Hi,
Guest
Re: [EM] MaxMinPA (C.Benham)
FS
Forest Simmons
Thu, Oct 20, 2016 8:03 PM
It seems to me that when it is possible and even likely that the two
methods using the same ballots will chose the same finalist that the
pushover incentive is greatly reduced.
From: "C.Benham" cbenham@adam.com.au
To: Michael Ossipoff email9648742@gmail.com,
election-methods@electorama.com
Subject: Re: [EM] MaxMinPA
Message-ID: 525944c5-e14e-62ec-2392-363d20330d9d@adam.com.au
Content-Type: text/plain; charset="utf-8"; Format="flowed"
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@adam.com.au
mailto:cbenham@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@pcc.edu
<mailto:fsimmons@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@gmail.com <mailto:email9648742@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@pcc.edu <mailto:fsimmons@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@t-online.de
<mailto:km_elmet@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
It seems to me that when it is possible and even likely that the two
methods using the same ballots will chose the same finalist that the
pushover incentive is greatly reduced.
From: "C.Benham" <cbenham@adam.com.au>
> To: Michael Ossipoff <email9648742@gmail.com>,
> election-methods@electorama.com
> Subject: Re: [EM] MaxMinPA
> Message-ID: <525944c5-e14e-62ec-2392-363d20330d9d@adam.com.au>
> Content-Type: text/plain; charset="utf-8"; Format="flowed"
>
> 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@adam.com.au
> > <mailto:cbenham@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@pcc.edu
> >> <mailto:fsimmons@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@gmail.com <mailto:email9648742@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@pcc.edu <mailto:fsimmons@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@t-online.de
> >> <mailto:km_elmet@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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