[EM] MaxMinPA

Michael Ossipoff email9648742 at gmail.com
Thu Oct 20 15:50:42 PDT 2016


I meant to say:

Improvements over Approval are largely, if not entirely, illusory.

Michael Ossipoff
On Oct 20, 2016 12:52 PM, "Forest Simmons" <fsimmons at pcc.edu> wrote:

> Very kind of you to suggest "Simmons" for this method, and I certainly
> don't mind associating my name with it, although every idea in it owes much
> to input from you all, especially Chris Benham, Michael Ossipoff, Kevin
> Venzke, Kristofer M, Jameson Q, Andy Jennings, Jobst Heitzig, Joe
> Weinstein, Craig Layton,Warren Smith, Toby Pereira, Rob LeGrand, Rob
> Lanphier, Richard Moore, Bart Ingles, Rick Denman. Steven J Brams, Steve
> Eppley, Francis Edward Su, Sylvia Owl, Adam Tarr, Alex Small, Stephane
> Rouillon, Craig Carey, Dave Ketchum, Douglas Greene, Blake Cretney, James
> Gilmour, Jan Kok, Josh Narins, Steve Barney, Joseph Malkevitch, Olli Salmi,
> Gervase Lam, Elisabeth Varin, Mike Rouse, Donald E Davison, Markus Schulze,
> Martin Harper, DEMOREP1, Buddha Buck,  David Catchpole, Anthony Simmons, James
> Green-Armytage, Kathy Dopp, Juho Laatu, and too many more to mention.
> If it turns out to have a serious Achilles heel, I will disavow the whole
> thing!
> When Approval doesn't elect the CWs, there are several possible excuses,
> among them ...
> (1) lack of information
> (2) too much disinformation
> (3) poor approval strategy by the CW supporters
> (4) sincere reflection of the intensity of support
> To elaborate on (4),  if the preference profile is
> 40 A=B>D(90%)
> 35 B=C>D(90%)
> 25 A=C>D(90%)
> then D is the sincere Range winner, as well as the Sincere Approval
> winner, but is the Condorcet Loser.
> I have constructed an example that yields this profile based on three
> neighborhoods whose centers form an equilateral triangle, and four proposed
> sites for a deep well (into a pure aquifer far below the contaminated
> surface water)
> Site D is the center of the triangle.  The other three sites (A, B, and C)
> are exterior to the triangle on the perpendicular bisectors of the segments
> connecting the neighborhood centers, but not quite as far from the
> midpoints of those segments as the center of the triangle.
> As for "sincere approval, " I have described it elsewhere.  Basically, for
> a score ballot divide the total score of the candidates on that ballot by
> the max possible score. Take the integer part and approve that many
> candidates.  The fractional part left over determines the probability of
> approving the next candidate in line.  A spin of a spinner can make that
> decision.
> Or in the above case, community spirit can make the difference..
> In this case Sincere Approval and Range give the same expected results:
> D(90), A(65), B(75), and C(60)
> In conclusion, I don't think we need to be embarrassed if Simmons doesn't
> choose the CWs revealed by the second (sincere) set of ballots, especially
> if the ballots in the second set are merely ranked preference ballots,
> which are perfectly adequate for their purpose.
> Thanks,
> Forest
> On Wed, Oct 19, 2016 at 2:24 PM, Michael Ossipoff <email9648742 at gmail.com>
> wrote:
>> Yes, saying that everyone ranked is approved would unnecessarily inhibit
>> people's MMPO rankings, as would a Score-count.
>> So an approval-cutoff inferred at the candidates rating-midrange would be
>> better. ...in the ratings from whose order the MMPO rankings are Inferred.
>> ...or an explicitly-voted  approval-cutoff in a ranked MMPO ballot.  If
>> course it comes to the same thing, just different ballot-implementation.
>> If I'd introduced this best-appearing method, I'd want it named after me.
>> Beatpath is named after Markus. So: Simmons' method, in its various
>> variations.
>> ...which, anyway, is lot less cumbersome than something like
>> MMPO/Approval-like Fnalist-Choice.
>> That is relevant because, when discussing something, it helps to have a
>> name by which to refer to it.
>> It avoids chicken dilemma, because, even if the A voters give an approval
>> to B, and B wins the Approval count, A (the MMPO winner) pairwise-beats B,
>> and so A wins & the defection fails.
>> Truncation of the CWs doesn't take away hir win in MMPO. Even if the
>> truncators' candidate wins the approval count, the CWs pairwise-beats hir,
>> & wins the runoff.
>> Burial of the CWs?:
>> Here, MMPO & wv need the CWs's voters to plump, or at least not rank the
>> buriers' candidate over the candidate insincerely ranked over hir.
>> So, too, Approval, Score & Bucklin need that plumping. It seems a
>> universal requirement.
>> So Simmons doesn't escape that requirement.
>> But, when done, that defensive plumping protects the CWs's win, in both
>> finalist-choosing counts.
>> ...And, if the burial is deterred,  as it often or usually will be in
>> MMPO,  but the plumping isn't actually done,   then the CWs still wins in
>> MMPO.
>> Even if the truncators' candidates wins in the Approval-like method, the
>> CWs pairbeats hir, & wins the runoff.
>> So Simmons has wv strategy.
>> But that means it also has the possibility of the perpetual burial
>> fiasco, which goes with it.
>> But that possibility doesn't keep wv from being one of the most popular
>> classes of methods.
>> Simmons, though using MMPO, doesn't have Kevin's MMPO bad-example:
>> C doesn't win in any Approval-like method. They give an A & B tie. A & B
>> pairbeat C, and would therefore win the runoff.
>> Michael Ossipoff
>> On Oct 18, 2016 1:42 PM, "Forest Simmons" <fsimmons at pcc.edu> wrote:
>>> I appreciate all of the great insights from Kristofer, Chris Benham, and
>>> Michael Ossipoff.
>>> Especially thanks to Kristofer for being a good sport about my
>>> forwarding an email with his private earlier input included.  It was too
>>> late when I realized I hadn't deleted that part.
>>> Intuitively, I think Chris is right that Pushover is the biggest
>>> potential problem.  But I don't see an obvious example.
>>> Michael is right that we need to consider other possibilities for the
>>> two base methods for picking the finalists.
>>> I like MMPO or Smith//MMPO as one of them since MMPO is one method that
>>> doesn't just reduce to Approval when all candidates are ranked or rated at
>>> the extremes.  I think that the other method should be one that does reduce
>>> to Approval at the extremes, like River, MAM/RankedPairs, or
>>> Beatpath/Tideman/Schulz.  It could be a Bucklin variant like MJ, Andy
>>> Jennings's Chiastic Approval, or Jameson's MAS.
>>>  Like Michael I think that Range itself gives too much incentive to vote
>>> at the extremes on the strategic ballots.  Better to use Approval or an
>>> approval variant so that the strategic ratings are not unduly compressed
>>> for the other base method.
>>> I like Kristofer's insights about the subtle differences between the
>>> proposed "manual" version in contradistinction to a DSV version that
>>> automates strategy for the two methods based on the first set of (perhaps
>>> somewhat pre-strategized) ratings.
>>> In particular he pointed out how certain procedural rules can
>>> externalize the paradoxes of voting.  To a certain extent Approval avoids
>>> bad properties by externalizing them.  The cost is the "burden" of the
>>> voter deciding whom to approve.  As Ron LeGrand has so amply demonstrated,
>>> any time you try to automate approval strategy in a semi-optimal way, you
>>> end up with a non-monotone method.  By the same token IRV can be thought of
>>> as a rudimentary DSV approach to plurality voting, so it should be no
>>> surprise that IRV/STV is non-monotone.
>>> A better example, closer to the Kristofer's, idea is Asset Voting.  It
>>> externalizes everything, which makes it impossible to contradict any nice
>>> ballot based property.  Because of this there is an extreme resulting
>>> strategic burden, but in this case that burden is placed squarely onto the
>>> shoulders of the candidates, not the voters. Presumably the candidates are
>>> up to that kind of burden since they are, after all, politicians (in our
>>> contemplated public applications).
>>> But this brings up another intriguing idea.  Let one of the two base
>>> methods be Asset Voting, so that the sincere ballots decide between (say)
>>> the MMPO winner and the Asset Voting winner.
>>> Thanks Again,
>>> Forest
>>> On Tue, Oct 18, 2016 at 12:32 PM, Michael Ossipoff <
>>> email9648742 at gmail.com> wrote:
>>>> If course the balloting for choosing between the 2 finalists need only
>>>> be rankings, to show preferences between the 2 finalists, whoever they turn
>>>> out to be.
>>>> Some variations occurred to me. I'm not saying that any of them would
>>>> be better. I just wanted to mention them, without any implication that they
>>>> haven't already occurred to everyone.
>>>> Both of the following possibilities have disadvantages, in comparison
>>>> to the initial proposal:
>>>> 1. What if, for the initial 2 counts, it were a Score-count, in
>>>> addition to the MMPO count.
>>>> One argument against that variation is that a voter's inferred
>>>> approvals are likely to be more optimal for hir than the Score ratings on
>>>> which they're based.
>>>> 2. For the 2 initial counts, what if the MMPO count used a separate
>>>> ranking, & the Approval count used a separate set of Approval-marks?
>>>> Would that make it easier for Chris's pushover strategist?
>>>> What other positive & negative results?
>>>> One possible disadvantage that occurs to me is that overcompromising
>>>> voters might approve lower than than necessary, if the approval were
>>>> explicitly voted.  ...in comparison to their ratings-which tend to soften
>>>> voting errors.
>>>> So far, it appears that the initial proposal is probably the best one.
>>>> Michael Ossipoff
>>>> On Oct 17, 2016 1:49 PM, "Forest Simmons" <fsimmons at pcc.edu> wrote:
>>>>> Kristofer,
>>>>> Perhaps the way out is to invite two ballots from each voter. The
>>>>> first set of ballots is used to narrow down to two alternatives.  It is
>>>>> expected that these ballots will be voted with all possible manipulative
>>>>> strategy ... chicken defection, pushover, burial, etc.
>>>>> The second set is used only to decide between the two alternatives
>>>>> served up by the first set.
>>>>> A voter who doesn't like strategic burden need not contribute to the
>>>>> first set, or could submit the same ballot to both sets.
>>>>> If both ballots were Olympic Score style, with scores ranging from
>>>>> blank (=0) to 10, there would be enough resolution for all practical
>>>>> purposes.  Approval voters could simply specify their approvals with 10 and
>>>>> leave the other candidates' scores blank.
>>>>> There should be no consistency requirement between the two ballots.
>>>>> They should be put in separate boxes and counted separately.  Only that
>>>>> policy can guarantee the sincerity of the ballots in the second set.
>>>>> In this regard it is important to realize that optimal perfect
>>>>> information approval strategy may require you to approve out of order, i.e.
>>>>> approve X and not Y even if you sincerely rate Y higher than X.  [We're
>>>>> talking about optimal in the sense of maximizing your expectation, meaning
>>>>> the expectation of your sincere ratings ballot, (your contribution to the
>>>>> second set).]
>>>>> Nobody expects sincerity on the first set of ballots.  If some of them
>>>>> are sincere, no harm done, as long as the methods for choosing the two
>>>>> finalists are reasonable.
>>>>> On the other hand, no rational voter would vote insincerely on hir
>>>>> contribution to the second set.  The social scientist has a near perfect
>>>>> window into the sincere preferences of the voters.
>>>>> Suppose the respective finalists are chosen by IRV and Implicit
>>>>> Approval, respectively, applied to the first set of ballots.  People's eyes
>>>>> would be opened when they saw how often the Approval Winner was sincerely
>>>>> preferred over the IRV winner.
>>>>> Currently my first choice of methods for choosing the respective
>>>>> finalists would be MMPO for one of them and Approval for the other, with
>>>>> the approval cutoff at midrange (so scores of six through ten represent
>>>>> approval).
>>>>> Consider the strategical ballot set profile conforming to
>>>>> 40  C
>>>>> 32  A>B
>>>>> 28  B
>>>>> The MMPO finalist would be A, and the likely Approval finalist would
>>>>> be B, unless too many B ratings were below midrange.
>>>>> If the sincere ballots were
>>>>> 40 C
>>>>> 32 A>B
>>>>> 28 B>A
>>>>> then the runoff winner determined by the second set of ballots would
>>>>> be A, the CWs.  The chicken defection was to no avail.  Note that even
>>>>> though this violates Plurality on the first set of ballots, it does not on
>>>>> the sincere set.
>>>>> On the other hand, if the sincere set conformed to
>>>>> 40 C>B
>>>>> 32 A>B
>>>>> 28 B>C
>>>>> then the runoff winner would be B, the CWs, and the C faction attempt
>>>>> to win by truncation of B would have no effect.  A burial of B by the C
>>>>> faction would be no more rewarding than their truncation of B.
>>>>> So this idea seems to take care of the tension between methods that
>>>>> are immune to burial and methods that are immune to chicken defection.
>>>>> Furthermore, the plurality problem of MMPO evaporates.  Even if all of
>>>>> the voters vote approval style in either or both sets of ballots, the
>>>>> Plurality problem will automatically evaporate; on approval style ballots
>>>>> the Approval winner pairwise beats all other candidates, including the MMPO
>>>>> candidate (if different from the approval winner).
>>>>> What do you think?
>>>>> Forest
>>>>> On Sun, Oct 16, 2016 at 1:30 AM, Kristofer Munsterhjelm <
>>>>> km_elmet at t-online.de> wrote:
>>>>>> On 10/15/2016 11:56 PM, Forest Simmons wrote:
>>>>>> > Thanks, Kristofer; it seems to be a folk theorem waiting for
>>>>>> formalization.
>>>>>> >
>>>>>> > That reminds me that someone once pointed out that almost all of the
>>>>>> > methods favored by EM list enthusiasts reduce to Approval when only
>>>>>> top
>>>>>> > and bottom votes are used, in particular when Condorcet methods
>>>>>> allow
>>>>>> > equal top and multiple truncation votes they fall into this category
>>>>>> > because the Approval Winner is the pairwise winner for approval
>>>>>> style
>>>>>> > ballots.
>>>>>> >
>>>>>> > Everything else (besides approval strategy) that we do seems to be
>>>>>> an
>>>>>> > effort to lift the strategical burden from the voter.  We would
>>>>>> like to
>>>>>> > remove that burden in all cases, but at least in the zero info case.
>>>>>> > Yet that simple goal is somewhat elusive as well.
>>>>>> Suppose we have a proof for such a theorem. Then you could have a
>>>>>> gradient argument going like this:
>>>>>> - If you're never harmed by ranking Approval style, then you should
>>>>>> do so.
>>>>>> - But figuring out the correct threshold to use is tough (strategic
>>>>>> burden)
>>>>>> - So you may err, which leads to a problem. And even if you don't, if
>>>>>> the voters feel they have to burden their minds, that's a bad thing.
>>>>>> Here, traditional game theory would probably pick some kind of mixed
>>>>>> strategy, where you "exaggerate" (Approval-ize) only to the extent
>>>>>> that
>>>>>> you benefit even when taking your errors into account. But such an
>>>>>> equilibrium is unrealistic (we'd have to find out why, but probably
>>>>>> because it would in the worst case require everybody to know about
>>>>>> everybody else's level of bounded rationality).
>>>>>> And if the erring causes sufficiently bad results, we're left with two
>>>>>> possibilities:
>>>>>> - Either suppose that the method is sufficiently robust that most
>>>>>> voters
>>>>>> won't use Approval strategy (e.g. the pro-MJ argument that Approval
>>>>>> strategy only is a benefit if enough people use it, so most people
>>>>>> won't, so we'll have a correlated equilibrium of sorts)
>>>>>> - That any admissible method must have a "bump in the road" on the way
>>>>>> from a honest vote to an Approval vote, where moving closer to
>>>>>> Approval-style harms the voter. Then a game-theoretical voter only
>>>>>> votes
>>>>>> Approval style if he can coordinate with enough other voters to pass
>>>>>> the
>>>>>> bump, which again is unrealistic.
>>>>>> But solution #2 will probably destroy quite a few nice properties
>>>>>> (like
>>>>>> monotonicity + FBC; if the proof is by contradiction, then we'd know
>>>>>> some property combinations we'd have to violate). So we can't have it
>>>>>> all.
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