[EM] MaxMinPA

C.Benham cbenham at adam.com.au
Thu Oct 20 09:28:29 PDT 2016

On 10/20/2016 6:35 AM, Michael Ossipoff wrote:
> An example is needed.

C: Not really. Logically it's impossible to have both any Push-over 
incentive and FBC.

Whenever you're determining the winner by who is pairwise preferred out 
of the winner of method A and the winner of method B,
there will always be situations where you do better by not equal-top 
voting your sincere favourite F so as to keep F out of the final
where F would lose to your worst W.

Chris  Benham

> An example is needed.
> On Oct 18, 2016 9:37 PM, "C.Benham" <cbenham at adam.com.au 
> <mailto: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
>>     <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.
>>     ----
>>     Election-Methods mailing list - seehttp://electorama.com/em  for list info

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