[EM] MaxMinPA

C.Benham cbenham at adam.com.au
Tue Oct 18 21:37:20 PDT 2016

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 
> <mailto: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 <mailto: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
>         <mailto: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 <mailto: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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