
> answer the question
> by normalizing[2], but this leads to strategy problems
> which I'll get to.)
>
> My attempts to generalize STAR came from asking "what if
> we want to be
> truly honest about what information it makes sense to
> ask of voters,
> while respecting OMOV?". Well, we could ask the voters
> about preferences
> over lotteries (as the 50-50 vs certainty example
> above). Doing so, the
> method acknowledges the ambiguity of comparing utility.
> Perhaps there's
> more we can do - e.g. by following MJ's reasoning of a
> common standard,
> or by separating "worse than nothing happening" events
> from "better than
> nothing happening" ones.
>
> But all of this is better than just saying "it means
> what you want it to
> mean", and then sweeping the resulting ambiguity in
> honest voters under
> the carpet.
>
> -
>
> As for the point that e.g. Range is superior to ordinal
> methods because
> Range passes IIA and the ordinal ones don't, I always
> feel like that's a
> bit of a sleight of hand. To explain, let's divide the
> ballot types into
> three:
>
> 1. The highest information honest ballot (ranking
> candidates in order of
> preference, reporting relative utility values in Range).
>
> 2. Other honest ballots: some monotone transformation of
> this.
>
> 3. Tactical/dishonest ballots (order reversal).
>
> Ranked methods have a very obvious category one, and
> going for some
> category two ballot instead (e.g. equal rank or
> truncation) doesn't
> usually produce much harm. Cardinal methods like Range
> replaces most of
> category three with category two because they pass FBC
> and IIA.
>
> As I've argued above, there's not really a category one
> for Range
> because it asks for more than the voter can provide. And
> we know from
> Gibbard's theorem that no deterministic voting method
> (cardinal or
> ordinal) is entirely free of strategy. So both
> categories one and three
> collapse into category two in Range: the former because
> there's no one
> honest ballot, and the latter because order-reversal
> isn't necessary
> (the famous FBC compliance, but it's actually stronger
> than just FBC).
>
> So, in ranked voting methods, voting strategy consists
> of choosing an
> appropriate category three ballot. In methods like
> Range, it consists of
> choosing an appropriate category two ballot.
>
> But here's the problem: having a clearly defined
> category one and a
> narrow category two means that a voter who values
> honesty *as such* can
> just choose the one honest ballot and then go home
> without regrets. But
> in Range, because "every ballot is honest", he has to
> carefully
> deliberate *which* honest vote to choose. And if he
> chooses wrong (e.g.
> in a Burr dilemma), he'll sure come to regret it.
>
> That kind of peril should only exist, IMHO, for voters
> who decide to
> play rough by choosing a category three ballot.
>
> And thus the sleight of hand: in a ranked method,
> "honest" means more or
> less category one[3]. So cardinal voting proponents can
> say "oh, but our
> category three is empty because of FBC!", but all
> they're really doing
> is shifting the Gibbard-mandated instrumental voting
> from category three
> over to category two. This lets them say "you can just
> vote honestly",
> thus giving the impression there's no risk in Range. But
> it's actually
> the other way around: it's not only determined strategic
> voters who may
> regret the strategy they chose, but also honest voters
> who just want to
> vote honestly and go home.
>
> This also poisons the value of IIA. If IIA is to be
> practically
> meaningful, it must mean that the outcome doesn't change
> when a
> candidate who didn't win drops out. But if every voter
> is deliberating
> which type-two ballot to go for, the ballots may change
> even if the
> sentiment doesn't.
>
> In other words: if enough voters normalize in Approval,
> then Approval's
> IIA compliance isn't worth much at all in practice. E.g.
> first round
> ballots:
>
> 25: A>B>>C
> 40: B>C>>A
> 35: C>A>>B
>
> The Approval winner is C.
>
> But now let A drop out, and the voters renormalize (as
> Warren suggests
> everybody would):
>
> 25: B>>C
> 40: B>>C
> 35: C>>B
>
> and then B wins, so even though Approval passes IIA de
> jure, it looks
> rather different de facto. Telling the voters to perform
> a particular
> algorithm on their ballots before submitting them, and
> then claiming the
> inputs to the method satisfies IIA, doesn't mean the
> method plus the
> manual algorithm passes IIA!
>
>
> So the problem, in summing up, is that there's too much
> vagueness to
> hide subtleties in. Cardinal methods measure utility
> (but they don't, so
> what do they measure?). Cardinal methods let you vote
> honestly (but
> honest doesn't mean the same thing anymore). Cardinal
> methods pass IIA
> and FBC (but it does them much less good than ranked
> methods). Bayesian
> regret evaluations show Range as superior to ranked
> methods (but
> questionable assumptions about voter strategy may
> invalidate the results).
>
> It's better to be honest about the limitations that
> exist. If we can
> only get lottery information, then the method should
> reflect that. If we
> can get more, then the method should show how we can get
> it. That way,
> there won't be anything up its sleeve.
>
> -km
>
> [1]
> https://www.oxfordhandbooks.com/view/10.1093/oxfordhb/9780195189254.001.0001/oxfordhb-9780195189254-e-020
>
> or, if you're more in a funny mood,
> https://www.smbc-comics.com/comic/2012-04-03 :-)
>
> [2] E.g. Warren Smith says voters will do so because
> they're not
> "strategic idiots", and that voters who don't normalize
> in a
> two-candidate election are simply "idiots".
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2006-December/084357.html
>
> and
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2007-January/084662.html
>
> respectively.
>
> [3] There's a caveat here because equal-rank/truncation
> seem to be in
> category two, and so a response to this reasoning would
> be "ranked
> ballots have category two too!". But there's very little
> regret in
> choosing category one instead of two, in practice.
> However, some ranked
> methods that pass FBC do so by making equal-rank
> stronger than strict
> ranking, and those reintroduce the problem.
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