[EM] MaxMinPA

Michael Ossipoff email9648742 at gmail.com
Sun Oct 23 09:27:54 PDT 2016

My 1st comments on Forest's example were based on a misreading of it.

Let me quote the example, & comment:

Sincere 0 to 1 ratings:

40: A1, B1, D.9, C0
35: B1, C1, D.9, A0
25: A1, C1, D.9, B0

CWs: B

Sincere Score elects D.

Approval, when probabilistically voted to simulate sincere Score likewise
elects D (if the numbers of voters are .multiplied by a large number).

Approval, with the approval-cutoff at the candidates' merit midrange,
elects D. (I recommend that strategy when there isn't a top-set.)

Of course if voters approve (only) their top-set, then Approval will elect
the candidate who is in the most people's top-set.

D, rated .9 by everyone, is probably in their top-set, and wins if people
approve only their top-set.

Electing the candidate in the most people's top-set is a good social

Approval is the method in which a sincere vote is a good strategic vote.

So this example isn't a bad-example for Approval.

What about the CWs? In rank methods I emphasize the importance of being
able to elect the CWs without drastic strategy.

But, with rank methods, it's assumed that many people are ranking sincerely
(instead of equal top ranking) because they want to choose among their
top-set, and get the best candidate they can.

That doesn't apply if the main goal, the most important goal, is to elect
from your top-set.

Approval does right in the example.

In this example,   Bucklin easily elects the CWs. Given the different goal
in a rank method, that isn't a wrong result either.

If you're majority-favored (MF), then sincere ranking by you & your mutual
majority (MM) ensures electing from your top-set.

But if you aren't MF, then electing the CWs at least greatly improves the
probability of electing from your top-set, because the CWs is especially
likely to be in top-sets.

...hence the desirability of electing the CWs without drastic strategy in
rank methods.

Because the CWs is especially likely to be in top-sets, then it might be
desirable, in Bucklin & Approval, to have an agreement among similar
voters, to not approve or rank past the CWs.

So, though that's suboptimal for you as an individual, it might be socially
best for your group of similar voters.

If my top-set includes candidates whom we both like less than the CWs, but
yours doesn't, then you'd rather that I not approve or rank past the CWs.
...meaning that you'd rather that I plump if my candidate is the CWs

A bonus for me is that, thereby, I'm choosing among my top-set. Suboptimal
for me, but bringing that slight reward, for complying with that social

I emphasize that such an agreement is an extra, a possible optional group
refinement, and needn't be added to Approval or Bucklin strategy

As an individual, your best strategy in Approval or Bucklin is to approve
or rank (only) your entire top-set.

In Bucklin, you might want to rank them in sincere order, to choose among
them, if you're sure that you're majority-favored. Otherwise equal top-rank

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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