[EM] MaxMinPA

[Forest Simmons]

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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