[EM] MaxMinPA

[Michael Ossipoff]

It should be MMPO, rather than Smith//MMPO, for one finalist-choosing
method, and Approval, Inferred-Approval, or Score for the other, because
MMPO, Approval, & Score meet FBC.

If Plain MMPO were replaced by anything else, Weak CD would be lost.

If, for the other finalist-choosing method, Approval, Inferred-Approval or
Score were replaced by MAM or Beatpath, then both finalist-choosing methods
would share the same strategic vulnerabilities.

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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