[EM] MaxMinPA

[Michael Ossipoff]

I forgot to mention:

Bucklin would be another good possibility for the other finalist-choosing
method, for use along with MMPO.

Bucklin's strategy has more in common with Approval than with the
pairwise-count methods.

Michael Ossipoff
On Oct 18, 2016 5:11 PM, "Forest Simmons" <fsimmons at pcc.edu> wrote:

> The reason I thought of restricting one of the methods to Smith was to
> increase the likelihood that at least one of the finalists came from
> sincere Smith, i.e. to make it unlikely that the sincere ballots reveal a
> CWs which is not one of the finalists, easy to explain to the experts, but
> hard to explain to the lay person.
>
> Do you see a way to do this?
>
> On Tue, Oct 18, 2016 at 2:40 PM, Michael Ossipoff <email9648742 at gmail.com>
> 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.
>>
>> 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.
>>>>>>
>>>>>
>>>>>
>>>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20161018/2876aa94/attachment-0001.htm>