[EM] MaxMinPA

C.Benham cbenham at adam.com.au
Mon Oct 17 20:35:37 PDT 2016

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.
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