# [EM] MaxMinPA

Forest Simmons fsimmons at pcc.edu
Thu Oct 20 16:41:01 PDT 2016

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On Thu, Oct 20, 2016 at 3:47 PM, Michael Ossipoff <email9648742 at gmail.com>
wrote:

>
> 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
>
> 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
>>>>>>> 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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