[EM] MaxMinPA

C.Benham cbenham at adam.com.au
Tue Oct 18 20:22:58 PDT 2016

On 10/19/2016 5:17 AM, Michael Ossipoff wrote:

> Specifically, how would that pushover strategy work? Make a sure-loser 
> win one of the finalist-choosing counts, while making your candidate 
> win the other?
> Can you give an example?
Yes, and I'll think about it.

> Suppose the respective finalists are chosen by IRV and Implicit 
> Approval, respectively, applied to the first set of ballots. 

Very easy for this version.  If  you are happy to see the likely IRV 
winner X win, then simply vote X top and then only rank candidates that you
think X can pairwise beat (taking advantage of IRV's compliance with 

If things go well for you then if X doesn't win both counts then X will 
be the IRV winner and one of the "turkeys" you also approved will be the
Implicit Approval winner and lose in the run-off to X.

(And of course if X doesn't make the final you have the happy fall-back 
of voting sincerely in the run-off).

Chris Benham

> Specifically, how would that pushover strategy work? Make a sure-loser 
> win one of the finalist-choosing counts, while making your candidate 
> win the other?
> Can you give an example?
> Surely, strategically putting the right winner in both initial 
> counts--especially if both counts operate on the same set of 
> ratings--sounds like a daunting task, doesn't it?
> Michael Ossipoff
> On Oct 17, 2016 8:36 PM, "C.Benham" <cbenham at adam.com.au 
> <mailto:cbenham at adam.com.au>> wrote:
>     This "each voter has two ballots" idea certainly (strategically)
>     allows the voter to be completely sincere on one of them,
>     but the cost is that the overall method becomes a festival of
>     fairly easy and obvious Push-over strategising.
>     Of course one way to monitor this would be to look at the
>     (strategically and so presumably) sincere ballots and discover
>     who would have won according to various methods on those ballots.
>     (But if that was done openly it might introduce some incentives
>     based on fear of embarrassment  and/or fear that the
>     method will be abolished.)
>     Chris Benham
>     On 10/18/2016 11:13 AM, Michael Ossipoff wrote:
>>     I think it sounds super. The best yet, with the best properties
>>     of the best methods, avoiding eachother's faults & vulnerabilities.
>>     More later.
>>     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
>>     No virus found in this message.
>>     Checked by AVG - www.avg.com <http://www.avg.com>
>>     Version: 2016.0.7797 / Virus Database: 4664/13226 - Release Date:
>>     10/17/16
> No virus found in this message.
> Checked by AVG - www.avg.com <http://www.avg.com>
> Version: 2016.0.7797 / Virus Database: 4664/13232 - Release Date: 10/18/16

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20161019/008bad03/attachment-0001.htm>

More information about the Election-Methods mailing list