[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
>>
>>
>>
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20161021/0a1be565/attachment-0001.htm>
More information about the Election-Methods
mailing list