[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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