[EM] ASM Decisions

[Forest Simmons]

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> escribió:

>
>
> El mié., 27 de oct. de 2021 9:19 p. m., Ted Stern <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> 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> escribió:
>>>
>>>> On 10/25/21 2:35 AM, 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.
>>>> ----
>>>> Election-Methods mailing list - see https://electorama.com/em for list
>>>> info
>>>>
>>> ----
>>> Election-Methods mailing list - see https://electorama.com/em for list
>>> info
>>>
>>
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