[EM] MaxMinPA

[Michael Ossipoff]

When I said that the 2 Approval strategies give the same Approval ballot
with two candidates & with three candidates, under certain conditions, I
meant three or four, not two or three.

Obviously, with only two, there's no decision to be made.

Michael Ossipoff
On Oct 20, 2016 4:41 PM, "Forest Simmons" <fsimmons at pcc.edu> wrote:

> Skip half a page to ***
>
> On Thu, Oct 20, 2016 at 3:47 PM, Michael Ossipoff <email9648742 at gmail.com>
> wrote:
>
>> This is just a brief partial reply, addressing one topic.
>>
>> Approval strategy is more important & interesting than most people think,
>> including most who discuss voting system.
>>
>> ...partly because, as I said, improvements in Approval are largely, if
>> not entirely, illusory.
>>
>> So I'm interested in discussion of Approval strategy, & different views
>> of it.
>>
>> Let me make a few comments on the example:
>>
>> 1. None of those voters should  approve or give Score points to their
>> last choice (D).
>>
> ****But D is not truncated on any of the ballots, while A, B, and C are
> truncated.  I guess I should have put ">>" symbols to indicate truncation:
>
> 40 A=B>D(90%)>>C
> 35 B=C>D(90%)>>A
> 25 A=C>D(90%)>>B
>
> Also, if you consult the context of the example, you will see that just a
> slight movement of A, B, and C further from the center of the triangle (D)
> converts the preference profile to
>
> 40 D>A=B(90%)>>C
> 35 D>B=C(90%)>>A
> 25 D>A=C(90%)>>B
>
> which converts D from the Condorcet Loser to the CWs.
>
> Forest
>
>> 2. If they all vote as I suggest, and approve (only) their top-set, then
>> of course it's inevitable that the winner will be the candidate regarded as
>> top-set by the most voters. A social optimization achieved by people voting
>> purely strategically.
>>
>> Each voter is voting to maximize hir Pt, Probability of electing from hir
>> top-set.
>>
>> B wins then.
>>
>> 3. Based on the sincere preferences, there's no CWs, and so
>> CWs-protective strategy doesn't apply.
>>
>> Even if there were one, approving down to it, if it's in your bottom-set,
>> would be suboptimal, and un-tempting.
>>
>> If the CWs is in your top-set, then should you refuse to Approval anyone
>> you like less, &, in particular, should you plump if that CWs is your
>> favorite?
>>
>> No. As an individual strategy, it's best to approve your entire top-set,
>> to maximize Pt.
>>
>> ...even though you might be tempted to choose among your top-set.
>>
>> But, as a _group_ strategy, that might not be so. Say you aren't
>> majority-favored (MF), and maybe aren't in a mutual-majority (MM) at all.
>>
>> Then (I'm assuming a 1D political spectrum) the CWs isn't your favorite,
>> and hir voters prefer someone you like less than hir to those you like more
>> than hir.
>>
>> Say that the CWs is at the far edge of your top-set.
>>
>> You'd like hir voters to plump, just as you'd like other voters on your
>> side of hir to not approve past hir.
>>
>> But then you're asking them to vote  suboptimally, if your request
>> contradicts my top-set voting advice.
>>
>> But maybe it would be best, for the group (the voters on your side of the
>> CWs) as a whole, to have such an agreement.
>>
>> Besides, though individually suboptimal, if the CWs's voters plump, they
>> get something for it, because they're helping their   favorite against
>> their other top-set candidates.
>>
>> Suboptimal, but not without some potential reward.
>>
>> Part 2 will follow.
>>
>> 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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