[EM] MaxMinPA

[Michael Ossipoff]

An example is needed.
On Oct 18, 2016 9:37 PM, "C.Benham" <cbenham at adam.com.au> wrote:

> On 10/19/2016 8:10 AM, Michael Ossipoff wrote:
>
> 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.
>
>
> FBC won't survive any Push-over incentive  (as I'm sure Kevin Venzke would
> confirm).
>
> Chris Benham
>
> 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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